Jackknife Kibria-Lukman M-Estimator: Simulation and Application

Authors

  • Segun L. Jegede
    Department of Mathematical Sciences, Kent State University
    https://orcid.org/0000-0002-9973-1377
  • Adewale F. Lukman
    Department of Mathematics, University of Medical Sciences, Nigeria; Institute of Mathematics, Eotvos Lorand University, Hungary
    https://orcid.org/0000-0003-2881-1297
  • Kayode Ayinde
    Department of Statistics, Federal University of Technology, Akure, Nigeria
  • Kehinde A. Odeniyi
    Department of Agricultural Economics and Agribusiness Management, Osun State University, Nigeria.

Keywords:

Jackknife Kibria-Lukman, M-estimator, Monte Carlo Simulation, Multicollinearity, Outliers, Robust

Abstract

The ordinary least square (OLS) method is very efficient in estimating the regression parameters in a linear regression model under classical assumptions. If the model contains outliers, the performance of the OLS estimator becomes imprecise. Multicollinearity is another issue that can reduce the performance of the OLS estimator. This study proposed the Robust Jackknife Kibria-Lukman (RJKL) estimator based on the M-estimator to deal with multicollinearity and outliers. We examine the superiority of the estimator over existing estimators using theoretical proofs and Monte Carlo simulations. We put the estimator to the test once more using real-world data. We observed that the estimator performs better than the existing estimators.

Dimensions

K. Ayinde, A. F. Lukman & O. Arowolo, “Robust regression diagnostics of influential observations in linear regression model”, Open Journal of Statistics 05 (2015) 273.

A. F. Lukman & K. Ayinde, “Review and classifications of the ridge parameter estimation techniques”, Hacettepe Journal of Mathematics and Statistics 46 (2017) 953.

A. F. Lukman, K. Ayinde, G. Kibria & S. L. Jegede, “Two-parameter modified ridge-type m-estimator for linear regression model”, The Scientific World Journal (2020).

¨O. G. Alma, “Comparison of robust regression methods in linear regression”, Int. J. Contemp. Math. Sciences 6 (2011) 409.

Hampel, F. R. (2002). Robust Inference, (In A. H. ElShaarawi & W. W. Piegorsch (Eds.), Encyclopedia of Environmetrics;(pp. 1865–1885). New York: Wiley & Sons.)

D. Gervini, “Robust adaptive estimators for binary regression models”, Quality control and applied statistics, 51 (2006) 565.

R. A.Maronna, R. D. Martin & V. J. Yohai, Robust Statistics, John Wiley, 2014.

Huber P.J, Robust Statistics, Wiley, New York, NY, USA, (1981).

A. E. Hoerl & R. W. Kennard, “Ridge regression: biased estimation for nonorthogonal problems”, Technometrics, 12 (1970) 55.

M.J.Silvapulle, “Robust ridge regression based on an m-estimator”, Australian Journal of Statistics, 33 (1991) 319.

B. M. Kibria & A. F. Lukman, “A new ridge-type estimator for the linear regression model: Simulations and applications”, Scientifica, (2020).

Y.Al-Taweel&Z.Algamal, “Almostunbiasedridgeestimator inthe zeroinated Poisson regression model”, TWMS Journal of Applied and Engineering Mathematics 12 (2022) 235.

N. M. Hammood & Z. Y. Algamal, “A new Jackknifing ridge estimator for logistic regression model”, International Journal of Nonlinear Analysis and Applications 13 (2022) 2127.

A. Alkhateeb & Z. Algamal, “Jackknifed Liu-type estimator in Poisson regression model”, Journal of the Iranian Statistical Society 19 (2020) 21.

F. I. Ugwuowo, H. E. Oranye & K. C. Arum, “On the jackknife KibriaLukman estimator for the linear regression model”, Communications in Statistics-Simulation and Computation, (2021) 1.

M. H. Quenouille, “Notes on bias in estimation”, Biometrika, 43 (1956) 353.

P. Filzmoser & F. S. Kurnaz, “A robust Liu regression estimator”, Communications in Statistics-Simulation and Computation 47 (2018) 432.

F. R. Hampel, E. M. Ronchetti, P. J. Rousseeuw & W. A. Stahel, Robust statistics: the approach based on influence functions, John Wiley & Sons, 196 (2011).

R. W. Farebrother, “Further results on the mean square error of ridge regression”, Journal of the Royal Statistical Society, Series B (Methodological), (1976) 248.

G. Trenkler & H. Toutenburg, “Mean squared error matrix comparisons between biased estimators -An overview of recent results”, Statistical papers 31 (1990) 165.

G. C. McDonald & D. I. Galarneau, “A Monte Carlo evaluation of some ridge-type estimators”, Journal of the American Statistical Association 70 (1975) 407.

B. G. Kibria, “Performance of some new ridge regression estimators”, Communications in Statistics-Simulation and Computation, 32 (2003) 419.

Z. Y. Algamal & M. M. Alanaz, “Proposed methods in estimating the ridge regression parameter in poisson regression model”, Electronic Journal of Applied Statistical Analysis, 11 (2018) 506.

Z. Y. Algamal, “A new method for choosing the biasing parameter in ridge estimator for generalized linear model”, Chemometrics and Intelligent (2018).

A. F. Lukman, S. L. Jegede, A. B. Bello & S. Binuomote, A. R. Haadi, “Modified ridge-type estimator with prior information”, International Journal of Engineering Research and Technology, 12 (2019) 1668.

A. F. Lukman, B. M. Kibria, K. Ayinde & S. L. Jegede, “Modified oneparameter Liu estimator for the linear regression model”, Modelling and Simulation in Engineering, (2020).

A. F. Lukman, A. Zakariya, B. M. G. Kibria & K. Ayinde, “The KL estimator for the inverse gaussian regression model”, Concurrency Computat Pract Exper. (2021) e6222.

O. G. Obadina, A. F. Adedotuun & O. A. Odusanya, “Ridge Estimation’s Effectiveness for Multiple Linear Regression with Multicollinearity: An investigation using Monte-Carlo simulations”, Journal of the Nigerian Society of Physical Sciences, (2021) 278.

Z. Y. Algamal & M. R, Abonazel, “Developing a Liu-type estimator in beta regression model”, Concurrency and Computation: Practice and Experience, 34 (2022) 6685.

J. P. Newhouse & S. D. Oman, “An evaluation of ridge estimators”, 1971.

N. A. Alao, K. Ayinde & G. S. Solomon, “A comparative study on sensitivity of multivariate tests of normality to outliers”, A SM Sc. J. 12 (2019) 65.

Y. Hussein & M. Zari, “Generalized two stage ridge regression estimator TR for multicollinearity and autocorrelated errors”, Canadian Journal on Science and Engineering Mathematics 3 (2012) 79. 263

Published

2022-05-29

How to Cite

Jackknife Kibria-Lukman M-Estimator: Simulation and Application. (2022). Journal of the Nigerian Society of Physical Sciences, 4(2), 251-264. https://doi.org/10.46481/jnsps.2022.664

Issue

Volume 4, Issue 2, May 2022

Section

Original Research
Copyright & Licensing

Copyright (c) 2022 Journal of the Nigerian Society of Physical Sciences

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Jackknife Kibria-Lukman M-Estimator: Simulation and Application. (2022). Journal of the Nigerian Society of Physical Sciences, 4(2), 251-264. https://doi.org/10.46481/jnsps.2022.664

Similar Articles

71-80 of 89

You may also start an advanced similarity search for this article.

Most read articles by the same author(s)