Efficient Estimation: The Rao-Zyskind Condition, Kruskal's Theorem and Ordinary Least Squares* (original) (raw)

Efficiency gains in least squares estimation: A new approach

Econometric Reviews

A. Mathematical derivations A1. The basic estimator expression A2. The infeasible PHLS estimator A3. The HOLS estimator A4. Homoskedasticity A5. Conditional heteroskedasticity A6. Estimating the HOLS VCV matrix A7. The HOLS estimator with Instrumental Variables B. Details of simulation studies and additional results B1. Homoskedasticity B2. Conditional heteroskedasticity B3. The IV-HOLS estimator under homoskedasticity C. The case of unconditional heteroskedasticity C1. Theoretical results C2. Simulation results (MSE and Bias)

1. CR Rao’s Contribution to Econometrics, SSRN 2011

SSRN Electronic Journal

Abstract: Calyampudi Radhakrishna Rao (Rao for brevity, henceforth) just celebrated his 90th birthday. He received numerous honors including 1972 fellow of Econometric Society and the 2002 US Medal of Science (the citation of which recognized his contributions to economics). He co-founded with Mahalanobis the Indian Econometric Society, and laid probabilistic foundations for linear structural economic relations in his Econometrica article in 1947, solving a problem suggested by Frisch. This paper reviews Rao’s contributions to economic science including: (i) specification of linear structural economic relations, (ii) identification of the model, (iii) efficient estimation of the model, and (iv) testing of hypotheses about the economic structure. Our review of his work also indicates a rich potential of his contributions advancing economic science as some of his contributions have not been fully exploited by economists. Number of Pages in PDF File: 37 Keywords: Linear Regression, Err...

Econometric Analysis on Efficiency of Estimators

LIBERTAS MATHEMATICA (vol.I-XXXI), 2003

This paper investigates the efficiency of an alternative to ratio estimator under the super population model with uncorrelated errors and a gamma-distributed auxiliary variable. Comparisons with usual ratio and unbiased estimators are also made.

An Alternative Perspective on Estimators

Lobachevskii Journal of Mathematics, 2021

The present article aims to shows that obtaining the best estimator does not depend on estimators’ terms and functions. To prove this situation, it is shown that there is no difference between the existing estimators and the proposed estimator by proposing new sophisticated estima- tors. Besides, theoretical, graphical, empirical and simulation studies are conducted to confirm the efficiency of these proposed estimators with the help of the method used by Wolter (2007). Also, the MSE values are evaluated by using the power coefficient of the interested estimators. In data sets with the known correlation coefficient, it is possible to determine which power coefficient estimator is better without computing the MSE value.

On A Method of Bias Reduction in the Product Method of Estimation

Asian Journal of Probability and Statistics, 2022

In this paper, we focused our attention on the creation of an almost unbiased predictive product estimator after estimating and correcting bias of the classical product estimator under predictive approach. Considering mean square error as the performance measure, superiority of the proposed estimator has been analyzed compared to the classical product estimator and Robson’s [1] unbiased product estimator under (i) a finite population set-up, (ii) an infinite population set-up assuming bivariate normal distribution between the variables, and (iii) the assumption of a super-population model.

Econometric Analysis on Efficiency of Estimator

This paper investigates the efficiency of an alternative to ratio estimator under the super population model with uncorrelated errors and a gamma-distributed auxiliary variable. Comparisons with usual ratio and unbiased estimators are also made.

Reshetov LA Some Comments on Six Inequalities Associated With the Inefficiency of Ordinary Least Squares With One Regressor

The study of the inefficiency of the ordinary least-squares estimator (OLSE) with one regressor by Watson (1951) required a lower bound for the efficiency defined as the ratio of the variance of the best linear unbiased estimator (BLUE) to the variance of the OLSE. Such a lower bound was provided by the Cassels inequality (1951), which we note is closely related to five other inequalities, including the well-known inequality usually attributed to Kantorovich (1948), but which was established already by . The main purpose in this paper is to show how these six inequalities are related, with a historical perspective. We present some proofs and conclude that all six inequalities are essentially equivalent, in the sense that any one inequality implies the other five. We identify conditions for equality in each inequality and present the six continuous integral analogues. We end the paper with English translations of the seminal papers by and , respec-LINEAR ALGEBRA AND ITS APPLICATIONS 264:13-54 (1997)