add: "The Annals of Statistics" submittion templates
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\documentclass[aos]{imsart}




%% Packages


\RequirePackage{amsthm,amsmath,amsfonts,amssymb}


\RequirePackage[numbers,sort&compress]{natbib}


%\RequirePackage[authoryear]{natbib}%% uncomment this for authoryear citations


\RequirePackage[colorlinks,citecolor=blue,urlcolor=blue]{hyperref}


\RequirePackage{graphicx}




\startlocaldefs


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% %%


%% Uncomment next line to change %%


%% the type of equation numbering %%


%% %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%\numberwithin{equation}{section}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% %%


%% For Axiom, Claim, Corollary, Hypothesis, %%


%% Lemma, Theorem, Proposition %%


%% use \theoremstyle{plain} %%


%% %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\theoremstyle{plain}


\newtheorem{axiom}{Axiom}


\newtheorem{claim}[axiom]{Claim}


\newtheorem{theorem}{Theorem}[section]


\newtheorem{lemma}[theorem]{Lemma}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% %%


%% For Assumption, Definition, Example, %%


%% Notation, Property, Remark, Fact %%


%% use \theoremstyle{remark} %%


%% %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\theoremstyle{remark}


\newtheorem{definition}[theorem]{Definition}


\newtheorem*{example}{Example}


\newtheorem*{fact}{Fact}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% Please put your definitions here: %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




\endlocaldefs




\begin{document}




\begin{frontmatter}


\title{A sample article title}


%\title{A sample article title with some additional note\thanksref{t1}}


\runtitle{A sample running head title}


%\thankstext{T1}{A sample additional note to the title.}




\begin{aug}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% Only one address is permitted per author. %%


%% Only division, organization and email is %%


%% included in the address. %%


%% Additional information can be included in %%


%% the Acknowledgments section if necessary. %%


%% ORCID can be inserted by command: %%


%% \orcid{0000000000000000} %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\author[A]{\fnms{First}~\snm{Author}\ead[label=e1]{first@somewhere.com}},


\author[B]{\fnms{Second}~\snm{Author}\ead[label=e2]{second@somewhere.com}\orcid{0000000000000000}}


\and


\author[B]{\fnms{Third}~\snm{Author}\ead[label=e3]{third@somewhere.com}}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% Addresses %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\address[A]{Department,


University or Company Name\printead[presep={,\ }]{e1}}




\address[B]{Department,


University or Company Name\printead[presep={,\ }]{e2,e3}}


\end{aug}




\begin{abstract}


The abstract should summarize the contents of the paper.


It should be clear, descriptive, selfexplanatory and not longer


than 200 words. It should also be suitable for publication in


abstracting services. Formulas should be used as sparingly as


possible within the abstract. The abstract should not make


reference to results, bibliography or formulas in the body


of the paperit should be selfcontained.




This is a sample input file. Comparing it with the output it


generates can show you how to produce a simple document of


your own.


\end{abstract}




\begin{keyword}[class=MSC]


\kwd[Primary ]{00X00}


\kwd{00X00}


\kwd[; secondary ]{00X00}


\end{keyword}




\begin{keyword}


\kwd{First keyword}


\kwd{second keyword}


\end{keyword}




\end{frontmatter}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% Please use \tableofcontents for articles %%


%% with 50 pages and more %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%\tableofcontents




\section{Introduction}




This template helps you to create a properly formatted \LaTeXe\ manuscript.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% `\ ' is used here because TeX ignores %%


%% spaces after text commands. %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


Prepare your paper in the same style as used in this sample .pdf file.


Try to avoid excessive use of italics and bold face.


Please do not use any \LaTeXe\ or \TeX\ commands that affect the layout


or formatting of your document (i.e., commands like \verb\textheight,


\verb\textwidth, etc.).




\section{Section headings}


Here are some subsections:


\subsection{A subsection}


Regular text.


\subsubsection{A subsubsection}


Regular text.




\section{Text}


\subsection{Lists}




The following is an example of an \emph{itemized} list,


two levels deep.


\begin{itemize}


\item


This is the first item of an itemized list. Each item


in the list is marked with a ``tick.'' The document


style determines what kind of tick mark is used.


\item


This is the second item of the list. It contains another


list nested inside it.


\begin{itemize}


\item This is the first item of an itemized list that


is nested within the itemized list.


\item This is the second item of the inner list. \LaTeX\


allows you to nest lists deeper than you really should.


\end{itemize}


This is the rest of the second item of the outer list.


\item


This is the third item of the list.


\end{itemize}




The following is an example of an \emph{enumerated} list of one level.




\begin{longlist}


\item This is the first item of an enumerated list.


\item This is the second item of an enumerated list.


\end{longlist}




The following is an example of an \emph{enumerated} list, two levels deep.


\begin{longlist}


\item[1.]


This is the first item of an enumerated list. Each item


in the list is marked with a ``tick.'' The document


style determines what kind of tick mark is used.


\item[2.]


This is the second item of the list. It contains another


list nested inside of it.


\begin{longlist}


\item


This is the first item of an enumerated list that


is nested within.


\item


This is the second item of the inner list. \LaTeX\


allows you to nest lists deeper than you really should.


\end{longlist}


This is the rest of the second item of the outer list.


\item[3.]


This is the third item of the list.


\end{longlist}




\subsection{Punctuation}


Dashes come in three sizes: a hyphen, an intraword dash like ``$U$statistics'' or ``the timehomogeneous model'';


a medium dash (also called an ``endash'') for number ranges or between two equal entities like ``12'' or ``CauchySchwarz inequality'';


and a punctuation dash (also called an ``emdash'') in place of a comma, semicolon,


colon or parentheseslike this.




Generating an ellipsis \ldots\ with the right spacing


around the periods requires a special command.




\subsection{Citation}


Only include in the reference list entries for which there are text citations,


and make sure all citations are included in the reference list.


Simple cite: \cite{r1}.


Multiple bibliography items cite: \cite{r1,r2,r3,r4}.


Citing bibliography with object: \cite{r1}, Theorem 1.




\section{Fonts}


Please use text fonts in text mode, e.g.:


\begin{itemize}


\item[]\textrm{Roman}


\item[]\textit{Italic}


\item[]\textbf{Bold}


\item[]\textsc{Small Caps}


\item[]\textsf{Sans serif}


\item[]\texttt{Typewriter}


\end{itemize}


Please use mathematical fonts in mathematical mode, e.g.:


\begin{itemize}


\item[] $\mathrm{ABCabc123}$


\item[] $\mathit{ABCabc123}$


\item[] $\mathbf{ABCabc123}$


\item[] $\boldsymbol{ABCabc123\alpha\beta\gamma}$


\item[] $\mathcal{ABC}$


\item[] $\mathbb{ABC}$


\item[] $\mathsf{ABCabc123}$


\item[] $\mathtt{ABCabc123}$


\item[] $\mathfrak{ABCabc123}$


\end{itemize}


Note that \verb\mathcal, \mathbb belongs to capital lettersonly font typefaces.




\section{Notes}


Footnotes\footnote{This is an example of a footnote.}


pose no problem.\footnote{Note that footnote number is after punctuation.}




\section{Quotations}




Text is displayed by indenting it from the left margin. There are short quotations


\begin{quote}


This is a short quotation. It consists of a


single paragraph of text. There is no paragraph


indentation.


\end{quote}


and longer ones.


\begin{quotation}


This is a longer quotation. It consists of two paragraphs


of text. The beginning of each paragraph is indicated


by an extra indentation.




This is the second paragraph of the quotation. It is just


as dull as the first paragraph.


\end{quotation}




\section{Environments}




\subsection{Examples for \emph{\texttt{plain}}style environments}


\begin{axiom}\label{ax1}


This is the body of Axiom \ref{ax1}.


\end{axiom}




\begin{proof}


This is the body of the proof of the axiom above.


\end{proof}




\begin{claim}\label{cl1}


This is the body of Claim \ref{cl1}. Claim \ref{cl1} is numbered after


Axiom \ref{ax1} because we used \verb[axiom] in \verb\newtheorem.


\end{claim}




\begin{theorem}\label{th1}


This is the body of Theorem \ref{th1}. Theorem \ref{th1} numbering is


dependent on section because we used \verb[section] after \verb\newtheorem.


\end{theorem}




\begin{theorem}[Title of the theorem]\label{th2}


This is the body of Theorem \ref{th2}. Theorem \ref{th2} has additional title.


\end{theorem}




\begin{lemma}\label{le1}


This is the body of Lemma \ref{le1}. Lemma \ref{le1} is numbered after


Theorem \ref{th2} because we used \verb[theorem] in \verb\newtheorem.


\end{lemma}






\begin{proof}[Proof of Lemma \ref{le1}]


This is the body of the proof of Lemma \ref{le1}.


\end{proof}




\subsection{Examples for \emph{\texttt{remark}}style environments}


\begin{definition}\label{de1}


This is the body of Definition \ref{de1}. Definition \ref{de1} is numbered after


Lemma \ref{le1} because we used \verb[theorem] in \verb\newtheorem.


\end{definition}




\begin{example}


This is the body of the example. Example is unnumbered because we used \verb\newtheorem*


instead of \verb\newtheorem.


\end{example}




\begin{fact}


This is the body of the fact. Fact is unnumbered because we used \verb\newtheorem*


instead of \verb\newtheorem.


\end{fact}




\section{Tables and figures}


Crossreferences to labeled tables: As you can see in Table~\ref{sphericcase}


and also in Table~\ref{parset}.




\begin{table*}


\caption{The spherical case ($I_1=0$, $I_2=0$)}


\label{sphericcase}


\begin{tabular}{@{}lrrrrc@{}}


\hline


Equil. \\


points & \multicolumn{1}{c}{$x$}


& \multicolumn{1}{c}{$y$} & \multicolumn{1}{c}{$z$}


& \multicolumn{1}{c}{$C$} & S \\


\hline


$L_1$ & $$2.485252241 & 0.000000000 & 0.017100631 & 8.230711648 & U \\


$L_2$ & 0.000000000 & 0.000000000 & 3.068883732 & 0.000000000 & S \\


$L_3$ & 0.009869059 & 0.000000000 & 4.756386544 & $$0.000057922 & U \\


$L_4$ & 0.210589855 & 0.000000000 & $$0.007021459 & 9.440510897 & U \\


$L_5$ & 0.455926604 & 0.000000000 & $$0.212446624 & 7.586126667 & U \\


$L_6$ & 0.667031314 & 0.000000000 & 0.529879957 & 3.497660052 & U \\


$L_7$ & 2.164386674 & 0.000000000 & $$0.169308438 & 6.866562449 & U \\


$L_8$ & 0.560414471 & 0.421735658 & $$0.093667445 & 9.241525367 & U \\


$L_9$ & 0.560414471 & $$0.421735658 & $$0.093667445 & 9.241525367 & U \\


$L_{10}$ & 1.472523232 & 1.393484549 & $$0.083801333 & 6.733436505 & U \\


$L_{11}$ & 1.472523232 & $$1.393484549 & $$0.083801333 & 6.733436505 & U \\


\hline


\end{tabular}


\end{table*}




\begin{table}


\caption{Sample posterior estimates for each model}


\label{parset}


%


\begin{tabular}{@{}lcrcrrr@{}}


\hline


&& & &\multicolumn{3}{c}{Quantile} \\


\cline{57}


Model &Parameter &


\multicolumn{1}{c}{Mean} &


Std. dev.&


\multicolumn{1}{c}{2.5\%} &


\multicolumn{1}{c}{50\%}&


\multicolumn{1}{c@{}}{97.5\%} \\


\hline


{Model 0} & $\beta_0$ & $$12.29 & 2.29 & $$18.04 & $$11.99 & $$8.56 \\


& $\beta_1$ & 0.10 & 0.07 & $$0.05 & 0.10 & 0.26 \\


& $\beta_2$ & 0.01 & 0.09 & $$0.22 & 0.02 & 0.16 \\[6pt]


{Model 1} & $\beta_0$ & $$4.58 & 3.04 & $$11.00 & $$4.44 & 1.06 \\


& $\beta_1$ & 0.79 & 0.21 & 0.38 & 0.78 & 1.20 \\


& $\beta_2$ & $$0.28 & 0.10 & $$0.48 & $$0.28 & $$0.07 \\[6pt]


{Model 2} & $\beta_0$ & $$11.85 & 2.24 & $$17.34 & $$11.60 & $$7.85 \\


& $\beta_1$ & 0.73 & 0.21 & 0.32 & 0.73 & 1.16 \\


& $\beta_2$ & $$0.60 & 0.14 & $$0.88 & $$0.60 & $$0.34 \\


& $\beta_3$ & 0.22 & 0.17 & $$0.10 & 0.22 & 0.55 \\


\hline


\end{tabular}


%


\end{table}




\begin{figure}


\includegraphics{figure1}


\caption{Pathway of the penicillin G biosynthesis.}


\label{penG}


\end{figure}




Sample of crossreference to figure.


Figure~\ref{penG} shows that it is not easy to get something on paper.




\section{Equations and the like}




Two equations:


\begin{equation}


C_{s} = K_{M} \frac{\mu/\mu_{x}}{1\mu/\mu_{x}} \label{ccs}


\end{equation}


and


\begin{equation}


G = \frac{P_{\mathrm{opt}}  P_{\mathrm{ref}}}{P_{\mathrm{ref}}} 100(\%).


\end{equation}




Equation arrays:


\begin{eqnarray}


\frac{dS}{dt} & = &  \sigma X + s_{F} F,\\


\frac{dX}{dt} & = & \mu X,\\


\frac{dP}{dt} & = & \pi X  k_{h} P,\\


\frac{dV}{dt} & = & F.


\end{eqnarray}


One long equation:


\begin{eqnarray}


\mu_{\text{normal}} & = & \mu_{x} \frac{C_{s}}{K_{x}C_{x}+C_{s}} \nonumber\\


& = & \mu_{\text{normal}}  Y_{x/s}\bigl(1H(C_{s})\bigr)(m_{s}+\pi /Y_{p/s})\\


& = & \mu_{\text{normal}}/Y_{x/s}+ H(C_{s}) (m_{s}+ \pi /Y_{p/s}).\nonumber


\end{eqnarray}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% Example with single Appendix: %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\begin{appendix}


\section*{Title}\label{appn} %% if no title is needed, leave empty \section*{}.


Appendices should be provided in \verb{appendix} environment,


before Acknowledgements.




If there is only one appendix,


then please refer to it in text as \ldots\ in the \hyperref[appn]{Appendix}.


\end{appendix}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% Example with multiple Appendixes: %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\begin{appendix}


\section{Title of the first appendix}\label{appA}


If there are more than one appendix, then please refer to it


as \ldots\ in Appendix \ref{appA}, Appendix \ref{appB}, etc.




\section{Title of the second appendix}\label{appB}


\subsection{First subsection of Appendix \protect\ref{appB}}




Use the standard \LaTeX\ commands for headings in \verb{appendix}.


Headings and other objects will be numbered automatically.


\begin{equation}


\mathcal{P}=(j_{k,1},j_{k,2},\dots,j_{k,m(k)}). \label{path}


\end{equation}




Sample of crossreference to the formula (\ref{path}) in Appendix \ref{appB}.


\end{appendix}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% Support information, if any, %%


%% should be provided in the %%


%% Acknowledgements section. %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\begin{acks}[Acknowledgments]


The authors would like to thank the anonymous referees, an Associate


Editor and the Editor for their constructive comments that improved the


quality of this paper.


\end{acks}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% Funding information, if any, %%


%% should be provided in the %%


%% funding section. %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\begin{funding}


The first author was supported by NSF Grant DMS????????.




The second author was supported in part by NIH Grant ???????????.


\end{funding}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% Supplementary Material, including data %%


%% sets and code, should be provided in %%


%% {supplement} environment with title %%


%% and short description. It cannot be %%


%% available exclusively as external link. %%


%% All Supplementary Material must be %%


%% available to the reader on Project %%


%% Euclid with the published article. %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\begin{supplement}


\stitle{Title of Supplement A}


\sdescription{Short description of Supplement A.}


\end{supplement}


\begin{supplement}


\stitle{Title of Supplement B}


\sdescription{Short description of Supplement B.}


\end{supplement}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% The Bibliography %%


%% %%


%% imsart???.bst will be used to %%


%% create a .BBL file for submission. %%


%% %%


%% Note that the displayed Bibliography will not %%


%% necessarily be rendered by Latex exactly as specified %%


%% in the online Instructions for Authors. %%


%% %%


%% MR numbers will be added by VTeX. %%


%% %%


%% Use \cite{...} to cite references in text. %%


%% %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




%% if your bibliography is in bibtex format, uncomment commands:


%\bibliographystyle{imsartnumber} % Style BST file (imsartnumber.bst or imsartnameyear.bst)


%\bibliography{bibliography} % Bibliography file (usually '*.bib')




%% or include bibliography directly:


\begin{thebibliography}{4}


%%


\bibitem{r1}


\textsc{Billingsley, P.} (1999). \textit{Convergence of


Probability Measures}, 2nd ed.


Wiley, New York.




\bibitem{r2}


\textsc{Bourbaki, N.} (1966). \textit{General Topology} \textbf{1}.


AddisonWesley, Reading, MA.




\bibitem{r3}


\textsc{Ethier, S. N.} and \textsc{Kurtz, T. G.} (1985).


\textit{Markov Processes: Characterization and Convergence}.


Wiley, New York.




\bibitem{r4}


\textsc{Prokhorov, Yu.} (1956).


Convergence of random processes and limit theorems in probability


theory. \textit{Theory Probab. Appl.}


\textbf{1} 157214.


\end{thebibliography}




\end{document}


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%% Template for the submission to:


%% The Annals of Statistics [AOS]


%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% In this template, the places where you %%


%% need to fill in your information are %%


%% indicated by '???'. %%


%% %%


%% Please do not use \input{...} to include %%


%% other tex files. Submit your LaTeX %%


%% manuscript as one .tex document. %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




\documentclass[aos]{imsart}




%% Packages


\RequirePackage{amsthm,amsmath,amsfonts,amssymb}


\RequirePackage[numbers]{natbib}


%\RequirePackage[authoryear]{natbib}%% uncomment this for authoryear citations


%\RequirePackage[colorlinks,citecolor=blue,urlcolor=blue]{hyperref}%% uncomment this for coloring bibliography citations and linked URLs


%\RequirePackage{graphicx}%% uncomment this for including figures




\startlocaldefs


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% %%


%% Uncomment next line to change %%


%% the type of equation numbering %%


%% %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%\numberwithin{equation}{section}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% %%


%% For Axiom, Claim, Corollary, Hypothesis, %%


%% Lemma, Theorem, Proposition %%


%% use \theoremstyle{plain} %%


%% %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%\theoremstyle{plain}


%\newtheorem{???}{???}


%\newtheorem*{???}{???}


%\newtheorem{???}{???}[???]


%\newtheorem{???}[???]{???}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% %%


%% For Assumption, Definition, Example, %%


%% Notation, Property, Remark, Fact %%


%% use \theoremstyle{remark} %%


%% %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%\theoremstyle{remark}


%\newtheorem{???}{???}


%\newtheorem*{???}{???}


%\newtheorem{???}{???}[???]


%\newtheorem{???}[???]{???}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% Please put your definitions here: %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




\endlocaldefs




\begin{document}




\begin{frontmatter}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% %%


%% Enter the title of your article here %%


%% %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\title{???}


%\title{A sample article title with some additional note\thanksref{T1}}


\runtitle{???}


%\thankstext{T1}{A sample of additional note to the title.}




\begin{aug}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% Only one address is permitted per author. %%


%% Only division, organization and email is %%


%% included in the address. %%


%% Additional information can be included in %%


%% the Acknowledgments section if necessary. %%


%% ORCID can be inserted by command: %%


%% \orcid{0000000000000000} %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\author[A]{\fnms{???}~\snm{???}\ead[label=e1]{???@???}},


\author[B]{\fnms{???}~\snm{???}\ead[label=e2]{???@???}}


\and


\author[B]{\fnms{???}~\snm{???}\ead[label=e3]{???@???}}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% Addresses %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\address[A]{???\printead[presep={,\ }]{e1}}




\address[B]{???\printead[presep={,\ }]{e2,e3}}


\end{aug}




\begin{abstract}


???.


\end{abstract}




\begin{keyword}[class=MSC]


\kwd[Primary ]{???}


\kwd{???}


\kwd[; secondary ]{???}


\end{keyword}




\begin{keyword}


\kwd{???}


\kwd{???}


\end{keyword}




\end{frontmatter}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% Please use \tableofcontents for articles %%


%% with 50 pages and more %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%\tableofcontents




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%% Main text entry area:






%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% Single Appendix: %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%\begin{appendix}


%\section*{???}%% if no title is needed, leave empty \section*{}.


%\end{appendix}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% Multiple Appendixes: %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%\begin{appendix}


%\section{???}


%


%\section{???}


%


%\end{appendix}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% Support information, if any, %%


%% should be provided in the %%


%% Acknowledgements section. %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%\begin{acks}[Acknowledgments]


% The authors would like to thank ...


%\end{acks}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% Funding information, if any, %%


%% should be provided in the %%


%% funding section. %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%\begin{funding}


% The first author was supported by ...


%


% The second author was supported in part by ...


%\end{funding}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% Supplementary Material, including data %%


%% sets and code, should be provided in %%


%% {supplement} environment with title %%


%% and short description. It cannot be %%


%% available exclusively as external link. %%


%% All Supplementary Material must be %%


%% available to the reader on Project %%


%% Euclid with the published article. %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%\begin{supplement}


%\stitle{???}


%\sdescription{???.}


%\end{supplement}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% The Bibliography %%


%% %%


%% imsart???.bst will be used to %%


%% create a .BBL file for submission. %%


%% %%


%% Note that the displayed Bibliography will not %%


%% necessarily be rendered by Latex exactly as specified %%


%% in the online Instructions for Authors. %%


%% %%


%% MR numbers will be added by VTeX. %%


%% %%


%% Use \cite{...} to cite references in text. %%


%% %%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




%% if your bibliography is in bibtex format, uncomment commands:


%\bibliographystyle{imsartnumber} % Style BST file (imsartnumber.bst or imsartnameyear.bst)


%\bibliography{bibliography} % Bibliography file (usually '*.bib')




%% or include bibliography directly:


% \begin{thebibliography}{}


% \bibitem{b1}


% \end{thebibliography}




\end{document}

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%% This is file `imsart.cls'


%%


%% LaTeX 2e class file for the processing of LaTeX2e files


%% of the following IMS/BS journals:


%%


%% The Annals of Probability


%% The Annals of Applied Probability


%% The Annals of Statistics


%% The Annals of Applied Statistics


%% Statistical Science


%% Probability Surveys


%% Statistics Surveys


%% Electronic Journal of Statistics


%% Bernoulli


%% Annales de l'Institut Henri Poincar\'e  Probabilit\'es et Statistiques


%% Brazilian Journal of Probability and Statistics


%% Bayesian Analysis


%%


%% Institute of Mathematical Statistics, U.S.A.


%% Bernoulli Society


%% Institut Henry Poincare


%% Brazilian Statistical Association


%% International Society for Bayesian Analysis


%%


%% Macros written by Vytas Statulevicius, VTeX, Lithuania


%% Maintained by Deimantas Galcius, VTeX, Lithuania


%% for Institute of Mathematical Statistics, U.S.A.


%% Please submit bugs or your comments to latexsupport@vtex.lt


%%


%% The original distribution is located at:


%% http://www.epublications.org/ims/support


%%


%% This class file loads standard "article.cls" with appropriate


%% settings and then style file "imsart.sty" with additional macros


%%


%% You are free to use this style file as you see fit, provided


%% that you do not make changes to the file.


%% If you DO make changes, you are required to rename this file.


%%


%% It may be distributed under the terms of the LaTeX Project Public


%% License, as described in lppl.txt in the base LaTeX distribution.


%% Either version 1.0 or, at your option, any later version.


%%


%% \CharacterTable


%% {Uppercase \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z


%% Lowercase \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z


%% Digits \0\1\2\3\4\5\6\7\8\9


%% Exclamation \! Double quote \" Hash (number) \#


%% Dollar \$ Percent \% Ampersand \&


%% Acute accent \' Left paren \( Right paren \)


%% Asterisk \* Plus \+ Comma \,


%% Minus \ Point \. Solidus \/


%% Colon \: Semicolon \; Less than \<


%% Equals \= Greater than \> Question mark \?


%% Commercial at \@ Left bracket \[ Backslash \\


%% Right bracket \] Circumflex \^ Underscore \_


%% Grave accent \` Left brace \{ Vertical bar \


%% Right brace \} Tilde \~}


%%


%%


%% Bug fixes and changes: at end of file


%


% TeX programming: Vytas Statulevicius, VTeX, Lithuania.


% TeX programming: Deimantas Galcius, VTeX, Lithuania.


% TeX programming: Edgaras Sakuras, VTeX, Lithuania.


% Requires Latex2e, ver.2000.06


%


\NeedsTeXFormat{LaTeX2e}


\ProvidesClass{imsart}[2022/04/21 driver class for package imsart.sty]


%


% set various options for different journals:


\DeclareOption{ps}{%


\PassOptionsToClass{10pt,oneside}{article}%


}


%


\DeclareOption{ss}{%


\PassOptionsToClass{10pt,oneside}{article}%


}


%


\DeclareOption{ejs}{%


\PassOptionsToClass{10pt,oneside}{article}%


}


%


\DeclareOption{aap}{%


\PassOptionsToClass{11pt,oneside,leqno}{article}%


\PassOptionsToPackage{leqno}{amsmath}%


}


%


\DeclareOption{aop}{%


\PassOptionsToClass{11pt,oneside,leqno}{article}%


\PassOptionsToPackage{leqno}{amsmath}%


}


%


\DeclareOption{aos}{%


\PassOptionsToClass{11pt,oneside,leqno}{article}%


\PassOptionsToPackage{leqno}{amsmath}%


}


%


\DeclareOption{aoas}{%


\PassOptionsToClass{11pt,oneside,leqno}{article}%


\PassOptionsToPackage{leqno}{amsmath}%


}


%


\DeclareOption{sts}{%


\PassOptionsToClass{11pt,oneside,leqno}{article}%


\PassOptionsToPackage{leqno}{amsmath}%


}


%


\DeclareOption{bj}{%


\PassOptionsToClass{10pt,oneside}{article}%


\g@addto@macro\@classoptionslist{,nosetpagesize}%


\PassOptionsToPackage{sort&compress}{natbib}%


}


%


\DeclareOption{aihp}{%


\PassOptionsToClass{10pt,oneside,leqno}{article}%


\PassOptionsToPackage{leqno}{amsmath}%


\PassOptionsToPackage{numbers,sort&compress}{natbib}%


}


%


\DeclareOption{bjps}{%


\PassOptionsToClass{11pt,twoside}{article}%


}


%


\DeclareOption{ba}{%


\PassOptionsToClass{10pt,oneside}{article}%


}


%


\PassOptionsToPackage{cmex10}{amsmath}


%


\DeclareOption*{\PassOptionsToClass{\CurrentOption}{article}}


\ProcessOptions*


%


\LoadClass{article}


%


\IfFileExists{imsart.sty}%


{}%


{%


\ClassError{imsart}%


{The complimentary style file "imsart.sty" is required}%


{%


The complimentary style file "imsart.sty" is required\MessageBreak


You need to install file "imsart.sty" in your system\MessageBreak


File could be downloaded from http://www.epublications.org/ims/support


}%


}


%


% Load additional macros and modifications for "article.cls"


\RequirePackage{imsart}


%


\endinput


%%


%% End of file `imsart.cls'.

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