Robinsar Pakpahan, Elmanani Simamora

Mengatasi Bias pada Penduga Parameter Metode Kuadrat Terkecil dalam Analisis Regresi Linear Sederhana dengan Bootstrap Data Berpasangan

Introduction

Mengatasi bias pada penduga parameter metode kuadrat terkecil dalam analisis regresi linear sederhana dengan bootstrap data berpasangan. Atasi bias penduga parameter MKT pada regresi linear sederhana akibat outlier. Studi ini menerapkan bootstrap data berpasangan untuk estimasi parameter yang lebih akurat.

Abstract

The assumption of normality cannot be fulfilled in regression analysis if there are outliers in observation data so that peduga parameters using LSM (Least Square Method) will produce biased estimators and not BLUE (Best Linear Unbiased Estimator). Based on this, the bootstrap method which is a repeat sampling method (resampling) that does not require distribution assumptions on the data can be used. In this study, paired bootstrap data method is used for simulation data with the number of outliers of 5%, 10% and 15%. This is to show how the influence of outliers on the distribution of data if the outliers given have different amounts. After estimating the parameters using paired bootstrap data, parameter estimator values and the resulting bias are not much different from the MKT parameter estimator values before being given an outlier. In this study at a 99% confidence interval for the case of simulation data with 10% and 15% of the parameter estimator outliers obtained in the previous study and in this study no longer produce BLUE estimators as in the simulation data with 5% outliers. [OVERCOMING BIAS IN PARAMETER ESTIMATORS OF THE LEAST SQUARE METHOD IN A SIMPLE LINEAR REGRESSION ANALYSIS WITH PAIRED DATA BOOTSTRAP] (J. Sains Indon., 42(2): 31-37, 2018)Keywords:Least Square Method, Best Linear Unbiased Estimator, Paired Bootstrap

Review

This study tackles a critical issue in regression analysis: the susceptibility of Least Squares Method (LSM) estimators to bias and the loss of the Best Linear Unbiased Estimator (BLUE) property when data contains outliers. The authors propose the paired bootstrap method as a robust alternative, leveraging its non-parametric nature to circumvent the violated normality assumption caused by outliers. This work is highly relevant as addressing data contamination is fundamental for reliable statistical inference, particularly in simple linear regression where the impact of outliers can be substantial. The paper sets out to demonstrate the effectiveness of paired bootstrap in overcoming these limitations, thereby contributing to the field of robust estimation. The methodology involves applying the paired bootstrap data method to simulated data, meticulously varying the percentage of outliers at 5%, 10%, and 15% to assess the method's robustness under different levels of contamination. A key finding, albeit somewhat ambiguously stated in the abstract, suggests that the bootstrap-derived parameter estimates and their biases are comparable to or improved relative to the ideal scenario where no outliers exist and LSM estimators would be unbiased. More definitively, the study reveals that while the paired bootstrap method appears capable of maintaining BLUE estimators at a 99% confidence interval for a modest 5% outlier presence, its efficacy diminishes significantly with higher outlier percentages (10% and 15%). In these more challenging scenarios, the estimators obtained through the method no longer retain the coveted BLUE property, indicating a clear limitation of the approach as outlier levels increase. Overall, this paper provides valuable insights into the performance of the paired bootstrap method for mitigating bias and restoring estimator properties in the presence of outliers in simple linear regression. A strength lies in its use of simulation to systematically evaluate the method across varying outlier intensities. However, the initial statement in the abstract regarding the comparison of bias could benefit from greater clarity to avoid potential misinterpretation. Future work could extend this investigation by comparing paired bootstrap with other robust regression techniques and validating its performance on diverse real-world datasets. Despite this minor clarity point, the study successfully highlights both the potential and the limitations of paired bootstrap in maintaining the BLUE property, making a worthwhile contribution to the literature on robust statistical methods.

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