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Adjustment of the Profile Likelihood for a Class of Normal Regression Models
Author(s) -
Durban Maria,
Currie I. D.
Publication year - 2000
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00205
Subject(s) - mathematics , statistics , variance function , variance (accounting) , autoregressive model , regression analysis , generalization , likelihood function , likelihood ratio test , restricted maximum likelihood , econometrics , maximum likelihood , mathematical analysis , accounting , business
We apply the method of McCullagh & Tibshirani (1990) to a generalization of the model for variance components in which the parameter of interest can appear in both the mean and variance. We obtain the exact adjusted profile log‐likelihood score function. For the variance components model, we obtain the adjusted profile log‐likelihood and show that it equals the restricted log‐likelihood of Patterson & Thompson (1971). We discuss an example due to Kempton (1982) of a regression model with autoregressive terms in which the parameter of interest appears in both the mean and variance.