Parameters Estimation Of Linear Models With Half-normal Errors

In this paper The following linear regression model is considered(?)where is yi the n×1 observed value,Xi is the known order 1×p design vector,?i is the random error,? is the unknown parameter,and ?i?HN(?)or ?i?SHN(?).Although there are many results of linear regression model,no one studies the linear model with(slashed)half-normal errors by the maximum L_q-likelihood estimate(ML_qE)method or the penalized L_q-likelihood estimate(PL_qE)method(as far as I know).Therefore,based on the ML_qE method,the PL_qE method and theories relative to linear regression models,we study the following contents.In chapter 2,based on the maximum L_q-likelihood method(ML_qE),and we investigate linear regression model with the error ?i?HN(?).The maximum L_q-likelihood estimators of unknown parameters ? and ? are obtained by the maximum L_q-likelihood estimation method.The consistency and asymptotic distribution of the estimators are discussed,and the simulation application is given.These results generalize the corresponding results of maximum L_q-likelihood estimation(qn=1)for linear models of half-normal errors and ML_qE(p=0)with half-normal distribution.In chapter 3,based on the maximum L_q-likelihood method and the penalized maximum likelihood method.We consider the linear regression model with half-normal error,In this model,the penalized L_q-likelihood estimators of unknown parameters?,?,? are obtained by using the density function of normal distribution as the penalized term,and the consistency and asymptotic normal distribution of the estimators are discussed.These results generalize the corresponding results of the maximum L_q-likelihood estimators and the penalized likelihood estimators of linear models under half-normal errors.In Chapter 4,we consider the linear regression model Z_i=?+?_i with slashed half-normal error ?i?SHN(?).By Chebyshev inequality and large number theorem,we obtain the strong and weak consistency of the(weighted)moment estimators of error parameters.