An Asymptotic Theory for Weighted Least Squares with Weights Estimated by Replication

Abstract

This document considers a heteroscedastic linear regression model with replication. To estimate the variances, one can use the sample variances or the sample average squared errors from a regression fit. The authors study the large sample properties of these weighted least squares estimates with estimated weights when the number of replicates is small. The estimates are generally inconsistent for asymmetrically distributed data. If sample variances are used based on m replicates, the weighted least squares estimates are inconsistent for m=2 replicates even when the data are normally distributed. With between 3 and 5 replicates, the rates of convergence are slower than the usual square root of N. With m > or = 6 replicates, the effect of estimating the weights is to increase variances by (m-5)/(m-3), relative to weighted least squares estimates with known weights.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1988
Accession Number
ADA198000

Entities

People

  • Daren B. Cline
  • Raymond J. Carroll

Organizations

  • Texas A&M University

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Air Force
  • Analytical Chemistry
  • Asymptotic Normality
  • Classification
  • Computer Programs
  • Consistency
  • Convergence
  • Covariance
  • Data Science
  • Estimators
  • Information Science
  • Notation
  • Numbers
  • Probability
  • Random Variables
  • Square Roots
  • Standards

Fields of Study

  • Mathematics

Readers

  • Mathematics or Statistics
  • Statistical inference.