Analytical expressions for Rao-Blackwell estimators in adaptive cluster sampling

被引：5
|
作者：
Félix-Medina, MH
机构：
[1] Penn State Univ, Dept Stat, University Pk, PA 16802 USA
[2] Univ Autonoma Sinaloa, Esc Ciencias Fis Matemat, Culiacan, Mexico
来源：
JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 2000年 / 84卷 / 1-2期
关键词：
adaptive cluster sampling; design-based inferential approach; finite population; minimal sufficient statistic; Rao-Blackwell theorem; simple random sampling; unequal probability sampling;
D O I：
10.1016/S0378-3758(99)00138-X
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
In this paper, we consider adaptive cluster sampling with the initial sample selected either by simple random sampling without replacement or by unequal probability sampling with replacement. We derive analytical expressions for the Rao-Blackwell versions of the following two estimators originally proposed by Thompson (1990, J. Amer. Statist. Assoc. 85, 1050-1059): the modified Horvitz-Thompson estimator and the modified Hansen-Hurwitz one. Furthermore, we derive analytical expressions for the variances of the two Rao-Blackwell estimators above mentioned, as well as analytical expressions for unbiased Rao-Blackwell estimators of those variances. In the without-replacement case, the derivations are based on the multivariate hypergeometric distribution, whereas in the with-replacement case, they are based on the multinomial distribution. (C) 2000 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：221 / 236
页数：16
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