Finite Sample Properties of Ridge Estimators

MSE performance and minimax regret significance points for a HPT estimator under a multivariate t error distribution

“…x 1 is an n × 1 vector of observations on an independent variable, X 2 is an n × (k − 1) matrix of 1 The double k-class estimator is proposed by Ullah and Ullah (1978 observations on other explanatory variables. β = [β 1 , β 2 ] is a k × 1 vector of regression coefficients for X, β 1 is a scalar coefficient for x 1 in which we have a special interest, β 2 is a (k − 1) × 1 vector of coefficients for X 2 , and ε is an n × 1 vector of error terms.…”

“…However, since the ridge regression estimator may have smaller MSE than the OLS estimator even if multicollinearity does not exist, many recent studies focused on the small sample properties of the ridge regression estimator. [See, for example, Dwivedi et al (1980) and Kozumi and Ohtani (1994).] In applied regression analysis, we may be interested in a specific regression coefficient rather than all of them.…”

The general expressions for the moments of lawless and wang's ordinary ridge regression estimator

“…The difference between these RR estimators will be discussed in Section 2. Dwivedi, Srivastava and Hall (1980) derived the exact first two moments of the GRR estimator and showed that the GRR estimator has a smaller mean square error (MSE) than the ordinary least squares (OLS) estimator if the noncentrality parameter does not exceed two. Based on their results, the exact finite sample properties of the GRR estimator and its variant (a, a pre-test estimator consisting of the GRR and OLS estimators) have been investigated from various aspects.…”

Risk performance of a pre-test ridge regression estimator under the LINEX loss function when each individual regression coefficient is estimated

“…After the finding of Hoerl and Kennard [1], lots of variants of the ridge regression estimator are proposed and their sampling properties have been investigated. Some examples are Dwivedi et al [2], Ohtani [3,4] and Firinguetti [5][6][7]. Huang [8] proposed the choice of the so-called ridge parameter which minimizes the MSE of the ridge regression estimator when our concern is to estimate each individual regression coefficient.…”