In general ridge (GR) regression p ridge parameters have to be determined, whereas simple ridge regression requires the determination of only one parameter. In a recent textbook on linear regression, Jü rgen Gross argues that this constitutes a major complication. However, as we show in this paper, the determination of these p parameters can fairly easily be done. Furthermore, we introduce a generalization of the GR estimator derived by Hemmerle and by Teekens and de Boer. This estimator, which is more conservative, performs better than the Hoerl and Kennard estimator in terms of a weighted quadratic loss criterion.
Maximum likelihood procedures for estimating sum-constrained models like demand systems, brand choice models and so on, break down or produce very unstable estimates when the number of categories (n) is large as compared with the number of observations (T ). In applied research, this problem is usually resolved by postulating the contemporaneous covariance matrix of the dependent variables to be known apart from a constant of proportionality. In this paper we develop a maximum likelihood procedure for sum-constrained models with large numbers of categories, which does not require too many observations, but nevertheless allows for n covariance parameters to be estimated freely.
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