\vsize=19.6cm \hsize=12.5cm \voffset=-.5cm \hoffset=-.1cm % %-------------- FONT -------------------- % \font\fourrm=cmr5 scaled 800 \font\fivrm=cmr5 \font\sixrm=cmr6 \font\sevrm=cmr7 \font\egtrm=cmr8 \font\ninrm=cmr9 \font\tenrm=cmr10 \font\twlrm=cmr12 % \font\sevit=cmti7 \font\egtit=cmti8 \font\ninit=cmti9 \font\tenit=cmti10 \font\twlit=cmti12 % \font\fivmit=cmmi5 \font\sixmit=cmmi6 \font\sevmit=cmmi7 \font\egtmit=cmmi8 \font\ninmit=cmmi9 \font\tenmit=cmmi10 \font\twlmit=cmmi12 % \font\egtbf=cmbx8 \font\ninbf=cmbx9 \font\tenbf=cmbx10 % \font\fivbi=cmbxti10 scaled 500 \font\sixbi=cmbxti10 scaled 600 \font\sevbi=cmbxti10 scaled 700 \font\egtbi=cmbxti10 scaled 800 \font\ninbi=cmbxti10 scaled 900 \font\tenbi=cmbxti10 \font\twlbi=cmbxti10 scaled 1200 \textfont9=\tenbi \scriptfont9=\sevbi \scriptscriptfont9=\fivbi \def\bx{\fam9 \tenbi} % \font\egtss=cmss8 \font\tenss=cmss10 \font\twlss=cmss12 % \font\tenssi=cmssi10 \font\twlssi=cmssi12 % \font\egtsc=cmcsc10 scaled 800 \font\sc=cmcsc10 % \font\twlsy=cmsy10 scaled 1200 \font\tensy=cmsy10 \font\ninsy=cmsy9 \font\egtsy=cmsy8 \font\sevsy=cmsy7 \font\sixsy=cmsy6 \font\fivsy=cmsy5 % \font\twlex=cmex10 scaled 1200 \font\ninex=cmex10 scaled 900 \font\egtex=cmex10 scaled 800 \font\sevex=cmex10 scaled 700 \font\sixex=cmex10 scaled 600 \font\fivex=cmex10 scaled 500 % \def\sevm{ \textfont0=\sevrm \scriptfont0=\sixrm \scriptscriptfont0=\fivrm \textfont1=\sevmit \scriptfont1=\sixmit \scriptscriptfont1=\fivmit \textfont2=\sevsy \scriptfont2=\sixsy \scriptscriptfont2=\fivsy \textfont9=\sevbi \scriptfont9=\sixbi \scriptscriptfont9=\fivbi \textfont3=\sevex \scriptfont3=\sixex \scriptscriptfont3=\fivex} \def\egtm{ \textfont0=\egtrm \scriptfont0=\sixrm \scriptscriptfont0=\fivrm \textfont1=\egtmit \scriptfont1=\sixmit \scriptscriptfont1=\fivmit \textfont2=\egtsy \scriptfont2=\sixsy \scriptscriptfont2=\fivsy \textfont9=\egtbi \scriptfont9=\sixbi \scriptscriptfont9=\fivbi \textfont3=\egtex \scriptfont3=\sixex \scriptscriptfont3=\fivex} \def\ninm{ \textfont0=\ninrm \scriptfont0=\sixrm \scriptscriptfont0=\fivrm \textfont1=\ninmit \scriptfont1=\sixmit \scriptscriptfont1=\fivmit \textfont2=\ninsy \scriptfont2=\sixsy \scriptscriptfont2=\fivsy \textfont9=\ninbi \scriptfont9=\sixbi \scriptscriptfont9=\fivbi \textfont3=\ninex \scriptfont3=\sixex \scriptscriptfont3=\fivex} \def\tenm{ \textfont0=\tenrm \scriptfont0=\sevrm \scriptscriptfont0=\fivrm \textfont1=\tenmit \scriptfont1=\sevmit \scriptscriptfont1=\fivmit \textfont2=\tensy \scriptfont2=\sevsy \scriptscriptfont2=\fivsy \textfont9=\tenbi \scriptfont9=\sevbi \scriptscriptfont9=\fivbi \textfont3=\tenex \scriptfont3=\sevex \scriptscriptfont3=\fivex} \def\twlm{ \textfont0=\twlrm \scriptfont0=\egtrm \scriptscriptfont0=\fivrm \textfont1=\twlmit \scriptfont1=\egtmit \scriptscriptfont1=\fivmit \textfont2=\twlsy \scriptfont2=\egtsy \scriptscriptfont2=\fivsy \textfont9=\twlbi \scriptfont9=\egtbi \scriptscriptfont9=\fivbi \textfont3=\twlex \scriptfont3=\egtex \scriptscriptfont3=\fivex} % %------------- STYLE ----------------- % \catcode`\@=11 % \def\header#1#2#3#4#5#6#7{\pageno=#3 \headline={\ifnum\pageno=#3 \hbox to 12.5cm{ \vbox{\hbox{\egtrm Ann.\ Inst.\ Statist.\ Math.\hfill\hfill}\hbox{\egtrm Vol.\ #1,\ No.\ #2,\ #4\ (#5)\hfill\hfill}\hfill\hfill}} \else{ \ifodd\pageno{\phantom{\egtrm\folio}\hfill {\egtrm\egtm #6}\hfill{\egtrm\folio}} \else{{\egtrm\folio}\hfill {\egtrm\egtm #7}\hfill\phantom{\egtrm\folio}} \fi} \fi} \footline={\ifnum\pageno=#3 {\hfill{\egtrm\folio}\hfill} \else{\hfill} \fi}} % \def\beginsection#1#2\par{{ \vskip0pt plus2cm\penalty-50 \vskip0pt plus-2cm\bigskip\vskip\parskip \leftskip 18pt \parindent -18pt \tenss {#1\m}#2 \tenrm \parindent 18pt \nobreak\bigskip}} \def\subsection#1#2{\vskip0pt plus2cm\penalty-50 \vskip0pt plus-2cm\bigskip\vskip\parskip \noindent{\tenit\ \unskip\hbox{\tenrm#1\m}#2} \nobreak\vskip0pt} \def\ssubsection#1#2{ \noindent{\tenit\ \unskip\hbox{\tenrm#1\m}#2} \nobreak\vskip0pt} \def\subsubsection#1#2{\vskip0pt plus2cm\penalty-50 \vskip0pt plus-2cm\vskip\parskip \noindent{\tenit\ \unskip\hbox{\tenrm#1\m}#2} \nobreak\vskip0pt} % \def\figcap#1#2{\leftskip 16pt\rightskip 16pt{ \egtrm\egtm\noindent\ \unskip\hbox{Fig. #1.}\hskip8pt#2}} \def\figcapcent#1#2{{\egtrm\egtm \centerline{\hbox{Fig. #1.}\hskip8pt#2}}} \def\tabcap#1#2{\noindent{\egtrm\egtm \unskip\hbox{Table #1.}\hskip8pt#2}} \def\tabcapcent#1#2{{\egtrm\egtm \centerline{\hbox{Table #1.}\hskip8pt#2}}} % \def\sqr#1#2{{\vcenter{\hrule height.#2pt \hbox{\vrule width.#2pt height#1pt \kern#1pt \vrule width.#2pt} \hrule height.#2pt}}} \def\square{\mathchoice\sqr54\sqr54\sqr{3.5}3\sqr23} % \def\pmb#1{\setbox0=\hbox{#1} \kern-.02em\copy0\kern-\wd0 \kern.02em\raise.015em\copy0\kern-\wd0 \kern-.015em\copy0\kern-\wd0 \kern-.02em\raise.015em\copy0\kern-\wd0 \kern.025em\copy0\kern-\wd0 \kern.015em\raise.02em\copy0\kern-\wd0 \kern-.025em\copy0\kern-\wd0 \kern-.02em\raise-.01em\box0} % \def\n{\enskip} \def\m{\quad} \def\ind{\par\indent \textindent} % \def\Exp{\mathop{\rm Exp}\nolimits} \def\sign{\mathop{\rm sign}\nolimits} \def\Min{\mathop{\rm Min}\nolimits} \def\Sup{\mathop{\rm Sup}\nolimits} \def\Vec{\mathop{\rm Vec}\nolimits} \def\grad{\mathop{\rm grad}\nolimits} \def\var{\mathop{\rm var}\nolimits} \def\Var{\mathop{\rm Var}\nolimits} \def\kei{\mathop{\rm kei}\nolimits} \def\prior{\mathop{\rm prior}\nolimits} \def\Diag{\mathop{\rm Diag}\nolimits} \def\diag{\mathop{\rm diag}\nolimits} \def\tr{\mathop{\rm tr}\nolimits} \def\co{\mathop{\rm co}\nolimits} \def\cov{\mathop{\rm cov}\nolimits} \def\Cov{\mathop{\rm Cov}\nolimits} \def\olim{\mathop{\overline{\lim}}} % overline lim \def\ulim{\mathop{\underline{\lim}}} % underline lim \def\iint{\int\!\!\!\int} % double integral % \def\bmatrix#1{\left[\matrix{#1}\right]} % \def\footn#1{\let\@sf=\empty \ifhmode\edef\@sf{\spacefactor=\the\spacefactor}\/\fi \baselineskip 10pt#1\@sf\vfootnote{\egtrm #1}} % \def\cases#1{\left\{\,\vcenter{\openup1\jot\m@th \ialign{$\displaystyle##\hfil$&\quad\enskip##\hfil\crcr#1\crcr}}\right.} % \def\frac#1#2{{#1\over #2}} % \def\mb#1{\oalign{\mit #1\crcr\hidewidth \vbox to.2ex{\hbox{\char 22}\vss}\hidewidth}} % \catcode`\@=12 \overfullrule0pt %------------------------------------------------------------- %------------------------------------------------------------- \baselineskip 16pt \centerline{\twlss ESTIMATION$\n$OF$\n$A$\n$SMOOTH$\n$QUANTILE$\n$FUNCTION} \centerline{\twlss UNDER$\n$THE$\n$PROPORTIONAL$\n$HAZARDS$\n$MODEL} \baselineskip 11pt \vskip 11pt \centerline{\tenss J. K. G{\egtss HORAI}} \vskip 10pt \centerline{\egtit Department of Mathematical Sciences, The University of Wisconsin-Milwaukee,} \centerline{\egtit P.O. Box 413, Milwaukee, WI 53201, U.S.A.} \vskip 20pt \centerline{\egtrm (Received April 16, 1990; revised September 20, 1990)} \vskip 30pt {\ninm\ninrm\narrower \baselineskip 11pt \parindent 0pt {\ninbf Abstract.}$\m$The problem of estimating a smooth quantile function, $Q(\cdot)$, at a fixed point $p$, $0