Expansions for the Conditional Density and Distribution of a Standard Estimate
Year: 2025
Type: article
Abstract: Conditioning is a very useful way of using correlated information to reduce the variability of an estimate. Conditioning an estimate on a correlated estimate, reduces its covariance, and so provides more precise inference than using an unconditioned estimate. Here we give expansions in powers of n−1/2 for the conditional density and distribution of any multivariate standard estimate based on a sample of size n. Standard estimates include most estimates of interest, including smooth functions of sample means and other empirical estimates. We also show that a conditional estimate is not a standard estimate, so that Edgeworth-Cornish-Fisher expansions cannot be applied directly.
Source: Stats
DOI: 10.3390/stats8040098
Author: C.S. Withers
Institution: Industrial Research Limited
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,930
OpenAlex ID: W4415283936