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Improving the estimators of the parameters of a probit regression model: a ridge regression approach. (English) Zbl 1242.62076

Summary: This paper considered the estimation of the regression parameters of a general probit regression model. Accordingly, we proposed five ridge regression (RR) estimators for the probit regression models for estimating the parameters \((\beta)\) when the weighted design matrix is ill-conditioned and it is suspected that the parameter \(\beta\) may belong to a linear subspace defined by \(H\beta =h\). Asymptotic properties of the estimators are studied with respect to quadratic biases, MSE matrices and quadratic risks. The regions of optimality of the proposed estimators are determined based on the quadratic risks. Some relative efficiency tables and risk graphs are provided to illustrate the numerical comparison of the estimators. We conclude that when \(q\geq 3\), one would use a probit restricted ridge regression estimator (PRRRE); otherwise one uses a preliminary test ridge regression estimator (PTRRE) with some optimum size \(\alpha\). We also discuss the performance of the proposed estimators compared to the alternative ridge regression method of K. Liu [Commun. Stat., Theory Methods 22, No. 2, 393–402 (1993; Zbl 0784.62065)].

MSC:

62J07 Ridge regression; shrinkage estimators (Lasso)
62F12 Asymptotic properties of parametric estimators
65C60 Computational problems in statistics (MSC2010)

Citations:

Zbl 0784.62065
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References:

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