Estimation and replicate variance estimation of deciles for complex survey data from positively skewed populations

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Stephen J. Kaputa and Katherine Jenny Thompson¹

Abstract

Thompson and Sigman (2000) introduced an estimation procedure for estimating medians from highly positively skewed population data. Their procedure uses interpolation over data-dependent intervals (bins). The earlier paper demonstrated that this procedure has good statistical properties for medians computed from a highly skewed sample. This research extends the previous work to decile estimation methods for a positively skewed population using complex survey data. We present three different interpolation methods along with the traditional decile estimation method (no bins) and evaluate each method empirically, using residential housing data from the Survey of Construction and via a simulation study. We found that a variant of the current procedure using the 95th percentile as a scaling factor produces decile estimates with the best statistical properties.

Key Words

Median; Modified half-sample replication; Interpolation; Deciles.

Table of content

1 Introduction

2 Methodology

3 Empirical analysis

4 Conclusion

 

 

 

 

 

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¹Stephen J. Kaputa and Katherine Jenny Thompson, Office of Statistical Methods and Research for Economic Programs, US Census Bureau, 4600 Silver Hill RD, Washington, DC 20233. E-mail: Stephen.kaputa@census.gov.