Performance of Some New Ridge Regression Estimators

By B. M. G. Kibria. 2003

657 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d29ff4f9d65294d1b6d5eab5387d9dc356ded6d4

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In Statistics and Probability

Citations in the corpus

Developing Ridge Parameters for SUR Model (2008, neutral): “In the single-equation environment, Kibria ( 2003 ) and Alkhamisi et al.”
Modified Ridge Regression Estimators (2013, methodology): “We choose the parameter values so that ∑p j 2 j = 1 which is a common restriction in simulations studies (see, for example Hoerl et al., 1975; Kibria, 2003; McDonald and Galarneau, 1975; Muniz and Kibria, 2009).”
Developing a Liu estimator for the negative binomial regression model: method and application (2013, methodology): “Furthermore, the following estimators, which are based on the ideas in Kibria [5], are proposed:”
The Restricted and Unrestricted Two-Parameter Estimators (2007, methodology): “Therefore when d approaches zero, k estimators in (3.3), (3.4), and (3.5) reduce to the estimators of k given by Hoerl et al. (1975) and Kibria (2003), respectively.”
Modified ridge‐type estimator to combat multicollinearity: Application to chemical data (2019, neutral): “Proof Considering the dispersion matrix difference between bαRE k ð Þ and bαMRT k; d ð Þ D1 1⁄4 σ(2)BkΛBk − σ(2) R ! kΛ −1 R !′ kÞ 1⁄4 σ(2) Λþ kI ð ÞΛ Λþ kI ð Þ − σ(2) Λþ k 1þ d ð ÞI ð ÞΛ Λþ k 1þ d ð ÞI ð Þ 1⁄4 σ(2) Λþ kI ð ÞΛ Λþ k 1þ d ð ÞI ð Þ Λþ k 1þ d ð ÞI ð Þ Λþ k 1þ d ð ÞI ð Þ− Λþ kI ð Þ Λþ kI”
A new modified Jackknifed estimator for the Poisson regression model (2016, background): “TheMSE is minimized when β is normalized eigen vectors corresponding to the largest eigen value of XTXmatrix subject to constraint that βTβ = 1 [15].”
Developing a ridge estimator for the gamma regression model (2018, positive): “The asymptotic properties of bτMJGRR are defined as respectively Bias bτMJGRR 1⁄2 1⁄4 E bτMJGRR 1⁄2 −τ 1⁄4 −k Iþ kD−1−k(2)D−2 D−1τ; (22)”
A New Two-Parameter Estimator in Linear Regression (2010, methodology): “Following the similar method proposed by Liu (1993) and Kaciranlar et al.”
Shrinkage estimators for gamma regression model (2018, neutral): “The response variable of n observations from gamma regression model is generated by Kurtoğlu and Özkale (2016) yi ∼ Gamma(θ2/var, var/θ) (35) where θ = exp(XTβ), var denotes θ2, β = (β1, ..., βp) with p∑ j=1 β2j = 1 and β1 = β2 = ... = βp (Kibria, 2003).”
On the performance of some new Liu parameters for the gamma regression model (2018, methodology): “We follow the work of Hoerl and Kennard [5], Kibria [12], Khalaf and Skukur [22] where the optimal value of the ridge parameter was estimated [3].”
ON THE LIU AND ALMOST UNBIASED LIU ESTIMATORS IN THE PRESENCE OF MULTICOLLINEARITY WITH HETEROSCEDASTIC OR CORRELATED ERRORS (2009, methodology): “According to Kibria [12], Alheety and Gore [1] and Muniz and Kibria [15], we consider the coefficient vector”
On Ridge Parameters in Logistic Regression (2011, methodology): “In this section, we describe logistic RR first proposed by Schaefer et al. (1984) and how this method can be improved by using newly introduced estimators of the ridge parameter proposed by Kibria (2003), Alkhamisi et al. (2006), and Muniz and Kibria (2009).”