Generalized Least Squares With Ignored Errors in Variables

Autor:	Tony Morton-Jones, Robin Henderson
Rok vydání:	2000
Předmět:	Statistics and Probability Residual sum of squares Mean squared error Applied Mathematics Modeling and Simulation Non-linear least squares Statistics Ordinary least squares Generalized least squares Total least squares Simple linear regression Least squares Mathematics
Zdroj:	Technometrics. 42:366-375
ISSN:	1537-2723 0040-1706
DOI:	10.1080/00401706.2000.10485709
Popis:	We present data, both real and simulated, that show generalized least squares (GLS) estimation, intended to account for correlated response error structure, can produce gross biasing in regression parameter estimates under misspecified models with ignored errors in explanatory-variable measurements. The bias, and its subsequent effect on mean squared error (MSE), can be much more severe than the apparently less appropriate ordinary least squares (OLS) estimator. This article provides a theoretical basis for these effects by deriving expressions for the bias and MSE for the general GLS estimator through Taylor-series expansions. The results are compared with simulations for two specific weight matrices and applied to a dataset relating atmospheric pollutant levels in Los Angeles with average recorded wind speed. We show that the bias (with subsequent implications for the MSE) is always worse for the exponential correlation model with equally spaced explanatory-variable observations and present a simple tes...
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::a1f33359a15a0640d989ad7b7819be70 https://doi.org/10.1080/00401706.2000.10485709 Zobrazit plný text záznamu