Abstract:
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In the analysis of complex survey data, one often uses a nominal pivotal quantity in a test of the null hypothesis of a parameter of interest. Due to limitations of the sample design, the data collection process or proposed estimation methods, test procedures based on this pivotal quantity may be affected by: 1.) bias of the point estimators; 2.) inflation in the variance of the point estimator; and 3.) bias of the variance estimator. This paper presents some methods to evaluate the relative magnitudes of the effects of 1.)-3.) on the power curve of the associated test. Special emphasis is placed on the construction of confidence bounds for this power curve.
The methods are applied to data from the U.S. Consumer Expenditure Survey, which collects data through two instruments known as the diary and the interview. For 78 expenditure items, data are collected through both the diary and interview but, currently, published estimates are based only on the diary data. Prospective methods to combine the diary and interview data sources involve trade-offs between 1.)-3.). Estimated power curves, and associated confidence bounds, provide an empirical assessment of these three factors.
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