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On conditional discrete density esti...

Hsu, Yu-Sheng.

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On conditional discrete density estimation.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	On conditional discrete density estimation./
Author:	Hsu, Yu-Sheng.
Description:	81 p.
Notes:	Director: Robert H. Berk.
Contained By:	Dissertation Abstracts International51-07B.
Subject:	Statistics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9034909

On conditional discrete density estimation.
Hsu, Yu-Sheng.

On conditional discrete density estimation. - 81 p.

Director: Robert H. Berk.

Thesis (Ph.D.)--Rutgers The State University of New Jersey - New Brunswick, 1990.

The purpose of this paper is to deal with the conditional discrete density estimation problem motivated from the discrimination problem using both continuous and unordered discrete variables. Let $\underline X$ and $\underline Y$ denote the continuous and the unordered discrete variables respectively. Let Subjects--Topical Terms:

517247
Statistics.

On conditional discrete density estimation.
LDR:02749nam 2200253 a 45 001 939858
005 20110517
008 110517s1990 ||||||||||||||||| ||eng d
035 $a (UMI)AAI9034909
035 $a AAI9034909
040 $a UMI $c UMI
100 1 $a Hsu, Yu-Sheng. $3 1263970
245 1 0 $a On conditional discrete density estimation.
300 $a 81 p.
500 $a Director: Robert H. Berk.
500 $a Source: Dissertation Abstracts International, Volume: 51-07, Section: B, page: 3443.
502 $a Thesis (Ph.D.)--Rutgers The State University of New Jersey - New Brunswick, 1990.
520 $a The purpose of this paper is to deal with the conditional discrete density estimation problem motivated from the discrimination problem using both continuous and unordered discrete variables. Let $\underline X$ and $\underline Y$ denote the continuous and the unordered discrete variables respectively. Let $f (\underline x, \underline y)$ denote the joint density of $\underline X$ and $\underline Y$, and $\ f\sb{j,n\sb j}(\underline x, \underline y)$ denote an estimator of $f \sb j(\underline x, \underline y)$ of population $\Pi\sb j$ based on a sample $(\underline x\sbsp{1}{(j)}, \underline y\sbsp{1}{(j)}, \..., (\underline x\sbsp{n\sb j}{(j)}, \underline y\sbsp{n\sb j}{(j)})$, 1 $\leq$ $j $ $\leq$ $p $. Then a new observation $(\underline x\sb0, \underline y\sb0)$ will be allocated to population $\Pi\sb i$ if$$\ f\sb{i,n\sb i}(\underline x, \underline y) = \max\sb{1\le j\le p}\ f\sb{j,n\sb j}(\underline x, \underline y).$ $i f m estimators assume the maximum then ($\underline x\sb0, \underline y\sb0$) will be allocated to one of those m populations with equal probability. Since(UNFORMATTED TABLE OR EQUATION FOLLOWS)$$\eqalignno{f(\underline x, \underline y)&= f(\underline x\vert\underline y)f(\underline y),&(0.1)\cr&= f(\underline y\vert\underline x)f(\underline x),&(0.2)\cr}$$(TABLE/EQUATION ENDS)there are two approaches to estimate $f (\underline x, \underline y)$. Some statisticians use formula (0.1), assuming a parametric model on $\underline X\vert\underline Y$. We will use formula (0.2) and the approach will be nonparametric. Since good estimators of $f (\underline x)$ are well known, our discussion will be restricted to the estimation of $f (\underline y\vert\underline x)$. Our estimators smooth the well known nearest neighbor estimator and the kernel estimator. The consistency, asymptotic normality and optimality in the sense of Hajek (1970) of our estimators are given.
590 $a School code: 0190.
650 4 $a Statistics. $3 517247
690 $a 0463
710 2 $a Rutgers The State University of New Jersey - New Brunswick. $3 1017590
773 0 $t Dissertation Abstracts International $g 51-07B.
790 $a 0190
790 1 0 $a Berk, Robert H., $e advisor
791 $a Ph.D.
792 $a 1990
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9034909