Signal Detection, Target Tracking and Differential Geometry Applications toStatistical Inference

摘要

Signal detection and target tracking. A novel method known as polynomial rootingapproach is proposed to obtain estimates of frequencies, amplitudes and noise variance of two-dimensional exponential signals. The consistency and asymptotic normality of the least squares estimators in a multidimensional exponential signal model are established. Significant contributions have been made to the design of observations, efficient estimation of target positions almost continuously in time and establishing correct association between estimates of target positions made at different time points. M-estimation. A unified theory of robust estimation is developed using the difference of two convex functions as the discrepancy measure. Quantile regression. The concept of a quantile regression function is introduced as the conditional mean of the response variable at the u-th quantile of the independent variable and applied to problems of inference when the independent variable in different samples are not comparable.