The authors discuss the unbalanced two-way ANOVA model under heteroscedasticity. By taking the generalized approach, the authors derive the generalized p-values for testing the equality of fixed effects and the genera...The authors discuss the unbalanced two-way ANOVA model under heteroscedasticity. By taking the generalized approach, the authors derive the generalized p-values for testing the equality of fixed effects and the generalized confidence regions for these effects. The authors also provide their frequentist properties in large-sample cases. Simulation studies show that the generalized confidence regions have good coverage probabilities.展开更多
Thepenalised least square estimator of non-convex penalties such as the smoothly clipped absolute deviation(SCAD)and the minimax concave penalty(MCP)is highly nonlinear and has many local optima.Finding a local soluti...Thepenalised least square estimator of non-convex penalties such as the smoothly clipped absolute deviation(SCAD)and the minimax concave penalty(MCP)is highly nonlinear and has many local optima.Finding a local solution to achieve the so-called oracle property is a challenging problem.We show that the orthogonalising EM(OEM)algorithm can indeed find such a local solution with the oracle property under some regularity conditions for a moderate but diverging number of variables.展开更多
基金This research is supported by the National Natural Science Foundation of China under Grant Nos.10771126 and 10771015.
文摘The authors discuss the unbalanced two-way ANOVA model under heteroscedasticity. By taking the generalized approach, the authors derive the generalized p-values for testing the equality of fixed effects and the generalized confidence regions for these effects. The authors also provide their frequentist properties in large-sample cases. Simulation studies show that the generalized confidence regions have good coverage probabilities.
基金Xiong’s research was supported by the National Natural Sci-ence Foundation of China[grant number 11471172],[grant number 11671386].
文摘Thepenalised least square estimator of non-convex penalties such as the smoothly clipped absolute deviation(SCAD)and the minimax concave penalty(MCP)is highly nonlinear and has many local optima.Finding a local solution to achieve the so-called oracle property is a challenging problem.We show that the orthogonalising EM(OEM)algorithm can indeed find such a local solution with the oracle property under some regularity conditions for a moderate but diverging number of variables.
