Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series B, Pt. 1, pp. 187--201

APPROXIMATE BALANCED HALF SAMPLE AND RELATED REPLICATION METHODS FOR IMPUTED SURVEY DATA*

By

JUN SHAO and YINZHONG CHEN University of Wisconsin, Madison

SUMMARY. The balanced half sample (BHS) method is a popular method for variance estimation under stratified multistage sampling. The standard BHS works when two units (or two first-stage clusters) are sampled from each stratum and when there is no imputed data. We consider the situation where the first-stage sample sizes are larger than two in some strata and where the data set contains nonrespondents imputed using some popular methods such as ratio and random hot deck imputation. The method we propose is a combination of an approximate BHS method (such as the grouped BHS method and its extensions) and the adjustment for imputation considered in Shao, Chen and Chen (1998). Consistency of the proposed BHS variance estimators is established under some regularity conditions. Some examples are presented for illustration.

AMS (1991) subject classification. Primary 62D05; secondary 62G05, 62G99.

Key words and phrases. Grouped half-samples, pseudo-strata; random repeated replication; ratio imputation; hot deck imputation; variance estimation.

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