Effect of Nonnormality on the Estimation of a Single Structural Equation with Structural Change

1989 ◽  
Vol 5 (1) ◽  
pp. 53-62 ◽  
Author(s):  
Jiro Hodoshima
Keyword(s):  
Structural Change ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Structural Equation ◽  
Minimum Distance ◽  
Asymptotic Covariance Matrix ◽  
Limited Information ◽  
Likelihood Estimator ◽  
Minimum Distance Estimator ◽  
Distance Estimator

Effect of nonnormality on the asymptotic property of three estimators of a single structural equation with structural change is examined. The three estimators are the limited information maximum likelihood estimator, derived under normality and equality of structural variances in different samples, given by Hodoshima, a two-stage least squares type estimator due to Barten and Bronsard, and a minimum distance estimator presented here. Normality is relaxed but the equality assumption of structural variances is retained. Under nonnormality the limited information maximum likelihood estimator is consistent but may not be efficient relative to the Barten and Bronsard's estimator. A sufficient condition is given under which the limited information maximum likelihood estimator dominates the Barten and Bronsard's estimator in terms of the asymptotic covariance matrix. The minimum distance estimator dominates other estimators.

scholarly journals Asymptotic Distribution of Cramer-von Mises Statistic When Contamination Exists

2015 ◽  
Vol 5 (1) ◽  
pp. 90
Author(s):  
Mayumi Naka ◽  
Ritei Shibata
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Distribution ◽  
Minimum Distance ◽  
Goodness Of Fit ◽  
Likelihood Estimator ◽  
Goodness Of Fit Test ◽  
Minimum Distance Estimator ◽  
Von Mises Statistic ◽  
Von Mises ◽  
Distance Estimator

In this paper, asymptotic distribution of Cram\'er-von Mises goodness-of-fit test statistic is investigated when contamination exists.<br />We first derive the asymptotic distribution of the Cram\'er-von Mises statistic when the observations are contaminated with noise as a mixture.<br />The result is extended to the case where the parameters are estimated by the minimum distance estimator,<br />which minimizes the Cram\'er-von Mises statistic.<br />In both cases the asymptotic distribution of the Cram\'er-von Mises statistic is given by that of the weighted infinite sum of non-central $\chi^2_1$ variables and the effect of contamination appears only in the non-centrality of the variables.<br />We also demonstrate the robustness of the goodness-of-fit test by Monte Carlo simulations when the parameters are estimated<br />by the minimum distance estimator and the maximum likelihood estimator.<br />Numerical experiments indicate that the use of the minimum distance estimator makes the test insensitive to contamination whereas the power is retained almost the same as that of the maximum likelihood estimator.

Estimation of a Single Structural Equation with Structural Change

1988 ◽  
Vol 4 (1) ◽  
pp. 86-96 ◽  
Author(s):  
Jiro Hodoshima
Keyword(s):  
Structural Change ◽  
Maximum Likelihood ◽  
Structural Equation ◽  
Asymptotic Efficiency ◽  
Covariance Matrices ◽  
Reduced Form ◽  
Limited Information ◽  
Likelihood Estimator ◽  
Asymptotically Normal ◽  
Alternative Estimator

Estimation of a single structural equation when there exists structural change is considered. Equality of structural variances in different samples is shown to affect the identification condition and asymptotic efficiency of best asymptotically normal estimators when the reduced-form covariance matrices differ by the structural change. The limited information maximum likelihood estimator is presented with its asymptotic property and compared with an alternative estimator.

Comparing Single-Equation Estimators in a Simultaneous Equation System

1986 ◽  
Vol 2 (1) ◽  
pp. 1-32 ◽  
Author(s):  
T. W. Anderson ◽  
Naoto Kunitomo ◽  
Kimio Morimune
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Maximum Likelihood Estimator ◽  
Equation System ◽  
Single Equation ◽  
Ordinary Least Squares ◽  
Limited Information ◽  
Likelihood Estimator ◽  
Mean Squared Errors ◽  
Simultaneous Equation System

Comparisons of estimators are made on the basis of their mean squared errors and their concentrations of probability computed by means of asymptotic expansions of their distributions when the disturbance variance tends to zero and alternatively when the sample size increases indefinitely. The estimators include k-class estimators (limited information maximum likelihood, two-stage least squares, and ordinary least squares) and linear combinations of them as well as modifications of the limited information maximum likelihood estimator and several Bayes' estimators. Many inequalities between the asymptotic mean squared errors and concentrations of probability are given. Among medianunbiasedestimators, the limited information maximum likelihood estimator dominates the median-unbiased fixed k-class estimator.

OPTIMAL INVARIANT INFERENCE WHEN THE NUMBER OF INSTRUMENTS IS LARGE

2009 ◽  
Vol 25 (3) ◽  
pp. 793-805 ◽  
Author(s):  
Laura Chioda ◽  
Michael Jansson
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Likelihood ◽  
Sample Size ◽  
Maximum Likelihood Estimator ◽  
Instrumental Variables ◽  
Asymptotic Efficiency ◽  
Rotation Invariance ◽  
Limited Information ◽  
Likelihood Estimator ◽  
Rotation Invariant

This paper studies the asymptotic behavior of a Gaussian linear instrumental variables model in which the number of instruments diverges with the sample size. Asymptotic efficiency bounds are obtained for rotation invariant inference procedures and are shown to be attainable by procedures based on the limited information maximum likelihood estimator. The bounds are obtained by characterizing the limiting experiment associated with the model induced by the rotation invariance restriction.

A simple derivation of the limited information maximum likelihood estimator

1982 ◽  
Vol 10 (3-4) ◽  
pp. 277-283 ◽  
Author(s):  
L.G. Godfrey ◽  
M.R. Wickens
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Limited Information ◽  
Likelihood Estimator ◽  
Simple Derivation

A Derivation of the Limited Information Maximum Likelihood Estimator

1992 ◽  
Vol 8 (2) ◽  
pp. 301-302 ◽  
Author(s):  
Kimio Morimune
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Limited Information ◽  
Likelihood Estimator

The Covariance Matrix of the Limited Information Maximum Likelihood Estimator

Econometrica ◽  
1972 ◽  
Vol 40 (5) ◽  
pp. 899 ◽  
Author(s):  
A. R. Bergstrom
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Covariance Matrix ◽  
Limited Information ◽  
Likelihood Estimator
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