Jackknife And Bootstrap Approximation Of Parameters Estimation In Signal Models

In this thesis we propose the estimation of the parameters for two different signal models by using Jackknife and Bootstrap methods, respectively. The thesis is divided into three parts. In the first chapter, we investigate the Jackknife approximation for one-dimensional complex response exponential signal model with white noise. We construct the Jackknife estimators of the parameters,then we prove the strong consistency and asymptotic unbias of the Jackknife estimators and asymptotic normality of the Jackknife virtual value. In the second chapter, we propose the Bootstrap method in two-dimensional real signal model, and give the Bootstrap estimators of the parameters by virtue of the construction method of Bootstrap approximation in regressive model and prove the strong consistency and asymtotic normality. In the third chapter, we provide numerical experiments. We present some simulation results for the proposed methods in the above two chapters by Monte-Carlo method. Simulation results indicate that the estimators are consistency and the Bootstrap estimators are better than Least-squares esimators when the noise don't obey the normal distribution.