基于高阶差分方法半参数回归模型中参数的minimax估计

Minimax estimates of parameters in a semiparametric regression model based on higher order difference

基于高阶差分方法给出半参数回归模型中参数β的minimax线性估计条件,并指出差分方法下得到的最小二乘估计^βdiff为β的minimax线性估计.另外对差分项存在多重共线性的情况,指出参数β的岭估计^βdiff(k)存在minimax估计优良性的条件.

The paper introduces conditions of difference-based minimax estimates of the regression parameters β in a semiparametric model. The ordinary least squares estimator βdiff based on higher order differences of the observations, and the minimax linear estimator of β are considered at the same time. Furthermore, the difference-based ridge regression estimator βdiff （k） that used in the presence of multicollinearity in a semiparametric model, and the conditions of βdiff （k） as a minimax linear estimator are also considered.