scholarly journals Performance of Ridge Estimators Based on Weighted Geometric Mean and Harmonic Mean

2020 ◽  
Vol 12 (1) ◽  
pp. 1-13
Author(s):  
S. S. Bhat ◽  
R. Vidya
Keyword(s):  
Simulation Study ◽  
Linear Dependence ◽  
Geometric Mean ◽  
Error Variance ◽  
Ordinary Least Squares ◽  
Regression Coefficients ◽  
Ridge Estimator ◽  
Wide Range ◽  
Ordinary Least Squares Estimator ◽  
Eigen Values

Ordinary least squares estimator (OLS) becomes unstable if there is a linear dependence between any two predictors. When such situation arises ridge estimator will yield more stable estimates to the regression coefficients than OLS estimator. Here we suggest two modified ridge estimators based on weights, where weights being the first two largest eigen values. We compare their MSE with some of the existing ridge estimators which are defined in the literature. Performance of the suggested estimators is evaluated empirically for a wide range of degree of multicollinearity. Simulation study indicates that the performance of the suggested estimators is slightly better and more stable with respect to degree of multicollinearity, sample size, and error variance.

scholarly journals On the Performance of Principal Component Liu-Type Estimator under the Mean Square Error Criterion

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Jibo Wu
Keyword(s):  
Principal Component Regression ◽  
Principal Component ◽  
Ordinary Least Squares ◽  
Mean Square ◽  
Ridge Estimator ◽  
Error Criterion ◽  
Ordinary Least Squares Estimator ◽  
The Mean ◽  
Mean Square Error Criterion ◽  
Theoretical Results

Wu (2013) proposed an estimator, principal component Liu-type estimator, to overcome multicollinearity. This estimator is a general estimator which includes ordinary least squares estimator, principal component regression estimator, ridge estimator, Liu estimator, Liu-type estimator,r-kclass estimator, andr-dclass estimator. In this paper, firstly we use a new method to propose the principal component Liu-type estimator; then we study the superior of the new estimator by using the scalar mean squares error criterion. Finally, we give a numerical example to show the theoretical results.

scholarly journals A Modified New Two-Parameter Estimator in a Linear Regression Model

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Adewale F. Lukman ◽  
Kayode Ayinde ◽  
Sek Siok Kun ◽  
Emmanuel T. Adewuyi
Keyword(s):  
Least Squares ◽  
Ordinary Least Squares ◽  
Least Squares Estimator ◽  
Parameter Estimator ◽  
Ridge Estimator ◽  
Error Matrix ◽  
Liu Estimator ◽  
Special Cases ◽  
Ordinary Least Squares Estimator ◽  
Two Parameter

The literature has shown that ordinary least squares estimator (OLSE) is not best when the explanatory variables are related, that is, when multicollinearity is present. This estimator becomes unstable and gives a misleading conclusion. In this study, a modified new two-parameter estimator based on prior information for the vector of parameters is proposed to circumvent the problem of multicollinearity. This new estimator includes the special cases of the ordinary least squares estimator (OLSE), the ridge estimator (RRE), the Liu estimator (LE), the modified ridge estimator (MRE), and the modified Liu estimator (MLE). Furthermore, the superiority of the new estimator over OLSE, RRE, LE, MRE, MLE, and the two-parameter estimator proposed by Ozkale and Kaciranlar (2007) was obtained by using the mean squared error matrix criterion. In conclusion, a numerical example and a simulation study were conducted to illustrate the theoretical results.

scholarly journals STUDY ON MEASUREMENT RELIABILITY BASED ON LIU ESTIMATOR

2018 ◽  
Vol 48 (3) ◽  
pp. 187-192
Author(s):  
J. W. HUANG ◽  
L. MA ◽  
R. LI
Keyword(s):  
Least Squares ◽  
Simulation Study ◽  
Ordinary Least Squares ◽  
Least Squares Estimator ◽  
Measurement Reliability ◽  
Liu Estimator ◽  
Process Measurement ◽  
Study Results ◽  
Ordinary Least Squares Estimator ◽  
Reasonable Range

In this paper, we introduce the Liu estimator in the measurement process as an alternative method to the ordinary least squares estimator. To compare the Liu estimator and the ordinary least squares estimator under the reliability criterion, a simulation study is conducted. Simulation study results show that Liu estimator is an effective method to replace OLS estimator in process measurement. When the Liu parameter choose in a reasonable range, Liu estimator superior to ordinary least squares estimator in terms of reliability.

scholarly journals Comparison of Some Estimators under the Pitman’s Closeness Criterion in Linear Regression Model

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Jibo Wu
Keyword(s):  
Least Squares ◽  
Principal Components ◽  
Mean Squared Error ◽  
Ordinary Least Squares ◽  
Least Squares Estimator ◽  
Regression Estimator ◽  
Principal Components Regression ◽  
Ridge Estimator ◽  
Error Matrix ◽  
Ordinary Least Squares Estimator

Batah et al. (2009) combined the unbiased ridge estimator and principal components regression estimator and introduced the modifiedr-kclass estimator. They also showed that the modifiedr-kclass estimator is superior to the ordinary least squares estimator and principal components regression estimator in the mean squared error matrix. In this paper, firstly, we will give a new method to obtain the modifiedr-kclass estimator; secondly, we will discuss its properties in some detail, comparing the modifiedr-kclass estimator to the ordinary least squares estimator and principal components regression estimator under the Pitman closeness criterion. A numerical example and a simulation study are given to illustrate our findings.

scholarly journals Lack of Informations about COVID-19 Vaccine: From Implications to Intervention for Supporting Public Health Communications in COVID-19 Pandemic

2021 ◽  
Vol 18 (11) ◽  
pp. 6141
Author(s):  
Silva Guljaš ◽  
Zvonimir Bosnić ◽  
Tamer Salha ◽  
Monika Berecki ◽  
Zdravka Krivdić Dupan ◽  
...  
Keyword(s):  
Vaccine Efficacy ◽  
Health Belief ◽  
Ordinary Least Squares ◽  
Vaccine Hesitancy ◽  
Equal Proportion ◽  
Least Squares Regression ◽  
Online Questionnaire ◽  
Demographic Groups ◽  
Population Immunity ◽  
Wide Range

Lack of knowledge and mistrust towards vaccines represent a challenge in achieving the vaccination coverage required for population immunity. The aim of this study is to examine the opinion that specific demographic groups have about COVID-19 vaccination, in order to detect potential fears and reasons for negative attitudes towards vaccination, and to gain knowledge on how to prepare strategies to eliminate possible misinformation that could affect vaccine hesitancy. The data collection approach was based on online questionnaire surveys, divided into three groups of questions that followed the main postulates of the health belief theory—a theory that helps understanding a behaviour of the public in some concrete surrounding in receiving preventive measures. Ordinary least squares regression analyses were used to examine the influence of individual factors on refusing the vaccine, and to provide information on the perception of participants on the danger of COVID-19 infection, and on potential barriers that could retard the vaccine utility. There was an equal proportion of participants (total number 276) who planned on receiving the COVID-19 vaccine (37%), and of those who did not (36.3%). The rest (26.7%) of participants were still indecisive. Our results indicated that attitudes on whether to receive the vaccine, on how serious consequences might be if getting the infection, as well as a suspicious towards the vaccine efficacy and the fear of the vaccine potential side effects, may depend on participants’ age (<40 vs. >40 years) and on whether they are healthcare workers or not. The barriers that make participants‘ unsure about of receiving the vaccine, such as a distrust in the vaccine efficacy and safety, may vary in different socio-demographic groups and depending on which is the point of time in the course of the pandemic development, as well as on the vaccine availability and experience in using certain vaccine formulas. There is a pressing need for health services to continuously provide information to the general population, and to address the root causes of mistrust through improved communication, using a wide range of policies, interventions and technologies.

scholarly journals How cann soccer improve statistical learning?

2014 ◽  
Vol 2 (7) ◽  
pp. 83-87
Author(s):  
Enivaldo C. Rocha ◽  
Dalson Britto Figueiredo Filho ◽  
Ranulfo Paranhos ◽  
José Alexandre Silva Jr. ◽  
Denisson Silva
Keyword(s):  
Linear Regression ◽  
Statistical Learning ◽  
Undergraduate Students ◽  
Ordinary Least Squares ◽  
Regression Coefficients ◽  
Least Squares Regression ◽  
Practical Application ◽  
Implementation Cost ◽  
Home Team ◽  
Classical Hypothesis

This paper presents an active classroom exercise focusing on the interpretation of ordinary least squares regression coefficients. Methodologically, undergraduate students analyze Brazilian soccer data, formulate and test classical hypothesis regarding home team advantage. Technically, our framework is simply adapted for others sports and has no implementation cost. In addition, the exercise is easily conducted by the instructor and highly enjoyable for the students. The intuitive approach also facilitates the understanding of linear regression practical application.

scholarly journals Pharmacokinetic Modeling and Optimal Sampling Strategies for Therapeutic Drug Monitoring of Rifampin in Patients with Tuberculosis

2015 ◽  
Vol 59 (8) ◽  
pp. 4907-4913 ◽  
Author(s):  
Marieke G. G. Sturkenboom ◽  
Leonie W. Mulder ◽  
Arthur de Jager ◽  
Richard van Altena ◽  
Rob E. Aarnoutse ◽  
...  
Keyword(s):  
Population Pharmacokinetic Model ◽  
Pharmacokinetic Model ◽  
Mean Squared Error ◽  
Geometric Mean ◽  
Plasma Concentrations ◽  
Therapeutic Drug ◽  
Population Pharmacokinetic ◽  
Optimal Sampling ◽  
Sampling Strategies ◽  
Wide Range

ABSTRACTRifampin, together with isoniazid, has been the backbone of the current first-line treatment of tuberculosis (TB). The ratio of the area under the concentration-time curve from 0 to 24 h (AUC0–24) to the MIC is the best predictive pharmacokinetic-pharmacodynamic parameter for determinations of efficacy. The objective of this study was to develop an optimal sampling procedure based on population pharmacokinetics to predict AUC0–24values. Patients received rifampin orally once daily as part of their anti-TB treatment. A one-compartmental pharmacokinetic population model with first-order absorption and lag time was developed using observed rifampin plasma concentrations from 55 patients. The population pharmacokinetic model was developed using an iterative two-stage Bayesian procedure and was cross-validated. Optimal sampling strategies were calculated using Monte Carlo simulation (n= 1,000). The geometric mean AUC0–24value was 41.5 (range, 13.5 to 117) mg · h/liter. The median time to maximum concentration of drug in serum (Tmax) was 2.2 h, ranging from 0.4 to 5.7 h. This wide range indicates that obtaining a concentration level at 2 h (C2) would not capture the peak concentration in a large proportion of the population. Optimal sampling using concentrations at 1, 3, and 8 h postdosing was considered clinically suitable with anr2value of 0.96, a root mean squared error value of 13.2%, and a prediction bias value of −0.4%. This study showed that the rifampin AUC0–24in TB patients can be predicted with acceptable accuracy and precision using the developed population pharmacokinetic model with optimal sampling at time points 1, 3, and 8 h.

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