Search results
Apr 1, 2022 · The Kibria-Lukman (KL) estimator is a recent estimator that has been proposed to solve the multicollinearity problem. In this paper, a generalized version of the KL estimator is...
Nov 26, 2021 · In this paper, we developed a Jackknifed version of the Kibria-Lukman estimator- the estimator is named the Jackknifed KL estimator (JKLE). We derived the statistical properties of the new estimator and compared it theoretically with the KLE and some other existing estimators.
INTRODUCTION. The statistical consequences of multicollinearity are well-known in statistics for a linear regression model. Multicollinearity is known as the approximately linear dependency among...
May 29, 2022 · This study proposed the Robust Jackknife Kibria-Lukman (RJKL) estimator based on the M-estimator to deal with multicollinearity and outliers.
- Lemma 1
- Lemma 2
- Lemma 3
- Lemma 4
- Theorem 2
- Proof
- Theorem 3
- Theorem 4
- Theorem 5
- Theorem 6
(Seber, 2007, Pg. 225) Let \(\varvec{A}> 0\) and let \(\varvec{B}\) be a \(p \times n\) of rank q (\(q \le p\)). Then, 1. (a) \(\varvec{B}\varvec{A}\varvec{B}^{\top } \ge 0\) 2. (b) \(\varvec{B}\varvec{A}\varvec{B}^{\top } > 0\) if \(q = p\). Let \(\hat{\varvec{\alpha }}_i^*\), \(i = 1, 2\) be two arbitrary estimators of \(\varvec{\alpha }\). The e...
(Seber, 2007, Pg. 228) Let \(n \times n\) matrices \(\varvec{M}>0\) and \(\varvec{N}>0\) (or \(\varvec{N}\ge 0\) ); then, \(\varvec{M}>\varvec{N}\) if and only if the eigenvalues \(\lambda _i\) of \(\varvec{N}\varvec{M}^{-1}\) all satisfy \(\lambda _i \le 1\) (\(\lambda _i < 1\)); or equivalently, \(\lambda _{\max }\left( \varvec{N}\varvec{M}^{-1}\...
(Farebrother 1976) Let \(\varvec{M}\) be an \(n \times n\) positive definite matrix, that is, \(\varvec{M}>0\) and \(\varvec{a}\) be some vector; then, \(\varvec{M}-\varvec{a}\varvec{a}^{\top } \ge 0\) if and only if \(\varvec{a}^{\top } \varvec{M}^{-1} \varvec{a}\le 1\).
(Trenklar 1980) Let \(\hat{\varvec{\alpha }}_i^* = \varvec{H}_i \varvec{y}\), \(i = 1, 2\), be two linear estimators of \(\varvec{\alpha }\). Suppose that \(\textbf{D}= \textrm{Var}(\hat{\varvec{\alpha }}_1^*) - \textrm{Var}(\hat{\varvec{\alpha }}_2^*) > 0\), where \(\textrm{Var}(\hat{\varvec{\alpha }}_i^*) =\sigma ^2 \varvec{H}_i \varvec{H}_i^{\to...
Assume \(k > 0\). The Almon principal component Kibria-Lukman estimator is superior to the Almon estimator using MSEM criterion, that is, \(\textrm{MSEM}\left( \hat{\varvec{\alpha }}^{\textrm{A}}\right) -\textrm{MSEM}\left( \hat{\varvec{\alpha }}_r^{\textrm{A}-\textrm{KL}}(k)\right) > 0\)if and only if where
Based on Eqs. (39) and (45), the differences between \(\text {MSEM}(\hat{\varvec{\alpha }}^{\textrm{A}})\) and \(\text {MSEM}(\hat{\varvec{\alpha }}_r^{\textrm{A}-\textrm{KL}}(k))\)is Due to the definition of the Almon and Almon-PC-KL estimators, it is sufficient to show that \(\textbf{D}_0 > 0\) using Lemma 4. Knowing that \(\textbf{C}= \varvec{T}...
If \(k > 0\), the Almon principal component Kibria-Lukman estimator is superior to the Almon principal component estimator using MSEM criterion, that is, \(\textrm{MSEM}\left( \hat{\varvec{\alpha }}_r^{\textrm{A}}\right) -\textrm{MSEM}\left( \hat{\varvec{\alpha }}_r^{\textrm{A}-\textrm{KL}}(k)\right) > 0\)if and only if where and \(\varvec{a}\) is ...
Let \(\lambda _r\) be the rth genvalue of \(\varvec{Z}^{\top } \varvec{Z}\) where \(\lambda _1 \ge \lambda _2 \ge \ldots \ge \lambda _r > 0\). For \(k < 2 \lambda _r\), the Almon principal component Kibria-Lukman estimator is superior to the Almon ridge estimator using MSEM criterion, that is, \(\textrm{MSEM}\left( \hat{\varvec{\alpha }}^{\textrm{A...
Let \(\lambda _r\) be the rth eigenvalue of \(\varvec{Z}^{\top } \varvec{Z}\) where \(\lambda _1 \ge \lambda _2 \ge \ldots \ge \lambda _r > 0\). For \(k < 2 \lambda _r\), the Almon principal component Kibria-Lukman estimator is superior to the Almon principal component ridge estimator using MSEM criterion, that is, \(\textrm{MSEM}\left( \hat{\varve...
Let \(\lambda _r\) be the rth eigenvalue of \(\varvec{Z}^{\top } \varvec{Z}\) where \(\lambda _1 \ge \lambda _2 \ge \ldots \ge \lambda _r > 0\). For \(k < 2 \lambda _r\), the Almon principal component Kibria-Lukman estimator is superior to the Almon Kibria-Lukman estimator using MSEM criterion, that is, \(\textrm{MSEM}\left( \hat{\varvec{\alpha }}^...
Jul 20, 2022 · In this paper, a new mixed KL estimator under stochastic restrictions is proposed, and its excellent properties under certain conditions are proved theoretically. The above theoretical results...
People also ask
What is the Kibria-Lukman estimator?
Can a Kibria-Lukman estimator solve a multicollinearity problem?
What is a jackknife Kibria-Lukman estimator?
Is KL estimator better than mixed estimator?
Does a mixed KL estimator have a minimum MSE?
Who proposed a two parameter estimator based on ridge estimator and Liu estimator?
Apr 20, 2022 · The Kibria-Lukman (KL) estimator is a recent estimator that has been proposed to solve the multicollinearity problem. In this paper, a generalized version of the KL estimator is proposed, along with the optimal biasing parameter of our proposed estimator derived by minimizing the scalar mean squared error.
