\relax 
\ifx\hyper@anchor\@undefined
\global \let \oldcontentsline\contentsline
\gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global \let \oldnewlabel\newlabel
\gdef \newlabel#1#2{\newlabelxx{#1}#2}
\gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\let \contentsline\oldcontentsline
\let \newlabel\oldnewlabel}
\else
\global \let \hyper@last\relax 
\fi

\@writefile{toc}{\contentsline {begintocitem}{}{}{}}
\@writefile{toc}{\contentsline {jobname}{Cavazos}{}{}}
\@writefile{toc}{\contentsline {doi}{0002/0000.0000}{}{}}
\@writefile{toc}{\contentsline {arxiv}{math.PR/0000002}{}{}}
\gdef\hy@title{Large Sample Statistical Inference for Skew-Symmetric Families on the Real Line}
\@writefile{toc}{\contentsline {title}{Large Sample Statistical Inference for Skew-Symmetric Families on the Real Line}{277}{}}
\thanksnewlabel{e1@email}{{rcavazos@uaaan.mx}{277}}
\thanksnewlabel{a1thanks}{{1}{277}}
\thanksnewlabel{e2@email}{{farias@cimat.mx}{277}}
\thanksnewlabel{a2thanks}{{2}{277}}
\thanksnewlabel{t1thanks}{{\ensuremath  {*}}{277}}
\@writefile{idx}{\indexentry {Cavazos--Cadena, R., \textit {Universidad Aut\'o\discretionary {-}{}{}no\discretionary {-}{}{}ma Agraria Antonio Narro}}{}}
\@writefile{idx}{\indexentry {Gonz\'alez--Far\'ias G., \textit {Centro de Investigaci\'on en Matem\'aticas A.\nobreakspace  {}C.}}{}}
\gdef\hy@author{Rolando Cavazos--Cadena and Graciela Gonz\'alez--Far\'ias}
\gdef\hy@subject{IMS Collections 2009 Vol. 0 277--304}
\gdef\hy@keywords{62F10, 62F12, Boundedness of maximum likelihood estimators, Kullback's inequality, Lateral Taylor series, Strong law of large numbers, Central limit theorem, Asymptotic normality, }
\@writefile{toc}{\contentsline {author}{Rolando Cavazos--Cadena and Graciela Gonz\'alez--Far\'ias}{277}{}}
\@writefile{toc}{\contentsline {endtocitem}{}{}{}}
\gdef\author@num{2}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{277}{section.1}}
\newlabel{Int}{{1}{277}{Introduction\relax }{section.1}{}}
\newlabel{G(x)=}{{1.1}{278}{Introduction\relax }{equation.1.1}{}}
\newlabel{rho(x,l)=}{{1.2}{278}{Introduction\relax }{equation.1.2}{}}
\newlabel{SkewFam}{{1.3}{278}{Introduction\relax }{equation.1.3}{}}
\newlabel{logLSO=}{{1.4}{278}{Introduction\relax }{equation.1.4}{}}
\newlabel{X1ton}{{1.5}{280}{Introduction\relax }{equation.1.5}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Identifiability}{280}{section.2}}
\newlabel{Identif}{{2}{280}{Identifiability\relax }{section.2}{}}
\newlabel{IdentifCon}{{2.1}{280}{Identifiability\relax }{assumption.2.1}{}}
\newlabel{Primitive}{{2.1}{280}{Identifiability\relax }{lemma.2.1}{}}
\newlabel{NullInt}{{2.1}{280}{Identifiability\relax }{equation.2.1}{}}
\newlabel{G=G}{{2.2}{281}{Identifiability\relax }{equation.2.2}{}}
\newlabel{Counter}{{2.1}{281}{Identifiability\relax }{example.2.1}{}}
\newlabel{TotVar=}{{2.3}{282}{Identifiability\relax }{equation.2.3}{}}
\newlabel{+onPandN}{{2.2}{282}{Identifiability\relax }{lemma.2.2}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Existence of Maximum Likelihood Estimators}{282}{section.3}}
\newlabel{EMLESect}{{3}{282}{Existence of Maximum Likelihood Estimators\relax }{section.3}{}}
\newlabel{Ln=}{{3.1}{282}{Existence of Maximum Likelihood Estimators\relax }{equation.3.1}{}}
\newlabel{Lnle}{{3.2}{283}{Existence of Maximum Likelihood Estimators\relax }{equation.3.2}{}}
\newlabel{MLEDef}{{3.1}{283}{Existence of Maximum Likelihood Estimators\relax }{definition.3.1}{}}
\newlabel{MLELimINF}{{3.3}{283}{Existence of Maximum Likelihood Estimators\relax }{equation.3.3}{}}
\newlabel{LimINFVerbal}{{3.1}{283}{Existence of Maximum Likelihood Estimators\relax }{remark.3.1}{}}
\newlabel{EMLE}{{3.1}{283}{Existence of Maximum Likelihood Estimators\relax }{thm.3.1}{}}
\newlabel{mn=def}{{3.4}{283}{Existence of Maximum Likelihood Estimators\relax }{equation.3.4}{}}
\newlabel{mn=}{{3.5}{283}{Existence of Maximum Likelihood Estimators\relax }{equation.3.5}{}}
\newlabel{Mcn=}{{3.6}{283}{Existence of Maximum Likelihood Estimators\relax }{equation.3.6}{}}
\newlabel{Scn=}{{3.7}{283}{Existence of Maximum Likelihood Estimators\relax }{equation.3.7}{}}
\newlabel{Max-n-Fixed}{{3.1}{284}{Existence of Maximum Likelihood Estimators\relax }{lemma.3.1}{}}
\newlabel{lambdan+=}{{3.8}{284}{Existence of Maximum Likelihood Estimators\relax }{equation.3.8}{}}
\newlabel{MeasSel}{{3.2}{284}{Existence of Maximum Likelihood Estimators\relax }{lemma.3.2}{}}
\newlabel{Ln-le-LnMax}{{3.9}{284}{Existence of Maximum Likelihood Estimators\relax }{equation.3.9}{}}
\newlabel{Ln0le}{{3.10}{284}{Existence of Maximum Likelihood Estimators\relax }{equation.3.10}{}}
\newlabel{Near1}{{3.3}{285}{Existence of Maximum Likelihood Estimators\relax }{lemma.3.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Consistency}{286}{section.4}}
\newlabel{CONMLESec}{{4}{286}{Consistency\relax }{section.4}{}}
\newlabel{CONSMLE}{{4.1}{286}{Consistency\relax }{thm.4.1}{}}
\newlabel{Omega*=}{{4.1}{286}{Consistency\relax }{equation.4.1}{}}
\newlabel{Omeganu+-=}{{4.2}{286}{Consistency\relax }{equation.4.2}{}}
\newlabel{POmegas=1}{{4.3}{286}{Consistency\relax }{equation.4.3}{}}
\newlabel{BoundMLE}{{4.1}{286}{Consistency\relax }{lemma.4.1}{}}
\newlabel{EmptyInt}{{4.4}{287}{Consistency\relax }{equation.4.4}{}}
\newlabel{Kullback}{{4.2}{288}{Consistency\relax }{lemma.4.2}{}}
\newlabel{ElesumBound}{{4.5}{288}{Consistency\relax }{equation.4.5}{}}
\newlabel{Omeganu0=}{{4.6}{289}{Consistency\relax }{equation.4.6}{}}
\newlabel{Omeganu1=}{{4.7}{289}{Consistency\relax }{equation.4.7}{}}
\newlabel{Omeganu2=}{{4.8}{289}{Consistency\relax }{equation.4.8}{}}
\newlabel{Omeganu=}{{4.9}{289}{Consistency\relax }{equation.4.9}{}}
\newlabel{POmeganu=1}{{4.10}{289}{Consistency\relax }{equation.4.10}{}}
\newlabel{LastIncl}{{4.11}{289}{Consistency\relax }{equation.4.11}{}}
\newlabel{nu*in(s,r)}{{4.12}{289}{Consistency\relax }{equation.4.12}{}}
\newlabel{hlambin(s,r)}{{4.13}{289}{Consistency\relax }{equation.4.13}{}}
\newlabel{KeyIneq}{{4.14}{290}{Consistency\relax }{equation.4.14}{}}
\@writefile{toc}{\contentsline {section}{\numberline {5}Asymptotic Distribution}{290}{section.5}}
\newlabel{AsymDistSec}{{5}{290}{Asymptotic Distribution\relax }{section.5}{}}
\newlabel{smoothg}{{5.1}{291}{Asymptotic Distribution\relax }{assumption.5.1}{}}
\newlabel{Densityg}{{5.1}{291}{Asymptotic Distribution\relax }{remark.5.1}{}}
\newlabel{Dgk0-=0+}{{5.1}{291}{Asymptotic Distribution\relax }{equation.5.1}{}}
\newlabel{DkG=0}{{5.2}{291}{Asymptotic Distribution\relax }{equation.5.2}{}}
\newlabel{DkG+-=}{{5.3}{291}{Asymptotic Distribution\relax }{equation.5.3}{}}
\newlabel{H(x)=}{{5.4}{291}{Asymptotic Distribution\relax }{equation.5.4}{}}
\newlabel{ell=log(H)}{{5.5}{291}{Asymptotic Distribution\relax }{equation.5.5}{}}
\newlabel{Dkell0+=}{{5.6}{291}{Asymptotic Distribution\relax }{equation.5.6}{}}
\newlabel{Dkell0-=}{{5.7}{292}{Asymptotic Distribution\relax }{equation.5.7}{}}
\newlabel{MomentDom}{{5.2}{292}{Asymptotic Distribution\relax }{assumption.5.2}{}}
\newlabel{DominCon2r+3}{{5.8}{292}{Asymptotic Distribution\relax }{equation.5.8}{}}
\newlabel{DomConComm}{{5.2}{292}{Asymptotic Distribution\relax }{remark.5.2}{}}
\newlabel{Vr+1=}{{5.9}{292}{Asymptotic Distribution\relax }{equation.5.9}{}}
\newlabel{AsymDist}{{5.1}{292}{Asymptotic Distribution\relax }{thm.5.1}{}}
\newlabel{Extensions}{{5.3}{293}{Asymptotic Distribution\relax }{remark.5.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {6}Technical Preliminaries}{293}{section.6}}
\newlabel{TechToo}{{6}{293}{Technical Preliminaries\relax }{section.6}{}}
\newlabel{DELTA=}{{6.1}{293}{Technical Preliminaries\relax }{equation.6.1}{}}
\newlabel{maintool}{{6.1}{293}{Technical Preliminaries\relax }{thm.6.1}{}}
\newlabel{Ln=EXPAND}{{6.2}{293}{Technical Preliminaries\relax }{equation.6.2}{}}
\newlabel{pLn=EXPAND}{{6.3}{294}{Technical Preliminaries\relax }{equation.6.3}{}}
\newlabel{sampMean}{{6.4}{294}{Technical Preliminaries\relax }{equation.6.4}{}}
\newlabel{LnConvDis}{{6.5}{294}{Technical Preliminaries\relax }{equation.6.5}{}}
\newlabel{LnConvAS}{{6.6}{294}{Technical Preliminaries\relax }{equation.6.6}{}}
\newlabel{HDeriv}{{6.1}{294}{Technical Preliminaries\relax }{lemma.6.1}{}}
\newlabel{DHr+1=}{{6.7}{295}{Technical Preliminaries\relax }{equation.6.7}{}}
\newlabel{DHgterr+1}{{6.8}{295}{Technical Preliminaries\relax }{equation.6.8}{}}
\newlabel{ellExplicit}{{6.2}{295}{Technical Preliminaries\relax }{lemma.6.2}{}}
\newlabel{pellr+2+=}{{6.9}{296}{Technical Preliminaries\relax }{equation.6.9}{}}
\newlabel{pellr+2-=}{{6.10}{296}{Technical Preliminaries\relax }{equation.6.10}{}}
\newlabel{DELTA1=}{{6.11}{296}{Technical Preliminaries\relax }{equation.6.11}{}}
\newlabel{TaylorExp}{{6.3}{297}{Technical Preliminaries\relax }{lemma.6.3}{}}
\newlabel{ell=TayExp}{{6.12}{297}{Technical Preliminaries\relax }{}{}}
\newlabel{pell=TayExp}{{6.12}{297}{Technical Preliminaries\relax }{}{}}
\newlabel{WsleW}{{6.12}{297}{Technical Preliminaries\relax }{equation.6.12}{}}
\newlabel{ell=exp}{{6.13}{297}{Technical Preliminaries\relax }{equation.6.13}{}}
\newlabel{pell=exp}{{6.14}{297}{Technical Preliminaries\relax }{equation.6.14}{}}
\newlabel{WsleWprel}{{6.15}{297}{Technical Preliminaries\relax }{equation.6.15}{}}
\@writefile{toc}{\contentsline {section}{\numberline {7}Proof of Theorem \ref  {AsymDist}}{300}{section.7}}
\newlabel{THEPROOF}{{7}{300}{Proof of Theorem \ref {AsymDist}\relax }{section.7}{}}
\newlabel{SimpleExp}{{7.1}{300}{Proof of Theorem \ref {AsymDist}\relax }{lemma.7.1}{}}
\newlabel{Ln=EXPANDS}{{7.1}{300}{Proof of Theorem \ref {AsymDist}\relax }{equation.7.1}{}}
\newlabel{pLn=EXPANDS}{{7.2}{300}{Proof of Theorem \ref {AsymDist}\relax }{equation.7.2}{}}
\newlabel{As=Op}{{7.3}{300}{Proof of Theorem \ref {AsymDist}\relax }{equation.7.3}{}}
\newlabel{BstoVr+1}{{7.4}{300}{Proof of Theorem \ref {AsymDist}\relax }{equation.7.4}{}}
\newlabel{P0lambda20}{{7.7}{301}{Proof of Theorem \ref {AsymDist}\relax }{equation.7.7}{}}
\newlabel{UFF!}{{7.2}{301}{Proof of Theorem \ref {AsymDist}\relax }{lemma.7.2}{}}
\newlabel{POMEGAto1}{{7.8}{302}{Proof of Theorem \ref {AsymDist}\relax }{equation.7.8}{}}
\newlabel{LastKeyDisp}{{7.9}{302}{Proof of Theorem \ref {AsymDist}\relax }{equation.7.9}{}}
\bibcite{Azzalini (1985)}{{1}{}{{}}{{}}}
\bibcite{Azzalini (1986)}{{2}{}{{}}{{}}}
\bibcite{Azzalini and Capitanio (1999)}{{3}{}{{}}{{}}}
\bibcite{Azzalini and Dalla Valle (1996)}{{4}{1996}{{Azzalini and Dalla Valle }}{{}}}
\bibcite{Azzalini (2005)}{{5}{}{{}}{{}}}
\bibcite{Billingsley (1995)}{{6}{}{{}}{{}}}
\bibcite{Cavazos Cadena and Gonzalez Farias (2007)}{{7}{}{{}}{{}}}
\bibcite{Chiogna (2005)}{{8}{}{{}}{{}}}
\bibcite{DiCiccio and Monti (2004)}{{9}{}{{}}{{}}}
\bibcite{Genton (2004)}{{10}{}{{}}{{}}}
\bibcite{Lehmann and Casella (1998)}{{11}{}{{}}{{}}}
\bibcite{Newey and McFadden (1993)}{{12}{}{{}}{{}}}
\bibcite{Pewsey (2000)}{{13}{}{{}}{{}}}
\newlabel{NewLast}{{7.10}{303}{Proof of Theorem \ref {AsymDist}\relax }{equation.7.10}{}}
\@writefile{toc}{\contentsline {section}{References}{303}{section*.3}}
\bibcite{Rotnitzky et al (2000)}{{14}{}{{}}{{}}}
\bibcite{Sartori (2006)}{{15}{}{{}}{{}}}
\bibcite{Shao (1999)}{{16}{}{{}}{{}}}
\global\NAT@numberstrue