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osu1202154248.pdf (668.19 KB)
ETD Abstract Container
Abstract Header
On concomitants of order statistics
Author Info
Wang, Ke
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1202154248
Abstract Details
Year and Degree
2008, Doctor of Philosophy, Ohio State University, Statistics.
Abstract
Let
(X
i
,Y
i
),1 ≤ i ≤ n
, be a sample of size
n
from an absolutely continuous random vector
(X,Y)
. Let
X
i:n
be the
i
th order statistic of the
X
-sample and
Y
[i:n]
be its concomitant. We study three problems related to the
Y
[i:n]
’s in this dissertation. The first problem is about the distribution of concomitants of order statistics (COS) in dependent samples. We derive the finite-sample and asymptotic distribution of COS under a specific setting of dependent samples where the
X
’s form an equally correlated multivariate normal sample. This work extends the available results on the distribution theory of COS in the literature, which usually assumes independent and identically distributed (i.i.d) or independent samples. The second problem we examine is about the distribution of order statistics of subsets of concomitants from i.i.d samples. Specifically, we study the finite-sample and asymptotic distributions of
V
s:m
and
W
t:n-m
, where
V
s:m
is the
s
th order statistic of the concomitants subset {
Y
[i:n]
, i=n-m+1,…,n
}, and
W
t:n-m
is the
t
th order statistic of the concomitants subset {
Y
[j:n]
,j=1,…,n-m
}. We show that with appropriate normalization, both
V
s:m
and
W
t:n-m
converge in law to normal distributions with a rate of convergence of order
n
-1/2
. We propose a higher order expansion to the marginal distributions of these order statistics that is substantially more accurate than the normal approximation even for moderate sample sizes. Then we derive the finite-sample and asymptotic joint distribution of
(V
s:m
, W
t:n-m
)
. We apply these results and determine the probability of an event of interest in commonly used selection procedures. We also apply the results to study the power of identifying the disease-susceptible gene in two-stage designs for gene-disease association studies. The third problem we consider is about estimating the conditional mean of the response variable (
Y
) given that the explanatory variable (
X
) is at a specific quantile of its distribution. We propose two estimators based on concomitants of order statistics. The first one is a kernel smoothing estimator, and the second one can be thought of as a bootstrap estimator. We study the asymptotic properties of these estimators and compare their finite sample behavior using simulation.
Committee
Haikady Nagaraja (Advisor)
Subject Headings
Statistics
Recommended Citations
Refworks
EndNote
RIS
Mendeley
Citations
Wang, K. (2008).
On concomitants of order statistics
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1202154248
APA Style (7th edition)
Wang, Ke.
On concomitants of order statistics.
2008. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1202154248.
MLA Style (8th edition)
Wang, Ke. "On concomitants of order statistics." Doctoral dissertation, Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1202154248
Chicago Manual of Style (17th edition)
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Document number:
osu1202154248
Download Count:
3,553
Copyright Info
© 2008, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.