The Exact Finite-Sample Distribution of the Limited-Information Maximum Likelihood Estimator in the Case of Two Included Endogenous Variables

1972 ◽  
Vol 67 (337) ◽  
pp. 159-163 ◽  
Author(s):  
Roberto S. Mariano ◽  
Takamitsu Sawa
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Limited Information ◽  
Finite Sample ◽  
Likelihood Estimator ◽  
Sample Distribution ◽  
Endogenous Variables ◽  
Finite Sample Distribution

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.

Using ranked set sampling with extreme ranks in estimating the population proportion

2019 ◽  
Vol 29 (1) ◽  
pp. 165-177 ◽  
Author(s):  
Ehsan Zamanzade ◽  
M Mahdizadeh
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Finite Sample ◽  
Likelihood Estimator ◽  
Population Proportion ◽  
Health And Nutrition ◽  
Finite Sample Size ◽  
Using Data

This article studies the properties of the maximum likelihood estimator of the population proportion in ranked set sampling with extreme ranks. The maximum likelihood estimator is described and its asymptotic distribution is derived. Finite sample size properties of the estimator are investigated using simulation studies. It turns out that the proposed estimator is substantially more efficient than its simple random sampling and ranked set sampling analogs, as the true population proportion tends to zero/unity. The method is illustrated using data from the National Health and Nutrition Examination Survey.

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