Comparison of Parametric and Non-Parametric Estimation Methods in Linear Regression Model

The aim of this study was to compare some estimation methods (LS, M, S, LTS and MM) for estimating the parameters of simple linear regression model in the presence of outlier and different sample size (10, 20, 30, 50 and 100). To compare methods, the effect of chest girth on body weights of Karayaka lambs at weaning period was examined. Chest girth of lambs was used as independent variable and body weight at weaning period was used as dependent variable in the study. Also, it was taken consideration that there were 10-20% outliers of data set for different sample sizes. Mean square error (MSE) and coefficient of determination (R2) values were used as criteria to evaluate the estimator performance. Research findings showed that LTS estimator is the best models with minimum MSE and maximum R2 values for different size of sample in the presence of outliers. Thereby, LTS method can be proposed, to predict best-fitted model for relationship between chest girth and body weights of Karayaka lambs at weaning period, to the researches who are studying on small ruminants as an alternative way to estimate the regression parameters in the presence of outliers for different sample size.

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Comparison of Some Methods for Estimating Parameters of General Linear Model in Presence of Heteroscedastic Problem and High Leverage Points

Journal of Economics and Administrative Sciences ◽

10.33095/jeas.v27i127.2145 ◽

2021 ◽

Vol 27 (127) ◽

pp. 213-228

Author(s):

Qasim Mohammed Saheb ◽

Saja Mohammad Hussein

Keyword(s):

Linear Regression ◽

Regression Model ◽

Linear Regression Model ◽

Standard Error ◽

Weighted Least Squares ◽

Estimation Methods ◽

General Linear ◽

Data Set ◽

Leverage Points ◽

Generalized Potential

Linear regression is one of the most important statistical tools through which it is possible to know the relationship between the response variable and one variable (or more) of the independent variable(s), which is often used in various fields of science. Heteroscedastic is one of the linear regression problems, the effect of which leads to inaccurate conclusions. The problem of heteroscedastic may be accompanied by the presence of extreme outliers in the independent variables (High leverage points) (HLPs), the presence of (HLPs) in the data set result unrealistic estimates and misleading inferences. In this paper, we review some of the robust weighted estimation methods that accommodate both Robust and classical methods in the detection of extreme outliers (High leverage points) (HLPs) and the determination of weights. The methods include both Diagnostic Robust Generalized Potential Based on Minimum Volume Ellipsoid (DRGP (MVE)), Diagnostic Robust Generalized Potential Based on Minimum Covariance Determinant (DRGP (MCD)), and Diagnostic Robust Generalized Potential Based on Index Set Equality (DRGP (ISE)). The comparison was made according to the standard error criterion of the estimated parameters SE ( ) and SE ( ) of general linear regression model, for sample sizes (n=60, n=100, n=160), with different degree (severity) of heterogeneity, and contamination percentage (HLPs) are (τ =10%, τ=30%). it was found through comparison that weighted least squares estimation based on the weights of the DRGP (ISE) method are considered the best in estimating the parameters of the multiple linear regression model because they have the lowest standard error values of the estimators ( ) and ( ) as compared to other methods. Paper type: A case study

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Parametric estimation for the simple linear regression model under moving extremes ranked set sampling design

Applied Mathematics-A Journal of Chinese Universities ◽

10.1007/s11766-021-3993-1 ◽

2021 ◽

Vol 36 (2) ◽

pp. 269-277

Author(s):

Dong-sen Yao ◽

Wang-xue Chen ◽

Chun-xian Long

Keyword(s):

Linear Regression ◽

Regression Model ◽

Linear Regression Model ◽

Sampling Design ◽

Ranked Set Sampling ◽

Parametric Estimation ◽

Simple Linear Regression ◽

Simple Linear Regression Model

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Non-parametric estimation of the directional distribution of stationary line and fibre processes

Advances in Applied Probability ◽

10.1017/s0001867800010600 ◽

2001 ◽

Vol 33 (1) ◽

pp. 6-24 ◽

Cited By ~ 5

Author(s):

Markus Kiderlen

Keyword(s):

Input Data ◽

Dimensional Space ◽

Parametric Estimation ◽

Estimation Methods ◽

Parametric Methods ◽

Likelihood Estimator ◽

Directional Distribution ◽

Line Processes ◽

Non Parametric Estimation ◽

Non Parametric

Two non-parametric methods for the estimation of the directional measure of stationary line and fibre processes in d-dimensional space are presented. The input data for both methods are intersection counts with finitely many test windows situated in hyperplanes. The first estimator is a measure valued maximum likelihood estimator, if applied to Poisson line processes. The second estimator uses an approximation of the associated zonoid (the Steiner compact) by zonotopes. Consistency of both estimators is proved (without use of the Poisson assumption). The estimation methods are compared empirically by simulation.

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Non-parametric Error Modeling for Ultra-wideband Localization Networks

10.31219/osf.io/hxver ◽

2019 ◽

Author(s):

Acshi Haggenmiller ◽

Maximilian Krogius ◽

Edwin Olson

Keyword(s):

Error Modeling ◽

Parametric Estimation ◽

Ultra Wideband ◽

Estimation Methods ◽

Line Of Sight ◽

Probability Densities ◽

Non Parametric Estimation ◽

Non Line Of Sight ◽

Non Parametric

ICRA 2019 Paper Submission Code and DatasetsWe propose an ultra-wideband-based (UWB) localization system that achieves high accuracy through non-parametric estimation of measurement probability densities and explicit modeling of antenna delays. This problem is difficult because non-line-of-sight conditions give rise to multimodal errors, which make linear estimation methods ineffective. The primary contribution in this paper is an approach for both characterizing these errors in situ and an optimization framework that recovers both positions and antenna delays. We evaluate our system with a network of 8 nodes based on the DecaWave DWM1000 and achieve accuracies from 3 cm RMSE in line-of-sight conditions to 30 cm RMSE in non-line-of-sight conditions. Collecting measurements and localizing the network in this manner requires less than a minute, after which the realized network may be used for dynamic real-time tracking.

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On OLS Estimation of Stochastic Linear Regression Model

International Journal of Engineering and Advanced Technology - Regular Issue ◽

10.35940/ijeat.f7930.088619 ◽

2019 ◽

Vol 8 (6) ◽

pp. 1953-1955

Keyword(s):

Linear Regression ◽

Statistical Model ◽

Regression Model ◽

Linear Regression Model ◽

Diagnostic Methods ◽

Estimation Methods ◽

Estimation Technique ◽

Linear Statistical Model ◽

Coefficient Vector ◽

Linear Restrictions

This paper mainly discusses the formulation of stochastic linear statistical model and its assumptions and finally explores an important aspect namely the Ordinary Least Squares (OLS) estimation of stochastic linear regression model. In addition to these inference in stochastic linear regression model is also presented here. Nimitozbay et.al [1], in their paper proposed the weighted mixed regression estimation of the coefficient vector in a linear regression model with stochastic linear restrictions binding the regression coefficients. In 1980, P.A.V.B. Swamy et.al proposed a linear regression model where the coefficient vector is a weekly stationary multivariate stochastic process and that model provides a convenient representation of a general class of non-stationary processes. They proposed prediction and estimation methods which are linear and easy to compute. Daojiang et.al [2] in 2014, in their paper depicted an innovative estimation technique to the multicollinearity in statistical model which is linear in the case of existence of stochastic linear constraints on the parameters and a very different estimation technique was presented by mixing the OME and PCR estimator also known as SRPC regression estimator. In 2014, Shuling Wang et.al [3] in their paper proposed some diagnostic methods in restricted stochastic statistical models which are linear. Gil Gonjalez et.al [4], in 2007, in their paper, derived the LSEs for the simple linear statistical model and examined them from a theoretical perspective.

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