B M Golam Kibria - Academia.edu (original) (raw)

Papers by B M Golam Kibria

nternational Journal of Statistical Sciences, 2024

In linear regression models, multicollinearity often results in unstable and unreliable parameter... more In linear regression models, multicollinearity often results in unstable and unreliable parameter
estimates. Ridge regression, a biased estimation technique, is commonly used to mitigate this issue
and produce more reliable estimates of regression coefficients. Several estimators have been
developed to select the optimal ridge parameter. This study focuses on the top 16 estimators from
the 366 evaluated by Mermi et al. (2024), along with seven additional estimators introduced over
time. These 23 estimators were compared to Ordinary Least Squares (OLS), Elastic-Net (EN),
Lasso, and generalized ridge (GR) regression, to evaluate their performance across different levels
of multicollinearity in multiple regression settings. Simulated data, both with and without outliers,
and various parametric conditions were used for the comparisons. The results indicated that certain
ridge regression estimators perform reliably with small sample sizes and high correlations (around
0.95) in the absence of outliers. However, when outliers were present, some estimators performed
better due to small sample sizes and increased variance. Furthermore, GR, EN, and Lasso
exhibited robustness with large datasets, except in cases with substantial outliers and high
variance.

jnanabha, Dec 31, 2022

Multiple Regression analysis is one of the most critical and widely used statistical techniques i... more Multiple Regression analysis is one of the most critical and widely used statistical techniques in medical and applied research. It is defined as a multivariate technique for determining the correlation between a response variable and some combination of two or more predictor variables. Moreover, it is wellknown in medical sciences that the obesity, high blood pressure and high cholesterol are major risk factors for cardiovascular health issues. The body mass index is a measure of body size, and combines a person's weight with their height, and therefore can affect their obesity, high blood pressure, high cholesterol and type 2 diabetes mellitus significantly, which are major risk factors for cardiovascular health issues in adults. Motivated by these facts, in this paper, a multiple linear regression model is developed to analyze the obesity in adults, based on a sample data of adult's age, height, weight, waist, diastolic blood pressure, systolic blood pressure, pulse, cholesterol, and the body mass index measurements. The use of multiple linear regression is illustrated in the prediction study of adult's obesity based on their body mass index. It is observed that in the presence of adult's age, weight, waist, diastolic blood pressure, systolic blood pressure, pulse, and cholesterol levels, height is a good predictor of the body mass index. Moreover, in the presence of age, height, waist, diastolic blood pressure, systolic blood pressure, pulse, and cholesterol levels, weight is a good predictor of the body mass index. Some concluding remarks are given in the end.

Wseas Transactions On Environment And Development, Dec 31, 2021

Coronavirus disease 2019 (COVID-19) is a novel infectious disease that was detected in Wuhan, Chi... more Coronavirus disease 2019 (COVID-19) is a novel infectious disease that was detected in Wuhan, China at the end of 2019. The virus quickly spread worldwide and caused a global pandemic. This paper investigates if there are any regressors that could help impact the number of deaths due to COVID-19. The variables that were used in the models were total deaths, hospitalizations, total cases, population, minimum temperature, average temperature, maximum temperature, precipitation, mobility index, median age, adults age 65 or older, PM2.5 average, ozone average, and positive non-residents. After fitting six different regression models, we found that the most significant regressors were hospitalizations per county, total cases per county, population per county, median age per county, positive adults 65 or older per county, and positive non-residents per county. The COVID-19 data of this paper will be an excellent source for illustrating the multicollinear linear regression models.

Frontiers in Applied Mathematics and Statistics

The Conway–Maxwell–Poisson (COMP) model is defined as a flexible count regression model used for ... more The Conway–Maxwell–Poisson (COMP) model is defined as a flexible count regression model used for over- and under-dispersion cases. In regression analysis, when the explanatory variables are highly correlated, this means that there is a multicollinearity problem in the model. This problem increases the standard error of maximum likelihood estimates. To manage the multicollinearity effects in the COMP model, we proposed a new modified Liu estimator based on two shrinkage parameters (k, d). To assess the performance of the proposed estimator, the mean squared error (MSE) criterion is used. The theoretical comparison of the proposed estimator with the ridge, Liu, and modified one-parameter Liu estimators is made. The Monte Carlo simulation and real data application are employed to examine the efficiency of the proposed estimator and to compare it with the ridge, Liu, and modified one-parameter Liu estimators. The results showed the superiority of the proposed estimator as it has the sma...

Introduction: Coronavirus disease 2019 (COVID-19), a respiratory disease caused by the coronaviru... more Introduction: Coronavirus disease 2019 (COVID-19), a respiratory disease caused by the coronavirus SARSCoV-2, has had an immense impact on a variety of sectors both worldwide and nationwide. Vast differences are observed among states within the United States of America in terms of COVID-19 cases and deaths. Objective: The objective of this paper is to present a means through which we can compare deaths between multiple states, using the index date approach applied by Middelburg and Rosendaal. Materials and Methods: Using the CDC COVID-19 tracker, we created two sets of ten states focusing on states with (1) the highest number of deaths and (2) the highest number of deaths per 100,000. We applied features of the authors’ technique in order to compare deaths between certain states through visualizations. We referred to the cumulative number of deaths on each day from January 21st, 2020 to September 30th, 2020, as a percentage of the cumulative deaths 40 days after the first death. Res...

Proceedings of the 2011 ACM Symposium on Applied Computing, 2011

In this paper, we propose an innovative suite of metrics based on a class abstraction that uses a... more In this paper, we propose an innovative suite of metrics based on a class abstraction that uses a taxonomy for OO classes (CAT) to capture aspects of software complexity through combinations of class characteristics. We empirically validate their ability to predict fault prone classes using fault data for six versions of the Java-based open-source Eclipse Integrated Development Environment. We conclude that this proposed CAT metric suite, even though it treats classes in groups rather than individually, is as effective as the traditional Chidamber and Kemerer metrics in identifying fault-prone classes.

Journal of Multivariate Analysis, 1999

This paper derives the prediction distribution of future responses from the linear model with err... more This paper derives the prediction distribution of future responses from the linear model with errors having an elliptical distribution with known covariance parameters. For unknown covariance parameters, the marginal likelihood function of the parameters has been obtained and the prediction distribution has been modified by replacing the covariance parameters by their estimates obtained from the marginal likelihood function. It is observed that the prediction distribution with elliptical error has a multivariate Student's t-distribution with appropriate degrees of freedom. The results for some special cases such as the Intra-class correlation model, AR(1), MA(1), and ARMA(1,1) models have been obtained from the general results. As an application, the ;-expectation tolerance region has been constructed. An example has been added.

International Journal of Computational and Theoretical Statistics, 2019

A new median ranked set sampling procedure for positively skew distributions (NMRSSS) is proposed... more A new median ranked set sampling procedure for positively skew distributions (NMRSSS) is proposed and used to estimate population mean. The estimators based on the proposed scheme are compared with the estimators based on ranked set sampling (RSS), median ranked set sampling (MRSS) and new median ranked set sampling (NMRSS) procedures. It is shown that the relative precisions of the estimators based on NMRSSS are higher than the estimators based on RSS, MRSS and NMRSS procedures.

WSEAS TRANSACTIONS ON MATHEMATICS

We proposed new two-parameter estimators to solve the problem called multicollinearity for the lo... more We proposed new two-parameter estimators to solve the problem called multicollinearity for the logistic regression model in this paper. We have derived these estimators’ properties and using the mean squared error (MSE) criterion; we compare theoretically with some of existing estimators, namely the maximum likelihood, ridge, Liu estimator, Kibria-Lukman, and Huang estimators. Furthermore, we obtain the estimators for k and d. A simulation is conducted in order to compare the estimators' performances. For illustration purposes, two real-life applications have been analyzed, that supported both theoretical and a simulation. We found that the proposed estimator, which combines the Liu estimator and the Kibria-Lukman estimator, has the best performance.

Journal of Statistical Theory and Applications, 2018

Characterizations of probability distributions play important roles in probability and statistics... more Characterizations of probability distributions play important roles in probability and statistics. Before a particular probability distribution model is applied to fit the real world data, it is essential to confirm whether the given probability distribution satisfies the underlying requirements by its characterization. A probability distribution can be characterized through various methods. In this paper, we provide the characterizations of Chen's two-parameter exponential power life-testing distribution by truncated moment.

Advances in Science, Technology and Engineering Systems Journal, 2020

We proposed two robust confidence interval estimators, namely, the median interquartile range con... more We proposed two robust confidence interval estimators, namely, the median interquartile range confidence interval (MDIQR) and the trimean interquartile range confidence interval (TRIQR) for the population mean (µ) as an alternative to the classical confidence interval. The proposed methods are based on the asymptotic normal theorem (ANT) for the sample median (MD) and the sample trimean (TR). We compare the performance of the proposed interval estimators with the classical estimators by using a simulation study through the following criteria: (i) average width (AW) and (ii) empirical coverage probability (CP). It is evident from simulation study is that the proposed robust interval estimator performs well under both criterion and when the observations are sampled from contaminated normal distribution. However, when the observations are sampled from non-normal distributions, the classical confidence interval performs the best in the shorter width sense, but the coverage probability tends to be smaller than the two proposed robust confidence interval estimators for all sample sizes. For illustration purposes, two real life data sets are analyzed, which supported the findings of the simulation study to some extent.

Journal of Statistics: Advances in Theory and Applications, 2019

This paper considers some bootstrap version of the existing confidence intervals for estimating t... more This paper considers some bootstrap version of the existing confidence intervals for estimating the parameter of an autoregressive process of order one model. A simulation study has been conducted to compare the performance of the proposed intervals using two important measures: coverage probability and average width. It appears from our simulation study that all methods have confidence coefficient closest to the given confidence coefficient, however, our proposed bootstrap intervals have small average widths as compare to its counterpart. A real life data are analyzed, which supported the simulation results to some extent. We believe that the findings of this study will make important contribution to the time series literature.

Production Engineering, 2019

This paper aims to compare the performances of modified confidence intervals based on robust scal... more This paper aims to compare the performances of modified confidence intervals based on robust scale estimators with classical confidence interval for process capability index (C p) when the process has a non-normal distribution. The estimated coverage probability and the average width of the confidence intervals were obtained by a Monte-Carlo simulation under different scenarios. Simulation results showed that the modified confidence intervals performed well in terms of coverage probability and average width for all cases. Two real-life numerical examples from industry are analyzed to illustrate the performance and the implementation of the classical and modified confidence intervals for the process capability index (C p) which also supported the results of the simulation study to some extent.

International Journal of Statistics in Medical Research, 2016

Computing a confidence interval for a population correlation coefficient is very important for re... more Computing a confidence interval for a population correlation coefficient is very important for researchers as it gives an estimated range of values which is likely to include an unknown population correlation coefficient. This paper studied some confidence intervals for estimating the population correlation coefficient ρ by means of a Monte Carlo simulation study. Data are randomly generated from several bivariate distributions with a various values of sample sizes. Assessment measures such as coverage probability, mean width and standard deviation of the width are selected for performances evaluation. Two real life data are analyzed to demonstrate the application of the proposed confidence intervals. Based on our findings, some good confidence intervals for a population correlation coefficient are suggested for practitioners and applied researchers.

Journal of Statistical Distributions and Applications, 2015

A probability distribution can be characterized through various methods. In this paper, we have e... more A probability distribution can be characterized through various methods. In this paper, we have established some new characterizations of folded Student's t distribution by truncated first moment, order statistics and upper record values. It is hoped that the results will be quite useful in the fields of probability, statistics, and other applied sciences.

Journal of Applied Statistics, 2013

ABSTRACT

Statistics, Optimization & Information Computing, 2019

This paper aims to compare the performance of proposed confidence intervals for population coeffi... more This paper aims to compare the performance of proposed confidence intervals for population coefficient of variation (CV) with the existing confidence intervals, namely, McKay, Miller, and Gulher et al. confidence intervals under both symmetric and skewed distributions. We observed that the proposed augmented-large-sample (AA&K-ALS) confidence interval performed well in terms of coverage probability in all cases. The large-sample (A&A-LS) and adjusted degrees of freedom (AA&K-ADJ) confidence intervals had much lower coverage probability than the nominal level for skewed distributions. However, the average widths of the AA&K-LS confidence interval are narrower than that of the rest confidence intervals. Two real-life data are analyzed to illustrate the implementation of the several methods.

Journal of Modern Applied Statistical Methods

A new Liu type of estimator for the seemingly unrelated regression (SUR) models is proposed that ... more A new Liu type of estimator for the seemingly unrelated regression (SUR) models is proposed that may be used when estimating the parameters vector in the presence of multicollinearity if the it is suspected to belong to a linear subspace. The dispersion matrices and the mean squared error (MSE) are derived. The new estimator may have a lower MSE than the traditional estimators. It was shown using simulation techniques the new shrinkage estimator outperforms the commonly used estimators in the presence of multicollinearity.

Scientific Reports, 2021

The maximum likelihood estimator (MLE) suffers from the instability problem in the presence of mu... more The maximum likelihood estimator (MLE) suffers from the instability problem in the presence of multicollinearity for a Poisson regression model (PRM). In this study, we propose a new estimator with some biasing parameters to estimate the regression coefficients for the PRM when there is multicollinearity problem. Some simulation experiments are conducted to compare the estimators' performance by using the mean squared error (MSE) criterion. For illustration purposes, aircraft damage data has been analyzed. The simulation results and the real-life application evidenced that the proposed estimator performs better than the rest of the estimators.