Estimate The Parameters in Presence of Multicollinearity And Outliers Using Bisquare Weighted Ridge Least Median Squares Regression (wrlms)

2020 ◽  
Vol 23 (2) ◽  
pp. 9-24
Author(s):  
Kafi Dano Pati
Keyword(s):  
Simulation Study ◽  
Ridge Regression ◽  
Robust Regression ◽  
Mean Squared Error ◽  
Medical Application ◽  
Least Square ◽  
Potential Candidate ◽  
Robust Detection ◽  
Ordinary Least Square ◽  
Numerical Example

The presence of multicollinearity and outliers are classical problems of data within the linear regression framework. We are going to present a proposal of a new method which can be a potential candidate for robust ridge regression as well as a robust detection of multicollinearity. This proposal arises as a logical combination of principles used in the ridge regression and the Bisquare weighted function. The technique of the Least Median of Squares (LMS) is used for the sake of overcoming the resulting regression problems. This paper investigates the non-resistance of Ordinary Least Square (OLS) to multicollinearity and outliers and proposes the utilization of robust regression for instance, Least Median Squares LMS to detect non-normality of residuals, the use of robust methods yields more reliable trend estimations and outlier detection. LMS is introduced as a robust regression technique and through medical application its effect on regression is discussed. The numerical example and simulation study shows that the outcome of the Weighted Ridge Least Median Squares (WRLMS) is better than other estimators in terms of its efficiency. This has been done by utilizing both Standard Error (SE) and the Root Mean Squared Error criterion for the numerical example and simulation study, respectively as far as a lot of combinations of error distribution and degree of multicollinearity are concerned.

scholarly journals KINERJA JACKKNIFE RIDGE REGRESSION DALAM MENGATASI MULTIKOLINEARITAS

2014 ◽  
Vol 3 (4) ◽  
pp. 146
Author(s):  
HANY DEVITA ◽  
I KOMANG GDE SUKARSA ◽  
I PUTU EKA N. KENCANA
Keyword(s):  
Linear Correlation ◽  
Ridge Regression ◽  
Minimum Variance ◽  
Sum Of Squares ◽  
Least Square ◽  
Bias Parameter ◽  
Ridge Estimator ◽  
Ordinary Least Square ◽  
Parameter Estimations

Ordinary least square is a parameter estimations for minimizing residual sum of squares. If the multicollinearity was found in the data, unbias estimator with minimum variance could not be reached. Multicollinearity is a linear correlation between independent variabels in model. Jackknife Ridge Regression(JRR) as an extension of Generalized Ridge Regression (GRR) for solving multicollinearity.  Generalized Ridge Regression is used to overcome the bias of estimators caused of presents multicollinearity by adding different bias parameter for each independent variabel in least square equation after transforming the data into an orthoghonal form. Beside that, JRR can  reduce the bias of the ridge estimator. The result showed that JRR model out performs GRR model.

scholarly journals Modified Robust Ridge M-Estimators in Two-Parameter Ridge Regression Model

2021 ◽  
Vol 2021 ◽  
pp. 1-24
Author(s):  
Seyab Yasin ◽  
Sultan Salem ◽  
Hamdi Ayed ◽  
Shahid Kamal ◽  
Muhammad Suhail ◽  
...  
Keyword(s):  
Ridge Regression ◽  
Mean Squared Error ◽  
Least Square ◽  
Ridge Estimator ◽  
Least Square Estimator ◽  
Squared Error ◽  
Joint Problem ◽  
Ridge Regression Estimator ◽  
Simulation Results ◽  
Two Parameter

The methods of two-parameter ridge and ordinary ridge regression are very sensitive to the presence of the joint problem of multicollinearity and outliers in the y-direction. To overcome this problem, modified robust ridge M-estimators are proposed. The new estimators are then compared with the existing ones by means of extensive Monte Carlo simulations. According to mean squared error (MSE) criterion, the new estimators outperform the least square estimator, ridge regression estimator, and two-parameter ridge estimator in many considered scenarios. Two numerical examples are also presented to illustrate the simulation results.

Impact of pricing mechanism on IPO oversubscription: evidence from Pakistan stock exchange

2020 ◽  
Vol 32 (2) ◽  
pp. 239-254 ◽  
Author(s):  
Waqas Mehmood ◽  
Rasidah Mohd-Rashid ◽  
Abd Halim Ahmad
Keyword(s):  
Initial Public Offerings ◽  
Robust Regression ◽  
Stock Exchange ◽  
Least Square ◽  
Cross Sectional ◽  
Content Type ◽  
Public Offerings ◽  
Ordinary Least Square ◽  
Pricing Mechanism ◽  
Available Information

Purpose The purpose of this paper is to examine the effects of pricing mechanism on initial public offerings (IPOs) oversubscription in Pakistan. Design/methodology/approach This study used cross-sectional data to analyse 85 listed IPOs on the Pakistan stock exchange during the period of 2000-2017 to assess hypotheses related to influential determinants of IPO oversubscription. Accordingly, ordinary least square, robust regression and quantile regression approaches were applied in this study to evaluate the factors that influenced oversubscription. Findings The outcome displayed pricing mechanism is negatively significant with an oversubscription of IPOs. This indicates firms using the fixed-price mechanism signalled higher information asymmetry and uncertainty in their value. Thus, investors are aware that they will be offset with underpricing, and it is expected the demand will be higher for the particular IPOs. Research limitations/implications This study is entirely focused on the available information of prospectus that should not be ignored by potential investors at the time of subscription of IPO. Therefore, the study contributes to extending the available literature in signalling theory whereby issuers should consider using the book-building pricing mechanism in enhancing the efficiency of the IPO offer price during the listing. Originality/value This paper provides evidence for the determinants of the IPO oversubscription.

scholarly journals SIMULASI PENANGANAN PENCILAN PADA ANALISIS REGRESI MENGGUNAKAN METODE LEAST MEDIAN SQUARE (LMS)

2018 ◽  
Vol 15 (2) ◽  
pp. 238-247
Author(s):  
Tusilowati Tusilowati ◽  
L Handayani ◽  
Rais Rais
Keyword(s):  
Regression Analysis ◽  
Robust Regression ◽  
Simple Calculation ◽  
Parameter Estimate ◽  
Least Square ◽  
Simulation Data ◽  
Ordinary Least Square ◽  
Research Findings ◽  
Lms Method ◽  
Better Than

The simulation of handling of outliers on regression analysis used the method which was commonly used to predict the parameter in regression analysis, namely Least Median Square (LMS) due to the simple calculation it had. The data with outliers would result in unbiased parameter estimate. Hence, it was necessary to draw up the robust regression to overcome the outliers. The data used were simulation data of the number of data pairs ( X,Y) by 25 and 100 respectively. The result of the simulation was divided into 5 subsets of data cluster of parameter regression prediction by Ordinary Least Square (OLS) and Least Median Square (LMS) methods. The prediction result of the parameter of each method on each subset of data cluster was tested with both method to discover the which better one. Based on the research findings, it was found that The Least Median Square (LMS) method was known better than Ordinary Least Square (OLS) method in predicting the regression parameter on the data which had up to 3% of the percentage of the outlier.

scholarly journals PERBANDINGAN REGRESI ROBUST PENDUGA MM DENGAN METODE RANDOM SAMPLE CONSENSUS DALAM MENANGANI PENCILAN

2014 ◽  
Vol 3 (2) ◽  
pp. 45
Author(s):  
NI PUTU NIA IRFAGUTAMI ◽  
I GUSTI AYU MADE SRINADI ◽  
I WAYAN SUMARJAYA
Keyword(s):  
Parameter Estimation ◽  
Random Sample ◽  
Robust Regression ◽  
Least Square ◽  
Robust Estimator ◽  
Ordinary Least Square ◽  
Random Sample Consensus

The presence of outliers in observation can result in biased in parameter estimation using ordinary least square (OLS). Robust regression MM-estimator is one of the estimations methods that able to obtain a robust estimator against outliers. Random sample consensus (ransac) is another method that can be used to construct a model for observations data and also estimating a robust estimator against outliers. Based on the study, ransac obtained model with less biased estimator than robust regression MM-estimator.

scholarly journals Related Party Transactions, Off Balance Sheet Items and Earnings Quality of Listed Deposit Money Banks in Nigeria

2020 ◽  
Author(s):  
Lawal I. Mohammed ◽  
Nafisa Abibakar
Keyword(s):  
Robust Regression ◽  
Earnings Quality ◽  
Balance Sheet ◽  
Least Square ◽  
Annual Reports ◽  
Related Party Transactions ◽  
Ordinary Least Square ◽  
Positive Effects ◽  
The Impact

This paper examines the impact of related party transactions, off balance sheet items on earnings quality of listed deposit money banks in Nigeria over the period of 4 years (2011 to 2014). Data were collected from annual reports of the sampled banks. Descriptive statistics and correlation analysis were employed and also Ordinary least square (OLS) robust regression technique was used as a tool of analysis using panel data. The study reveals that related party transactions are positively and significantly related to earnings quality. On the contrary, off balance sheet items were found to be negatively and insignificantly related to earnings quality. Based on the findings, the study concluded that related party transactions have significant impact on the earnings quality of the Nigeria deposit money bank. The study recommends that Management of the Nigeria money deposit banks should be more aggressive towards the number of genuine related party transactions that can add value to their firms when making financial decision because it is likely to have positive effects on the quality of their earnings.  

REGULARIZATION METHODS FOR ESTIMATING A MULTI-FACTOR CORPORATE BOND PRICING MODEL: AN APPLICATION FOR BRAZIL

2021 ◽  
pp. 2150005
Author(s):  
PAULO ROBERTO GUIMARÃES ◽  
OSVALDO CANDIDO ◽  
ANDRÉ RONZANI
Keyword(s):  
Mean Squared Error ◽  
Predictive Performance ◽  
Least Square ◽  
Corporate Bond ◽  
Ridge Estimator ◽  
Explanatory Variables ◽  
Ordinary Least Square ◽  
Optimal Value ◽  
Selection Operator ◽  
Public Offering

The present work focused on studying which factors affect Brazilian inflation-linked corporate bond prices in a primary market setting. The explanatory variables tested were rating, maturity, duration, issuer governance level, industrial classification, collateral, tax exemption, public offering modality, financial volume, coupon frequency, number of issues, number of days since going public, and the Brazilian basic interest rate target. In order to choose the set of variables with best predictive performance, best subsets ordinary least square (OLS) and least absolute shrinkage and selection operator (LASSO) were applied on a testing sample. For estimating purposes, we also tested the Ridge estimator. For both LASSO and Ridge, we used the k-fold approach to choose the optimal value for the lambda penalty. In terms of smallest mean squared error, the OLS estimator outperformed both the Ridge and the LASSO. This result suggests that the variance-bias trade-off might not be a concern for the Brazilian case.

scholarly journals Regression-in-Ratio Estimators for Population Mean by Using Robust Regression in Two Phase Sampling

2021 ◽  
Author(s):  
Aamir Raza ◽  
Muhammad Noor-ul-Amin
Keyword(s):  
Simulation Study ◽  
Robust Regression ◽  
Real Life ◽  
Least Square Method ◽  
Least Square ◽  
Two Phase ◽  
Extensive Simulation ◽  
Population Mean ◽  
Phase Sampling ◽  
Two Phase Sampling

The estimation of population mean is not meaningful using ordinary least square method when data contains some outliers. In the current study, we proposed efficient estimators of population mean using robust regression in two phase sampling. An extensive simulation study is conduct to examine the efficiency of proposed estimators in terms of mean square error (MSE). Real life example and extensive simulation study are cited to demonstrate the performance of the proposed estimators. Theoretical example and simulation studies showed that the suggested estimators are more efficient than the considered estimators in the presence of outliers.

scholarly journals New Versions of Liu-type Estimator in Weighted and non-weighted Mixed Regression Model

2020 ◽  
Vol 17 (1(Suppl.)) ◽  
pp. 0361
Author(s):  
Mustafa Ismaeel Naif Alheety
Keyword(s):  
Regression Model ◽  
Simulation Study ◽  
Goodness Of Fit ◽  
Prior Information ◽  
Mean Squared Error ◽  
Numerical Example ◽  
Squared Error ◽  
Mixed Regression ◽  
The Mean ◽  
Stochastic Restrictions

This paper considers and proposes new estimators that depend on the sample and on prior information in the case that they either are equally or are not equally important in the model. The prior information is described as linear stochastic restrictions. We study the properties and the performances of these estimators compared to other common estimators using the mean squared error as a criterion for the goodness of fit. A numerical example and a simulation study are proposed to explain the performance of the estimators.

scholarly journals PENERAPAN METODE GENERALIZED RIDGE REGRESSION DALAM MENGATASI MASALAH MULTIKOLINEARITAS

2013 ◽  
Vol 2 (1) ◽  
pp. 54
Author(s):  
NI KETUT TRI UTAMI ◽  
I KOMANG GDE SUKARSA
Keyword(s):  
Parameter Estimation ◽  
Regression Analysis ◽  
Ridge Regression ◽  
Estimation Method ◽  
Minimum Variance ◽  
Least Square ◽  
Ordinary Least Square ◽  
Parameter Estimation Method ◽  
Alternative Method ◽  
Highly Correlated

Ordinary least square is parameter estimation method for linier regression analysis by minimizing residual sum of square. In the presence of multicollinearity, estimators which are unbiased and have a minimum variance can not be generated. Multicollinearity refers to a situation where regressor variables are highly correlated. Generalized Ridge Regression is an alternative method to deal with multicollinearity problem. In Generalized Ridge Regression, different biasing parameters for each regressor variables were added to the least square equation after transform the data to the space of orthogonal regressors. The analysis showed that Generalized Ridge Regression was satisfactory to overcome multicollinearity.

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