| We examine the asymptotic efficiency of the least square estimator (LSE), relative to the best linear unbiased estimator (BLUE) in linear regression with dependent errors. First, some definitions and notations are given. Next, we introduce LSE and BLUE in chapter 3. With dependent errors, we are more interested in LSE than BLUE, since the covariance matrix of the errors is seldom known. In chapter 4, we find that the LSE b&d4; of the regression coefficients is asymptotically efficient relative to the BLUE if and only if the spectral density is constant on each of the elements of S (regression spectrum). In addition, we study the asymptotic properties of M-estimators of regression parameters in linear models with dependent errors in chapter 5. We derive the Bahadur representations and establish a central limit theorem for LSE and BLUE. At last, we illustrate the conclusions in chapter 4 and 5 with simulated data. |
