DEVELOPMENT OF SOME RIDGE ESTIMATORS FOR CLASSICAL AND GENERALIZED LINEAR REGRESSION MODELS

ALADEITAN, BOLUWAJI BENEDICTA (2022) DEVELOPMENT OF SOME RIDGE ESTIMATORS FOR CLASSICAL AND GENERALIZED LINEAR REGRESSION MODELS. ["eprint_fieldopt_thesis_type_phd" not defined] thesis, Landmark University, Omu Aran, Kwara State.

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Abstract

Regression analysis is a statistical tool usually used to study the relationship between a dependent variable and independent variables. The classical linear regression model (CLRM) and Generalized Linear Regression Model (GLRM) are examples of regression analysis techniques. The Ordinary Least Squares (OLS) and the Maximum Likelihood Estimator (MLE) are used in estimating parameters in CLRM and GLRM respectively when there is no violation of any assumptions made on the models. Recent researches have shown that time series variables and economic variables grow together which results into the problem of multicollinearity. The aim of this study was to develop some estimators to address multicollinearity problem in CLRM and GLRMs more efficiently. The objectives were to propose some ridge estimators and their parameters by modifying the KL estimator; compare performances of the proposed ridge estimators and their ridge parameters with some existing ones; identify the ridge parameters that are more efficient; and apply the estimators to real life data sets. The Kibria Lukman (KL) estimator recently developed was modified by replacing the β ̂_OLS with β ̂_K and a new Modified KL (MKL) estimator was obtained. New generalized versions of the shrinkage parameters were developed from the KL and MKL parameters. These generalized ridge parameters were further considered in forms of minimum, maximum, median, mid-range, arithmetic mean, geometric mean and harmonic mean of the eigen values of the design matrix to obtain other generalized and ordinary ridge parameters. The new estimator and different versions of the shrinkage parameters were introduced to the Linear, Poisson and Logistic regression models and their performance examined through Monte Carlo simulation study and real life data sets. The MRKLHM, GMKL1AM and the MAMKL2 with frequency of 142, 57 and 132 were selected for KL, MKL1 and MKL2 respectively as the best performing parameters in the linear regression model. The MAMKL2 consistently performed well in a simulation and real life study. The GMKLHM, MNMKL1 and GMMKL2GM with frequency of 34, 58 and 39 were selected for the KL, MKL1 and MKL2 estimators respectively for the Poisson regression model. The GMKLHM parameter showed more consistency and efficiency in the simulation and real life study. The MAKLMN, GMKL1MN and AMMKL2HM were selected with frequency of 20, 20 and 19 for the KL, MKL1 and MKL2 estimators respectively for the logistic regression model. The AMMKL2HM parameter performed consistently and efficiently in the simulation and real life study. The parameter(s) with highest frequency after being ranked between 1 and 10 for the KL and MKL estimators were considered the most efficient parameters for the KL and MKL estimators respectively. The different forms and types of these ridge parameters for KL, MKL1 and MKL2 were extended to the Poisson and logistic regression models. Versions of MKL2 ridge parameter that performed well for the Linear and Logistic regression models could be adopted for estimating parameters in the presence of multicollinearity while the versions of KL ridge parameter that performed well for the Poisson regression model could be used for parameter estimation in the presence of multicollinearity.

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