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.

scholarly journals Robust Reliability Estimation for Lindley Distribution—A Probability Integral Transform Statistical Approach

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1634
Author(s):  
Muhammad Aslam Mohd Safari ◽  
Nurulkamal Masseran ◽  
Muhammad Hilmi Abdul Majid
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Maximum Likelihood Estimator ◽  
Integral Transform ◽  
Ordinary Least Squares ◽  
Likelihood Estimator ◽  
Reliability Data ◽  
Lindley Distribution ◽  
Probability Integral Transform ◽  
Probability Integral

In the modeling and analysis of reliability data via the Lindley distribution, the maximum likelihood estimator is the most commonly used for parameter estimation. However, the maximum likelihood estimator is highly sensitive to the presence of outliers. In this paper, based on the probability integral transform statistic, a robust and efficient estimator of the parameter of the Lindley distribution is proposed. We investigate the relative efficiency of the new estimator compared to that of the maximum likelihood estimator, as well as its robustness based on the breakdown point and influence function. It is found that this new estimator provides reasonable protection against outliers while also being simple to compute. Using a Monte Carlo simulation, we compare the performance of the new estimator and several well-known methods, including the maximum likelihood, ordinary least-squares and weighted least-squares methods in the absence and presence of outliers. The results reveal that the new estimator is highly competitive with the maximum likelihood estimator in the absence of outliers and outperforms the other methods in the presence of outliers. Finally, we conduct a statistical analysis of four reliability data sets, the results of which support the simulation results.

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.

scholarly journals Institutional ownership and firm value: A study on BIST manufacturing index

Ekonomika ◽  
2020 ◽  
Vol 66 (4) ◽  
pp. 29-46
Author(s):  
Mesut Doğan
Keyword(s):  
Least Squares ◽  
Firm Value ◽  
Institutional Ownership ◽  
Equation System ◽  
Ordinary Least Squares ◽  
Simultaneous Equation ◽  
Positive Relation ◽  
Two Stage ◽  
Hausman Test ◽  
Simultaneous Equation System

The aim of this research is to test the relation between institutional ownership and firm value. To accomplish this aim, data from 104 firms listed in the BIST (i.e. Borsa Istanbul) industrial index between 2006 and 2018 have been used. Studies on the structure of ownership have problems with endogeneity. In order to avoid these problems, this study adopted Durbin-Wu-Hausman test with advanced econometric techniques, Ordinary Least Squares (i.e. OLS), and Two-Stage Least Squares (i.e. 2SLS). As a result of the simultaneous equation system improved in this study, a positive relation between institutional ownership as an endogenous variable, and firm value has been located. Besides, it has been found that institutional investors are more interested in the firms that have a higher market performance.

scholarly journals Optimality of the maximum likelihood estimator in astrometry

2018 ◽  
Vol 616 ◽  
pp. A95 ◽  
Author(s):  
Sebastian Espinosa ◽  
Jorge F. Silva ◽  
Rene A. Mendez ◽  
Rodrigo Lobos ◽  
Marcos Orchard
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Maximum Likelihood Estimator ◽  
Weighted Least Squares ◽  
Least Square ◽  
Performance Limits ◽  
Likelihood Estimator ◽  
Weighted Least Square ◽  
Wide Range ◽  
Close Form

Context. Astrometry relies on the precise measurement of the positions and motions of celestial objects. Driven by the ever-increasing accuracy of astrometric measurements, it is important to critically assess the maximum precision that could be achieved with these observations. Aims. The problem of astrometry is revisited from the perspective of analyzing the attainability of well-known performance limits (the Cramér–Rao bound) for the estimation of the relative position of light-emitting (usually point-like) sources on a charge-coupled device (CCD)-like detector using commonly adopted estimators such as the weighted least squares and the maximum likelihood. Methods. Novel technical results are presented to determine the performance of an estimator that corresponds to the solution of an optimization problem in the context of astrometry. Using these results we are able to place stringent bounds on the bias and the variance of the estimators in close form as a function of the data. We confirm these results through comparisons to numerical simulations under a broad range of realistic observing conditions. Results. The maximum likelihood and the weighted least square estimators are analyzed. We confirm the sub-optimality of the weighted least squares scheme from medium to high signal-to-noise found in an earlier study for the (unweighted) least squares method. We find that the maximum likelihood estimator achieves optimal performance limits across a wide range of relevant observational conditions. Furthermore, from our results, we provide concrete insights for adopting an adaptive weighted least square estimator that can be regarded as a computationally efficient alternative to the optimal maximum likelihood solution. Conclusions. We provide, for the first time, close-form analytical expressions that bound the bias and the variance of the weighted least square and maximum likelihood implicit estimators for astrometry using a Poisson-driven detector. These expressions can be used to formally assess the precision attainable by these estimators in comparison with the minimum variance bound.

Sign in / Sign up

Export Citation Format

Share Document