In this paper,a theory on sieve likelihood ratio inference on general parameter spaces(including infinite dimensional) is studied.Under fairly general regularity conditions,the sieve log-likelihood ratio statistic is proved to be asymptotically x2 distributed,which can be viewed as a generalization of the well-known Wilks' theorem.As an example,a emiparametric partial linear model is investigated.
For partial linear model Y=X^Tβ0 +go(T)+εwith unknown β∈R^d and an unknown smooth function go， this paper considers the Huber-Dutter estimators of β0, scale σ for the errors and the function g0 respectively, in which the smoothing B-spline function is used. Under some regular conditions, it is shown that the Huber-Dutter estimators of β0 and σ are asymptotically normal with convergence rate n^-1/2 and the B-spline Huber-Dutter estimator of g0 achieves the optimal convergence rate in nonparametric regression. A simulation study demonstrates that the Huber-Dutter estimator of β0 is competitive with its M-estimator without scale parameter and the ordinary least square estimator. An example is presented after the simulation study.
The issue of optimal blocking for fractional factorial split-plot (FFSP) designs is considered under the two criteria of minimum aberration and maximum estimation capacity. The criteria of minimum secondary aberration (MSA) and maximum secondary estimation capacity (MSEC) are developed for discriminating among rival nonisomorphic blcoked FFSP designs. A general rule for identifying MSA or MSEC blocked FFSP designs through their blocked consulting designs is established.
Al Mingyao & HE Shuyuan Key Laborartory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, China
Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey’s one degree of freedom test and a nonparametric version of Rao’s score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernel-based tests. The score test is found to have a good overall performance.
Heng-jian CUI, Xu-ming HE & Li LIU Department of Statistics and Financial Mathematics, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
