A Class of Nonparametric Estimators of Regression Coefficients in an Autoregressive Scheme.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO
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This dissertation is concerned with estimation of parameters of an autoregressive process. In Chapter II, some results from least squares estimation are presented for linear input-output systems and multiple autoregressive processes when the residual sequence may have infinite variance. A restricted survey of some of the literature in this vast area is also presented in the introduction to Chapter II. Chapter III contains two nonstandard estimators for the regression coefficient in the linear Markov process. Both of the estimators are shown to be unbiased and to have normal limiting distributions. The asymptotic relative efficiencies A.R.E. of these estimators versus least squares estimators are presented in Chapter IV. We propose an iterative scheme for estimating the regression coefficients in the general A.R.p process in Chapter V. Monte Carlo simulations are done for the estimators presented in Chapter II and for the estimator theta of Chapter III. These results are reported in Chapters II and IV. Simulations for the A.R.2 process are given in Chapter IV. Chapter VI summarizes the work accomplished and suggests further research.
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