文档介绍：
A Semiparametric Empirical Likelihood Estimation for
Generalized Linear Models under e Dependent
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Sampling#
Ding Jieli*
(School of Mathematics and Statistics, Wuhan University, Wuhan, 430072)
Abstract: Epidemiologic studies use e-dependent sampling (ODS) schemes where, in addition
to a simple random sample, there are also a number of supplement samples that are collected based on
e variable. ODS scheme is a cost effective way to improve study efficiency. We develop a
maximum semiparametric empirical likelihood estimation (MSELE) for data from ODS design under a
general linear model framework. What is more, we prove the asymptotic properties of MSELE.
Key words: e-dependent sampling; Generalized linear models; Empirical likelihood;
Consistency; Asymptotic normality.
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0 Introduction
Epidemiologic observational studies that relate disease occurrence to individual exposures and
other characteristics play an important role in understanding the determinants of diseases. Major
cost and effect are relative to the assembly of exposure measurements for the large cohort
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members. Case-control method has e a fundamental statistical tool in environmental
epidemiology to reduce the cost. plex sampling designs could enhance the efficiency
further. Well-known sampling schemes for survival data include case-cohort design and
generalized case-cohort design. Case-cohort design is advocated especially when the failure rate is
low (White, 1982; Prentice, 1986; Cai and Zeng, 2004). A generalized case-cohort design
assembles the covariate information only for a fraction taken from the cases instead of all cases
outside of the subcohort when the number of failures is large (Cai and Zeng, 2007; Kang and Cai,
2009).
A general bias sampling scheme, e dependent sampling (ODS), has been widely used in
recent epidemiologic researches to enhance the efficiency and reduce the cost. An ODS design is a
retrospective sampling scheme where one