For the semiparametric regression model:Y^((j))(x_(in),t_(in))=t_(in)β+g(x_(in))+e^((j))(x_(in)),1≤j≤k,1≤i≤n,where t_(in)∈R and x(in)∈Rpare known to be nonrandom,g is an unknown continuous function on a compact...For the semiparametric regression model:Y^((j))(x_(in),t_(in))=t_(in)β+g(x_(in))+e^((j))(x_(in)),1≤j≤k,1≤i≤n,where t_(in)∈R and x(in)∈Rpare known to be nonrandom,g is an unknown continuous function on a compact set A in R^(p),e^(j)(x_(in))are m-extended negatively dependent random errors with mean zero,Y^((j))(x_(in),t_(in))represent the j-th response variables which are observable at points xin,tin.In this paper,we study the strong consistency,complete consistency and r-th(r>1)mean consistency for the estimatorsβ_(k,n)and g__(k,n)ofβand g,respectively.The results obtained in this paper markedly improve and extend the corresponding ones for independent random variables,negatively associated random variables and other mixing random variables.Moreover,we carry out a numerical simulation for our main results.展开更多
基金supported by the National Natural Science Foundation of China(11671012,11871072)the Natural Science Foundation of Anhui Province(1808085QA03,1908085QA01,1908085QA07)the Provincial Natural Science Research Project of Anhui Colleges(KJ2019A0003)。
文摘For the semiparametric regression model:Y^((j))(x_(in),t_(in))=t_(in)β+g(x_(in))+e^((j))(x_(in)),1≤j≤k,1≤i≤n,where t_(in)∈R and x(in)∈Rpare known to be nonrandom,g is an unknown continuous function on a compact set A in R^(p),e^(j)(x_(in))are m-extended negatively dependent random errors with mean zero,Y^((j))(x_(in),t_(in))represent the j-th response variables which are observable at points xin,tin.In this paper,we study the strong consistency,complete consistency and r-th(r>1)mean consistency for the estimatorsβ_(k,n)and g__(k,n)ofβand g,respectively.The results obtained in this paper markedly improve and extend the corresponding ones for independent random variables,negatively associated random variables and other mixing random variables.Moreover,we carry out a numerical simulation for our main results.
