﻿

Efficiency of heterosceastic linear model

Abstract

In order to investigate the asymptotic  efficiency of estimators under two different simulation techniques, normal-normal double sided Heteroscedastic error structure was adopted.  We explored Direct Monte Carlo method of A. Zellner (2010) and Metropolis Hasting Algorithm experiments, an approach of Markov Chain Monte Carlo.

We truncated the model with one error component of two sided error structure. A Metropolis-Hasting Algorithm and Direct Monte Carlo adopted to perform simulation on joint posterior distribution of heteroscedastic linear econometric model. Since Ordinary Least squares is invalid and inefficient in the presence of heteroscedastic, heteroscedastic linear model was conjugated with informative priors to form posterior distribution. Maximum Likelihood Estimation was compared with Bayesian Maximum Likelihood Estimation, Mean Squares Error criterion was use to identify  which estimator and/or simulation method outperform other.  We chose the following sample sizes: 25; 50; 100; and 200. Thus 10,000 simulations with varying degree of heteroscedastic error structures were adopted. This is subjected to the level of convergence.

The overall using minimum mean squares error criterion revealed improving performance asymptotically regardless of the degree of heteroscedasticity. The results showed that Direct Monte Carlo Method outperformed Markov Chain Monte Carlo Method and Maximum Likelihood Estimator with minimum mean square error at any degree of heteroscedasticity.

DOI Code: 10.1285/i20705948v7n2p362

Keywords: Markov Chain Monte Carlo Method, Heteroscedasticity, Bayesian Maximum Likelihood Estimator, Metropolis-Hasting Algorithm, Direct Monte Carlo Method.

References

Andrew A etal (2008): Bayesian Estimation of Linear Statistical Model Bias. American mathematical society

Arto Luoma and Jani Luoto(2008):Bayesian Two Stage Regression with Parametric Heteroscedasticity.http://www.bus.lsu.edu/hill/aie/luoma.pdf

Carlos Alberto Rideiro Dimz et'al (2012): The Multiplicative Heteroscedasticity Von Bertalanffy Model Volume 26, Number 1(2012),71-81 http://projecteuclid.org/euclid.bjps/1321043152

Gelman, A. and Rubin, D.B. (1992), "Inference from Iterative Simulation Using Multiple Sequences (with discussion)." Statistical Science, 7,457-511.

Germa Coenders and Marc Saez (2000): Collinearity, Heteroscedasticity and outlier Diagnostic in Regression. Do They Always Offer What They Claim? New approaches in Applied Statistics, Metodoloski zvezki, 16, Ljubljana:FDV.

Goldfeld S. M and Quandt R.E (1972): Nonlinear Methods in Econometrics , Amsterdam, North Holland.

Hadri K and C Guermat (1999): Heteroscedasticity in Stochastic Frontier Models : A Monte Carlo Analysis pp1:8

Harvey A.C (1976): Estimating Regression models with Multiplicative heteroscedasticity . Econometrica vol. 44 , no 33.

John Geweke (1989): Bayesian Inference in Econometric Models Using Monte Carlo Integration, Econometrica, Vol. 57, No. 6 (Nov., 1989), pp. 1317-1339, The Econometric Society . http://www.jstor.org/stable/1913710

John Geweke (2005): Contemporary Bayesian Econometrics and Statistics, John Wiley & Sons, Inc., Hoboken, New Jersey

Mackinnon J.G and White H (1985): Some Heteroscedasticity–Consistent Covariance Matrix Estimators with Improved Finite Sample Properties, Journal of Econometrics.

Metropolis N. et al (1953):Equation of State Calculation by First Computing Machine, Journal of Chemical Physics vol.11, no 4

Nicholas Metropolis; S. Ulam (1949): The Monte Carlo Method Journal of the American Statistical Association, Vol. 44, No. 247. (Sep., 1949), pp. 335-341.

Oloyede I. (2010): A bootstrap investigation of the power of two test of heteroscedasticity in an intrinsically nonlinear econometric model, unpublished Master thesis, Olabisi Onabanjo University Ago-Iwoye, Ogun State, Nigeria.

Robinson P.M (1987): Asymptotic Efficient Estimation in the Presence of Heteroscedasticity of Unknown Form, Econometrica Vol. 55 no 4 pp 875-891

Senyo B S K Adjibolosoo (1993): Estimation of Parameters of Heteroscedastic Error Models under various Hypothesized Error Structures. The Statistician 42, pp123-133.

Surekha K and Griffiths W.E (1984): A Monte Carlo Comparison of Some Bayesian and Sampling Theory Estimators in Two Heteroscedastic Error Models, Communications in Statistics, Series B, 13 pp 85-105

Whites H(1980): A Heteroscedasticity Consistent Covariance Matrix and Direct Test for Heteroscedasticity, Econometrica 48, pp817-838

Zellner, A. and Chen, B, (2002), “Bayesian Modeling of Economies and Data Requirements,’’ Macroeconomic Dynamics, 5, 673–700.

Zellner A. and Tomohiro Ando (2010): areweb.berkeley.edu/documents/seminar/zellner.doc

Full Text: pdf
کاغذ a4