scholarly journals A robust adaptive modified maximum likelihood estimator for the linear regression model

2020 ◽  
pp. 1-21
Author(s):  
Sukru Acitas ◽  
Peter Filzmoser ◽  
Birdal Senoglu
Keyword(s):  
Maximum Likelihood ◽  
Linear Regression ◽  
Regression Model ◽  
Maximum Likelihood Estimator ◽  
Linear Regression Model ◽  
Likelihood Estimator ◽  
Modified Maximum Likelihood ◽  
Robust Adaptive ◽  
Modified Maximum Likelihood Estimator

scholarly journals Inference in Multiple Linear Regression Model with Generalized Secant Hyperbolic Distribution Errors

2021 ◽  
Vol 17 (33) ◽  
pp. 45-70
Author(s):  
Álvaro Alexander Burbano Moreno ◽  
Oscar Orlando Melo-Martinez ◽  
M Qamarul Islam
Keyword(s):  
Maximum Likelihood ◽  
Linear Regression ◽  
Regression Model ◽  
Multiple Linear Regression ◽  
Linear Regression Model ◽  
Multiple Linear Regression Model ◽  
Least Square ◽  
Model Parameters ◽  
Modified Maximum Likelihood ◽  
Test Of Hypothesis

We study multiple linear regression model under non-normally distributed random error by considering the family of generalized secant hyperbolic distributions. We derive the estimators of model parameters by using modified maximum likelihood methodology and explore the properties of the modified maximum likelihood estimators so obtained. We show that the proposed estimators are more efficient and robust than the commonly used least square estimators. We also develop the relevant test of hypothesis procedures and compared the performance of such tests vis-a-vis the classical tests that are based upon the least square approach.

scholarly journals Inference in Multiple Linear Regression Model with Generalized Secant Hyperbolic Distribution Errors

2021 ◽  
Vol 17 (33) ◽  
pp. 45-70
Author(s):  
Álvaro Alexander Burbano Moreno ◽  
Oscar Orlando Melo-Martinez ◽  
Q Qamarul Islam
Keyword(s):  
Maximum Likelihood ◽  
Linear Regression ◽  
Regression Model ◽  
Multiple Linear Regression ◽  
Linear Regression Model ◽  
Multiple Linear Regression Model ◽  
Least Square ◽  
Model Parameters ◽  
Modified Maximum Likelihood ◽  
Test Of Hypothesis

We study multiple linear regression model under non-normally distributed random error by considering the family of generalized secant hyperbolic distributions. We derive the estimators of model parameters by using modified maximum likelihood methodology and explore the properties of the modified maximum likelihood estimators so obtained. We show that the proposed estimators are more efficient and robust than the commonly used least square estimators. We also develop the relevant test of hypothesis procedures and compared the performance of such tests vis-a-vis the classical tests that are based upon the least square approach.

scholarly journals Edgeworth Expansion for the Whittle Maximum Likelihood Estimator of Linear Regression Processes with Long Memory Residuals

2021 ◽  
Vol 10 (4) ◽  
pp. 119
Author(s):  
Mosisa Aga
Keyword(s):  
Maximum Likelihood ◽  
Linear Regression ◽  
Regression Model ◽  
Maximum Likelihood Estimator ◽  
Long Memory ◽  
Edgeworth Expansion ◽  
Spectral Density Function ◽  
Likelihood Estimator ◽  
Extra Condition ◽  
Parameter Values

We establish an Edgeworth expansion for the distribution of the Whittle maximum likelihood estimator of the parameter of a time series generated by a linear regression model with Gaussian, stationary, and long-memory residuals. This is done by imposing an extra condition on coefficients of the regression model in addition to the standard conditions imposed on the the spectral density function and the parameter values and making use of the results of Andrews et al. (2005), who provided an Edgeworth expansion for the residual component.

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