Determination of Estimators with Minimum Asymptotic Covariance Matrices

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 L null -estimation, 1 ≤ p

[1]  H. White,et al.  Misspecified models with dependent observations , 1982 .

[2]  H. White,et al.  A Unified Theory of Consistent Estimation for Parametric Models , 1985, Econometric Theory.

[3]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[4]  Jerry A. Hausman,et al.  An Instrumental Variable Approach to Full-Information Estimators for Linear and Non-Linear Econometric Models , 1975 .

[5]  C. R. Rao,et al.  Information and the Accuracy Attainable in the Estimation of Statistical Parameters , 1992 .

[6]  F. N. David,et al.  Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability. , 1973 .

[7]  J. D. Sargan,et al.  THREE-STAGE LEAST-SQUARES AND FULL MAXIMUM LIKELIHOOD ESTIMATES , 1964 .

[8]  W. J. Hall,et al.  Information and Asymptotic Efficiency in Parametric-Nonparametric Models , 1983 .

[9]  T. Rothenberg,et al.  Efficient Estimation of Simultaneous Equation Systems , 1964 .

[10]  C. L. Chiang.  ON REGULAR BEST ASYMPTOTICALLY NORMAL ESTIMATES , 1956 .

[11]  R. Fisher,et al.  On the Mathematical Foundations of Theoretical Statistics , 1922 .

[12]  P. J. Huber.  Robust Estimation of a Location Parameter , 1964 .

[13]  J. Hájek.  A characterization of limiting distributions of regular estimates , 1970 .

[14]  P. Robinson.  Asymptotically efficient estimation in the presence of heteroskedasticity of unknown form , 1987 .

[15]  H. White,et al.  Instrumental Variables Regression with Independent Observations , 1982 .

[16]  S. Kaufman.  Asymptotic efficiency of the maximum likelihood estimator) , 1966 .

[17]  L. Hansen.  LARGE SAMPLE PROPERTIES OF GENERALIZED METHOD OF , 1982 .

[18]  R. Z. Khasʹminskiĭ,et al.  Statistical estimation : asymptotic theory , 1981 .

[19]  P. Hall,et al.  Martingale Limit Theory and Its Application , 1980 .

[20]  Lionel Weiss,et al.  Asymptotic Properties of Maximum Likelihood Estimators in Some Nonstandard Cases , 1971 .

[21]  J. G. Cragg.  MORE EFFICIENT ESTIMATION IN THE PRESENCE OF HETEROSCEDASTICITY OF UNKNOWN FORM , 1983 .

[22]  H. Theil,et al.  Three-Stage Least Squares: Simultaneous Estimation of Simultaneous Equations , 1962 .

[23]  Dale W. Jorgenson,et al.  EFFICIENT ESTIMATION OF NONLINEAR SIMULTANEOUS EQUATIONS WITH ADDITIVE DISTURBANCES , 2022 .

[24]  H. White.  Asymptotic theory for econometricians , 1985 .

[25]  P. Zarembka.  Frontiers in econometrics , 1973 .

[26]  Takeshi Amemiya,et al.  The Maximum Likelihood and the Nonlinear Three-Stage Least Squares Estimator in the General Nonlinear Simultaneous Equation Model , 1977 .

[27]  George G. Roussas,et al.  Contiguity of probability measures: some applications in statistics: Preface , 1972 .

[28]  P. J. Huber.  Robust Regression: Asymptotics, Conjectures and Monte Carlo , 1973 .

[29]  G. Chamberlain.  Asymptotic efficiency in semi-parametric models with censoring , 1986 .

[30]  A. Zellner.  An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias , 1962 .

[31]  L. Lecam.  On the Assumptions Used to Prove Asymptotic Normality of Maximum Likelihood Estimates , 1970 .

[32]  P. Phillips.  Partially Identified Econometric Models , 1988, Econometric Theory.

[33]  Takeshi Amemiya,et al.  The nonlinear two-stage least-squares estimator , 1974 .

[34]  G. Darmois,et al.  Sur les limites de la dispersion de certaines estimations , 1945 .

[35]  L. Hansen.  A method for calculating bounds on the asymptotic covariance matrices of generalized method of moments estimators , 1985 .

[36]  Maxwell B. Stinchcombe,et al.  Adaptive Efficient Weighted Least Squares With Dependent Observations , 1991 .

[37]  M. Fréchet.  Sur l'extension de certaines evaluations statistiques au cas de petits echantillons , 1943 .

[38]  A. C. Aitken.  IV.—On Least Squares and Linear Combination of Observations , 1936 .

[39]  J. Wolfowitz.  Asymptotic Efficiency of the Maximum Likelihood Estimator , 1965 .

[40]  D. Andrews.  Asymptotics for Semiparametric Econometric Models: I. Estimation , 1990 .

[41]  R. R. Bahadur.  On Fisher's Bound for Asymptotic Variances , 1964 .

[42]  J. Wooldridge.  Asymptotic properties of econometric estimators , 1986 .

[43]  William A. Barnett,et al.  Dynamic Econometric Modeling , 1988 .

[44]  Rory A. Fisher,et al.  Theory of Statistical Estimation , 1925, Mathematical Proceedings of the Cambridge Philosophical Society.