Determination of Estimators with Minimum Asymptotic Covariance Matrices

1993 ◽  
Vol 9 (4) ◽  
pp. 633-648 ◽  
Author(s):  
Charles E. Bates ◽  
Halbert White
Keyword(s):  
Least Squares ◽  
Rate Of Convergence ◽  
Asymptotic Variance ◽  
Generalized Least Squares ◽  
Covariance Matrices ◽  
Variance Estimator ◽  
Objective Functions ◽  
Generalized Least Squares Estimator ◽  
Asymptotic Covariance

We give a straightforward condition sufficient for determining the minimum asymptotic variance estimator in certain classes of estimators relevant to econometrics. These classes are relatively broad, as they include extremum estimation with smooth or nonsmooth objective functions; also, the rate of convergence to the asymptotic distribution is not required to be n−½. We present examples illustrating the content of our result. In particular, we apply our result to a class of weighted Huber estimators, and obtain, among other things, analogs of the generalized least-squares estimator for least Lp-estimation, 1 ≤ p < ∞.

ASYMPTOTIC EFFICIENCY OF THE ORDINARY LEAST SQUARES ESTIMATOR FOR REGRESSIONS WITH UNSTABLE REGRESSORS

2002 ◽  
Vol 18 (5) ◽  
pp. 1121-1138 ◽  
Author(s):  
DONG WAN SHIN ◽  
MAN SUK OH
Keyword(s):  
Least Squares ◽  
Asymptotic Efficiency ◽  
Characteristic Root ◽  
Sufficient Conditions ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Least Squares Estimator ◽  
Characteristic Roots ◽  
Generalized Least Squares Estimator ◽  
Ordinary Least Squares Estimator

For regression models with general unstable regressors having characteristic roots on the unit circle and general stationary errors independent of the regressors, sufficient conditions are investigated under which the ordinary least squares estimator (OLSE) is asymptotically efficient in that it has the same limiting distribution as the generalized least squares estimator (GLSE) under the same normalization. A key condition for the asymptotic efficiency of the OLSE is that one multiplicity of a characteristic root of the regressor process is strictly greater than the multiplicities of the other roots. Under this condition, the covariance matrix Γ of the errors and the regressor matrix X are shown to satisfy a relationship (ΓX = XC + V for some matrix C) for V asymptotically dominated by X, which is analogous to the condition (ΓX = XC for some matrix C) for numerical equivalence of the OLSE and the GLSE.

Confidence Sets for the Coefficients Vector of a Linear Regression Model with Nonspherical Disturbances

1997 ◽  
Vol 13 (3) ◽  
pp. 406-429 ◽  
Author(s):  
Anoop Chaturvedi ◽  
Hikaru Hasegawa ◽  
Ajit Chaturvedi ◽  
Govind Shukla
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Least Squares ◽  
Linear Regression Model ◽  
Generalized Least Squares ◽  
Least Squares Estimator ◽  
Regression Coefficients ◽  
Confidence Sets ◽  
Generalized Least Squares Estimator ◽  
Coverage Probabilities

In this present paper, considering a linear regression model with nonspherical disturbances, improved confidence sets for the regression coefficients vector are developed using the Stein rule estimators. We derive the large-sample approximations for the coverage probabilities and the expected volumes of the confidence sets based on the feasible generalized least-squares estimator and the Stein rule estimator and discuss their ranking.

Regression Analysis and Determination of Activity Coefficients of Cd-Pb Alloy

2011 ◽  
Vol 311-313 ◽  
pp. 736-741
Author(s):  
Shun Zhong Yao ◽  
Yong Nian Dai ◽  
Hao Huang ◽  
Xiao Hong Wan
Keyword(s):  
Regression Analysis ◽  
Least Squares ◽  
Activity Coefficients ◽  
Reference Data ◽  
Generalized Least Squares ◽  
Chemical Compositions ◽  
Cadmium And Lead ◽  
Determination Of Activity

Chemical compositions of Cadmium and lead were measured with conditions that the temperature between 400-700°C and remaining pressure of 10-60 Pa as in which Materials containing Cadmium and lead evaporate. Activity coefficients of cadmium and lead were calculated using the generalized least squares（GLS）, three relations were deduced in Cd-Pb system，namely relation between activity coefficients and temperatures, relation between activity coefficients and chemical compositions, and that of activity coefficients and temperatures together with chemical compositions. This article provides a theoretical reference data for separation of alloys in cadmium systems.

scholarly journals A STUDY OF INDONESIA’S STOCK MARKET

2019 ◽  
pp. 465-476 ◽  
Author(s):  
Dinh Hoang Bach Phan ◽  
Thi Thao Nguyen Nguyen
Keyword(s):  
Exchange Rate ◽  
Interest Rate ◽  
Stock Market ◽  
Least Squares ◽  
Generalized Least Squares ◽  
Stock Index ◽  
Monthly Data ◽  
Generalized Least Squares Estimator ◽  
The Interest Rate ◽  
Stock Index Returns

Using monthly data from January 1995 to December 2017, this paper tests whetherIndonesian stock index returns are predictable. In particular, we use eight macrovariables to predict the Indonesian composite and six sectoral index returns using thefeasible generalized least squares estimator. Our results suggest that the Indonesianstock index returns are predictable. However, the predictability depends not only onthe macro predictor used but also on the indexes examined. Second, we find that themost popular predictor is the exchange rate, followed by the interest rate. Finally, ourmain findings hold for a number of robustness tests.

scholarly journals Effect of exchange rate on trade of Afghanistan with its trade partners

2020 ◽  
pp. 9-23
Keyword(s):  
Exchange Rate ◽  
Least Squares ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Trade Partner ◽  
Independent Variable ◽  
The Exchange Rate ◽  
Trade Partners ◽  
India And China

The exchange rate is one of the most significant variables in the determination of export or import amount, and its shifts cause decrease and increase in the amount of foreign trade, so it is a prominent economic variable for trade policymaking in developing countries. This topic seeks to investigate the effect of exchange rate on Afghanistan’s do business with its partners that includes: Iran, Pakistan, India, and China. Data collected monthly from 2015 through 2017; and also time serious data used for analyses that there are one dependent variable and one independent variable. The ordinary least-squares (OLS) and generalized least squares (GLS) methods estimate 16 models. Results show that the exchange rate of trade partner of Afghanistan has insignificant effects on Afghanistan trade or Afghanistan exchange rate show unimportant effects on Afghanistan trade partners. In some models which coefficients are significant, the R2 is so small, and it shows a low level of explaining. 4 models are useful among the 16 models. Finally, we can say that the exchange rate of Afghanistan and its trade partners don’t affect the trade amount.

scholarly journals Panel Data Estimation for Correlated Random Coefficients Models

Econometrics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 7
Author(s):  
Cheng Hsiao ◽  
Qi Li ◽  
Zhongwen Liang ◽  
Wei Xie
Keyword(s):  
Panel Data ◽  
Least Squares ◽  
Asymptotic Properties ◽  
Generalized Least Squares ◽  
Random Coefficients ◽  
Least Squares Estimator ◽  
Finite Sample ◽  
Correlation Pattern ◽  
Panel Data Estimation ◽  
Generalized Least Squares Estimator

This paper considers methods of estimating a static correlated random coefficient model with panel data. We mainly focus on comparing two approaches of estimating unconditional mean of the coefficients for the correlated random coefficients models, the group mean estimator and the generalized least squares estimator. For the group mean estimator, we show that it achieves Chamberlain (1992) semi-parametric efficiency bound asymptotically. For the generalized least squares estimator, we show that when T is large, a generalized least squares estimator that ignores the correlation between the individual coefficients and regressors is asymptotically equivalent to the group mean estimator. In addition, we give conditions where the standard within estimator of the mean of the coefficients is consistent. Moreover, with additional assumptions on the known correlation pattern, we derive the asymptotic properties of panel least squares estimators. Simulations are used to examine the finite sample performances of different estimators.

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