Statistical Communication Theory and Robust Estimation

摘要

Research completed includes consistent estimation of (nonrandom) signals from nonlinear transformations of noisy samples; approximations of non-bandlimited signals using a finite number of samples and their rate of convergence; (infinite) sampling approximations for non-bandlimited signals, and sampling representations for bounded linear operations on bandlimited signals, and for generalized bandlimited signals; the evaluation of linear estimates and regression estimates in stable processes, including regression and linear filtering of signals in noise; and certain probability and expectation inequalities. Research completed includes work in the following areas: trimming least squares estimators in the linear model by using a preliminary estimator; tests for heteroscedasticity in the linear model; estimation of regression coefficients in a heteroscedastic linear model; almost sure properties of robust regression estimates with applications to sequential clinical trials; robust methods in factorial experiments; studying sequential procedures for estimating the largest of three normal means; nonparametric estimation of regression functions. (RH)