Maximum Asymptotic Efficiency Research Articles

A Geometric Approach to Improve Interference Mitigation in Multi-User Detection and Equalization

We apply maximal asymptotic conditional efficiency joint successive interference cancellation (MACE-JSIC) to frequency-selective channel equalization and propose improvements that extend MACE-JSIC detection to the broader paradigm of time-varying and imprecisely known communication systems. The need for expensive redesign to include any change in the interfering signals is a fundamental limitation of MACE-JSIC detection despite its high performance and low detection complexity. In this work, we derive sufficiency criteria that reduce maximum asymptotic efficiency (MAE) detection to low-complexity decorrelation and exploit this relationship to extend the MACE-JSIC approach to time-varying communication systems. Simulations on several multi-user systems and frequency-selective channels demonstrate that the performance of the proposed detectors is consistent with theoretical expectations.

R-Estimates vs. GMM: A Theoretical Case Study of Validity and Efficiency

What role should assumptions play in inference? We present a small theoretical case study of a simple, clean case, namely the nonparametric comparison of two continuous distributions using (essentially) information about quartiles, that is, the central information displayed in a pair of boxplots. In particular, we contrast a suggestion of John Tukey—that the validity of inferences should not depend on assumptions, but assumptions have a role in efficiency—with a competing suggestion that is an aspect of Hansen’s generalized method of moments—that methods should achieve maximum asymptotic efficiency with fewer assumptions. In our case study, the practical performance of these two suggestions is strikingly different. An aspect of this comparison concerns the unification or separation of the tasks of estimation assuming a model and testing the fit of that model. We also look at a method (MERT) that aims not at best performance, but rather at achieving reasonable performance across a set of plausible models.

Asymptotically Efficient Estimation of Cointegration Regressions

An asymptotic optimality theory for the estimation of cointegration regressions is developed in this paper. The theory applies to a reasonably wide class of estimators without making any specific assumptions about the probability distribution or short-run dynamics of the data-generating process. Due to the nonstandard nature of the estimation problem, the conventional minimum variance criterion does not provide a convenient measure of asymptotic efficiency. An alternative criterion, based on the concentration or peakedness of the limiting distribution of an estimator, is therefore adopted. The limiting distribution of estimators with maximum asymptotic efficiency is characterized in the paper and used to discuss the optimality of some known estimators. A new asymptotically efficient estimator is also introduced. This estimator is obtained from the ordinary least-squares estimator by a time domain correction which is nonparametric in the sense that no assumption of a finite parameter model is required. The estimator can be computed with least squares without any initial estimations.

The Asymptotic Efficiency of Daniels’s Generalized Correlation Coefficients

SUMMARY The asymptotic efficiency of the generalized correlation coefficient devised by Daniels, used as a test of association in the bivariate function H(x, y) = F(x) G(y) {1 + αA(x) B(y)}, is shown to depend in a simple way on the score-matrices used to define the coefficient. Two coefficients for which the corresponding row sums of the two score-matrices, written in a standard form, are proportional are shown to have the same asymptotic efficiency. In particular, this is shown to be true for Spearman’s rank correlation coefficient and Kendall’s alternative coefficient, τ. For alternatives of the above type, maximum efficiency can be obtained within Daniels’s family of coefficients; for a more general class of alternatives a weighted combination of Daniels’s coefficients is necessary to attain maximum asymptotic efficiency.