The Consistency For The Estimators Of Semi-parametric Regression Model For ?? Mixing Sequences

Combining the advantages of parametric regression model and non-parametric regres-sion model,statisticians have proposed semi-parametric regression models.The simple semi-parametric regression model,as shown in Eq.(1):(?)Many domestic and foreign scholars have actively beel studying the consistency of the parameter estimates of ? and g,when the random error sequences {(?)}are of different types,the main types of research are ??mixing random error sequences ??mixing random error sequences,?*-mixing random error sequences,N A sequences,independent random error sequence.Based on the existing research results,this paper has studied the consistency of parameters ? and g,when{(?)} are ??mixing random error sequences and 1<r ? 2,we study the consistency for the ?m,n and gm,n.Under the assumption of Hypothesis ? and Hypothesis ?,the following results can be drawn through calculations:Theorem 1 In Eq.(1),where the {(?),j ? 1} are ??mixing random error sequences with mean zero and j ? 1,if Hypothesis I and Hypothesis II are established,and exists r ?(1,2],which will make the following formula established:sup E(?) when n = n(m)satisfy the following formula:then lim (?)if we further design point sequences and weight function satisfy the following formula:(?)thenTheorem 2 In Eq.(1),when the{(?),j ?1}are ??mixing random error sequences with mean zero and j ? 1,if Hypothesis I is established,and there exists r ?(1,2]make Eq.(2)and Eq.(3)are established,then:(?)If we further design point sequences and weight function to satisfy Eq.(4)then:lim sup E(?)...