Reconciliation of asymptotics for unequal probability sampling without replacement

Mohammad Ashraf Chaudhary; Pranab Kumar Sen

doi:10.1016/S0378-3758(01)00169-0

Reconciliation of asymptotics for unequal probability sampling without replacement

Mohammad Ashraf Chaudhary, Pranab Kumar Sen

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In simple random sampling without replacement (SRSWOR), certain reverse martingale structures render simple asymptotics for the conventional linear statistics. In unequal probability sampling (UPS) WOR, such martingale-based methodology may not be generally adoptable. General asymptotics for UPSWOR sampling schemes, developed by Hartley and Rao (Ann. Math. Statist. 33 (1962) 350), and Hájek (Ann. Math. Statist. 35 (1964) 1491), rest on different sets of regularity assumptions, and they differ in their treatise too. Some anomalies in this context are eliminated here with a reconciliation of both the approaches, and estimation of the asymptotic variance of linear estimators is considered in the same vein. Applications to small area sampling are also stressed.

Original language	English (US)
Pages (from-to)	71-81
Number of pages	11
Journal	Journal of Statistical Planning and Inference
Volume	102
Issue number	1
DOIs	https://doi.org/10.1016/S0378-3758(01)00169-0
State	Published - Mar 1 2002
Externally published	Yes

Keywords

Finite population correction
Horvitz-Thompson estimator
Inclusion probabilities
Poisson sampling scheme
Rejective sampling
SRSWOR
SRSWR
Successive sampling
Variance estimators

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1016/S0378-3758(01)00169-0

Cite this

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title = "Reconciliation of asymptotics for unequal probability sampling without replacement",

abstract = "In simple random sampling without replacement (SRSWOR), certain reverse martingale structures render simple asymptotics for the conventional linear statistics. In unequal probability sampling (UPS) WOR, such martingale-based methodology may not be generally adoptable. General asymptotics for UPSWOR sampling schemes, developed by Hartley and Rao (Ann. Math. Statist. 33 (1962) 350), and H{\'a}jek (Ann. Math. Statist. 35 (1964) 1491), rest on different sets of regularity assumptions, and they differ in their treatise too. Some anomalies in this context are eliminated here with a reconciliation of both the approaches, and estimation of the asymptotic variance of linear estimators is considered in the same vein. Applications to small area sampling are also stressed.",

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N2 - In simple random sampling without replacement (SRSWOR), certain reverse martingale structures render simple asymptotics for the conventional linear statistics. In unequal probability sampling (UPS) WOR, such martingale-based methodology may not be generally adoptable. General asymptotics for UPSWOR sampling schemes, developed by Hartley and Rao (Ann. Math. Statist. 33 (1962) 350), and Hájek (Ann. Math. Statist. 35 (1964) 1491), rest on different sets of regularity assumptions, and they differ in their treatise too. Some anomalies in this context are eliminated here with a reconciliation of both the approaches, and estimation of the asymptotic variance of linear estimators is considered in the same vein. Applications to small area sampling are also stressed.

AB - In simple random sampling without replacement (SRSWOR), certain reverse martingale structures render simple asymptotics for the conventional linear statistics. In unequal probability sampling (UPS) WOR, such martingale-based methodology may not be generally adoptable. General asymptotics for UPSWOR sampling schemes, developed by Hartley and Rao (Ann. Math. Statist. 33 (1962) 350), and Hájek (Ann. Math. Statist. 35 (1964) 1491), rest on different sets of regularity assumptions, and they differ in their treatise too. Some anomalies in this context are eliminated here with a reconciliation of both the approaches, and estimation of the asymptotic variance of linear estimators is considered in the same vein. Applications to small area sampling are also stressed.

KW - Finite population correction

KW - Horvitz-Thompson estimator

KW - Inclusion probabilities

KW - Poisson sampling scheme

KW - Rejective sampling

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KW - Successive sampling

KW - Variance estimators

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Reconciliation of asymptotics for unequal probability sampling without replacement

Abstract

Keywords

ASJC Scopus subject areas

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