scholarly journals An Application of Proposed Ridge Regression Methods to Real Data Problem

2018 ◽  
Vol 7 (4.30) ◽  
pp. 106
Author(s):  
N S M Shariff ◽  
H M B Duzan
Keyword(s):  
Least Squares ◽  
Consumer Price Index ◽  
Market Price ◽  
Real Data ◽  
Ordinary Least Squares ◽  
Parameter Estimates ◽  
Least Squares Regression ◽  
Ridge Estimator ◽  
Data Set ◽  
Explanatory Variables

The Ordinary Least Squares (OLS) is a common method to investigate the linear relationship among variable of interest. The presence of multicollinearity will produce unreliable result in the parameter estimates if OLS is applied to estimate the model. Due to such reason, this study aims to use the proposed ridge estimator as linear combinations of the coefficient of least squares regression of explanatory variables to the real application. The numerical example of stock market price and macroeconomic variables in Malaysia is employed using both methods with the aim of investigating the relationship of the variables in the presence of multicollinearity in the data set.  The variables on interest are Consumer Price Index (CPI), Gross Domestic Product (GDP), Base Lending Rate (BLR) and Money Supply (M1). The obtained findings show that the proposed procedure is able to estimate the model and produce reliable result by reducing the effect of multicollinearity in the data set.

scholarly journals Tolerance Intervals in a Heteroscedastic Linear Regression Context with Applications to Aerospace Equipment Surveillance

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Janet Myhre ◽  
Daniel R. Jeske ◽  
Michael Rennie ◽  
Yingtao Bi
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Performance Metrics ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Automated System ◽  
Least Squares Regression ◽  
Data Set ◽  
Tolerance Intervals ◽  
Power Of The Test

A heteroscedastic linear regression model is developed from plausible assumptions that describe the time evolution of performance metrics for equipment. The inherited motivation for the related weighted least squares analysis of the model is an essential and attractive selling point to engineers with interest in equipment surveillance methodologies. A simple test for the significance of the heteroscedasticity suggested by a data set is derived and a simulation study is used to evaluate the power of the test and compare it with several other applicable tests that were designed under different contexts. Tolerance intervals within the context of the model are derived, thus generalizing well-known tolerance intervals for ordinary least squares regression. Use of the model and its associated analyses is illustrated with an aerospace application where hundreds of electronic components are continuously monitored by an automated system that flags components that are suspected of unusual degradation patterns.

scholarly journals An Improvised SIMPLS Estimator Based on MRCD-PCA Weighting Function and Its Application to Real Data

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2211
Author(s):  
Siti Zahariah ◽  
Habshah Midi ◽  
Mohd Shafie Mustafa
Keyword(s):  
Least Squares ◽  
Partial Least Squares ◽  
Weighting Function ◽  
Real Data ◽  
Least Squares Regression ◽  
Regression Problem ◽  
Leverage Points ◽  
Explanatory Variables ◽  
Diagnostic Plot ◽  
Data Points

Multicollinearity often occurs when two or more predictor variables are correlated, especially for high dimensional data (HDD) where p>>n. The statistically inspired modification of the partial least squares (SIMPLS) is a very popular technique for solving a partial least squares regression problem due to its efficiency, speed, and ease of understanding. The execution of SIMPLS is based on the empirical covariance matrix of explanatory variables and response variables. Nevertheless, SIMPLS is very easily affected by outliers. In order to rectify this problem, a robust iteratively reweighted SIMPLS (RWSIMPLS) is introduced. Nonetheless, it is still not very efficient as the algorithm of RWSIMPLS is based on a weighting function that does not specify any method of identification of high leverage points (HLPs), i.e., outlying observations in the X-direction. HLPs have the most detrimental effect on the computed values of various estimates, which results in misleading conclusions about the fitted regression model. Hence, their effects need to be reduced by assigning smaller weights to them. As a solution to this problem, we propose an improvised SIMPLS based on a new weight function obtained from the MRCD-PCA diagnostic method of the identification of HLPs for HDD and name this method MRCD-PCA-RWSIMPLS. A new MRCD-PCA-RWSIMPLS diagnostic plot is also established for classifying observations into four data points, i.e., regular observations, vertical outliers, and good and bad leverage points. The numerical examples and Monte Carlo simulations signify that MRCD-PCA-RWSIMPLS offers substantial improvements over SIMPLS and RWSIMPLS. The proposed diagnostic plot is able to classify observations into correct groups. On the contrary, SIMPLS and RWSIMPLS plots fail to correctly classify observations into correct groups and show masking and swamping effects.

scholarly journals Voluntary appointment of independent directors: evidence from Taiwan

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mao-Feng Kao ◽  
Lynn Hodgkinson ◽  
Aziz Jaafar
Keyword(s):  
Corporate Governance ◽  
Least Squares ◽  
Research Work ◽  
Ordinary Least Squares ◽  
Independent Directors ◽  
Parameter Estimates ◽  
Two Stage ◽  
Data Set ◽  
Content Type ◽  
Two Stage Least Squares

Purpose Using a data set of Taiwanese listed firms from 2002 to 2015, this paper aims to examine the determinants to voluntarily appoint independent directors. Design/methodology/approach This study uses panel estimation to exploit both the cross-section and time-series nature of the data. Further, this paper uses Tobit regression, generalized linear model (GLM) in the additional analysis and the two-stage least squares to mitigate for a possible endogeneity issue. Findings The main findings show that Taiwanese firms with large board sizes tend to voluntarily appoint independent directors and firms that already have independent supervisors more willingly to accept additional independent directors onto the board. Furthermore, ownership concentration and institutional ownership are positively associated with the voluntary appointment of independent directors. On the contrary, firms controlled by family members are generally reluctant to voluntarily appoint independent directors. Research limitations/implications The findings are important for managers, shareholders, creditors and policymakers. In particular, when considering the determinants of the voluntary appointment of independent directors, the results indicate that independent supervisors, outside shareholders and institutional investors are significant factors in influencing effective internal and external corporate governance mechanisms. This research work focuses on the voluntary appointment of independent directors. It would be interesting to compare the effectiveness of voluntary appointments with a mandatory appointment within Taiwan and with other jurisdictions. Originality/value This study incrementally contributes to the corporate governance literature in several ways. First, this study extends the earlier research by using a more comprehensive data set of non-financial Taiwanese firms and using alternative methodologies to investigate the determinants of voluntary appointment of independent directors. Second, prior studies tend to neglect the possible issue of using a censored and fractional dependent variable, the proportion of independent directors, which might yield biased and inconsistent parameter estimates when using ordinary least squares regression estimation. Finally, this study addresses the relevant econometric issues by using the Tobit, GLM and the two-stage least squares for a possible endogeneity concern.

Linear regression models for biomass table construction, using cluster samples

1989 ◽  
Vol 19 (5) ◽  
pp. 664-673 ◽  
Author(s):  
Andrew J. R. Gillespie ◽  
Tiberius Cunia
Keyword(s):  
Least Squares ◽  
Regression Models ◽  
Predictor Variable ◽  
Ordinary Least Squares ◽  
Cluster Sampling ◽  
Parameter Estimates ◽  
Least Squares Regression ◽  
Linear Regression Models ◽  
Estimation Procedures ◽  
Biased Estimates

Biomass tables are often constructed from cluster samples by means of ordinary least squares regression estimation procedures. These procedures assume that sample observations are uncorrelated, which ignores the intracluster correlation of cluster samples and results in underestimates of the model error. We tested alternative estimation procedures by simulation under a variety of cluster sampling methods, to determine combinations of sampling and estimation procedures that yield accurate parameter estimates and reliable estimates of error. Modified, generalized, and jack-knife least squares procedures gave accurate parameter and error estimates when sample trees were selected with equal probability. Regression models that did not include height as a predictor variable yielded biased parameter estimates when sample trees were selected with probability proportional to tree size. Models that included height did not yield biased estimates. There was no discernible gain in precision associated with sampling with probability proportional to size. Random coefficient regressions generally gave biased point estimates with poor precision, regardless of sampling method.

scholarly journals A Comparison of OLS and Ridge Regression Methods in the Presence of Multicollinearity Problem in the Data

2018 ◽  
Vol 7 (4.30) ◽  
pp. 36
Author(s):  
N S M Shariff ◽  
H M B Duzan
Keyword(s):  
Regression Analysis ◽  
Least Squares ◽  
Ridge Regression ◽  
Regression Modeling ◽  
Parameter Estimates ◽  
Least Squares Regression ◽  
Ridge Estimator ◽  
Common Procedure ◽  
Monte Carlo Simulation Study ◽  
Regression Methods

The presence of multicollinearity will significantly lead to inconsistent parameter estimates in regression modeling. The common procedure in regression analysis that is Ordinarily Least Squares (OLS) is not robust to multicollinearity problem and will result in inaccurate model. To solve this problem, a number of methods are developed in the literatures and the most common method is ridge regression. Although there are many studies propose variety method to overcome multicolinearity problem in regression analysis, this study proposes the simplest model of ridge regression which is based on linear combinations of the coefficient of the least squares regression of independent variables to determine the value of  k (ridge estimator in ridge regression model). The performance of the proposed method is investigated and compared to OLS and some recent existing methods. Thus, simulation studies based on Monte Carlo simulation study are considered. The result of this study is able to produce similar findings as in existing method and outperform OLS in the existence of multicollinearity in the regression modeling.

scholarly journals Insights from analysing tourist expenditure using quantile regression

2016 ◽  
Vol 23 (5) ◽  
pp. 1138-1145 ◽  
Author(s):  
António Almeida ◽  
Brian Garrod
Keyword(s):  
Quantile Regression ◽  
Least Squares ◽  
Empirical Studies ◽  
Ordinary Least Squares ◽  
Estimation Technique ◽  
Least Squares Regression ◽  
Data Set ◽  
Detailed Understanding ◽  
Tourism Destinations ◽  
Single Data

Mature tourism destinations are increasingly needing to diversify their products and markets. To be successful, such strategies require a very detailed understanding of potential tourists’ levels and patterns of spending. Empirical studies of tourist expenditure have tended to employ ordinary least squares regression for this purpose. There are, however, a number of important limitations to this technique, chief among which is its inability to distinguish between tourists who have higher- and lower-than-average levels of spending. As such, some researchers recommend the use of an alternative estimation technique, known as quantile regression, which does allow such distinctions to be made. This study uses a single data set, collected among rural tourists in Madeira, to analyse the determinants of tourist expenditure using both techniques. This enables direct comparison to be made and illustrates the additional insights to be gained using quantile regression.

Exploratory Multivariable Analyses of California Driver Record Accident Rates

1998 ◽  
Vol 1635 (1) ◽  
pp. 72-80 ◽  
Author(s):  
Michael A. Gebers
Keyword(s):  
Least Squares ◽  
Negative Binomial ◽  
Weighted Least Squares ◽  
Statistical Significance ◽  
Ordinary Least Squares ◽  
Parameter Estimates ◽  
Least Squares Regression ◽  
Sample Sizes ◽  
Regression Techniques ◽  
Linear Probability

Since 1964 the California Department of Motor Vehicles has issued several monographs on driver characteristics and accident risk factors as part of a series of analyses known as the California driver record study. A number of regression analyses were conducted of driving record variables measured over a 6-year time period (1986 to 1991). The techniques presented consist of ordinary least squares, weighted least squares, Poisson, negative binomial, linear probability, and logistic regression models. The objective of the analyses was to compare the results obtained from several different regression techniques under consideration for use in the in-progress California driver record study. The results are informative in determining whether the various regression methods produce similar results for different sample sizes and in exploring whether reliance on ordinary least squares techniques in past California driver record study analyses has produced biased significance levels and parameter estimates. The results indicate that, for these data, the use of the different regression techniques do not lead to any greater increase in individual accident prediction beyond that obtained through application of ordinary least squares regression. The methods produce almost identical results in terms of the relative importance and statistical significance of the independent variables. It therefore appears safe to employ ordinary least squares multiple regression techniques on driver accident count distributions of the type represented by California driver records, at least when the sample sizes are large.

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

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