基于模态回归的半参数部分线性模型的稳健估计
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摘要
以半参数部分线性模型为对象,研究了基于模态回归的稳健估计方法。非参数部分采用B样条近似,在模型的回归中通过控制核函数的带宽来实现估计的稳健性,结合局部二次算法(LQA)和模型期望值最大化算法(MEM),提出EM估计算法,得到了参数估计以及非参数部分估计的收敛速度。通过蒙特卡洛模拟和实例分析,验证了本文方法的有效性。
A robust estimation method for semiparametric partially linear model is studied based on modal regression.The nonparametric components are approximated by B-spline basis function.In the regression of the model,robustness of the estimator is achieved by controlling the bandwidth of kernel function.With the aid of local quadratic algorithm(LQA)and modal expectation-maximization(MEM)algorithm,an EM type algorithm is developed,and the convergence rates of parametric and non-parametric estimations are obtained.Monte Carlo simulation and real data analysis verify the effectiveness of the proposed method.
A robust estimation method for semiparametric partially linear model is studied based on modal regression.The nonparametric components are approximated by B-spline basis function.In the regression of the model,robustness of the estimator is achieved by controlling the bandwidth of kernel function.With the aid of local quadratic algorithm(LQA)and modal expectation-maximization(MEM)algorithm,an EM type algorithm is developed,and the convergence rates of parametric and non-parametric estimations are obtained.Monte Carlo simulation and real data analysis verify the effectiveness of the proposed method.
引文
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[10]Yao W X,Li L H.A new regression model:modal linear regression[J].Scandinavian Journal of Statistics,2014,41:656-671.
[11]Li R Z,Liang H.Variable selection in semiparametric regression modeling[J].The Annals of Statistics,2008,36(1):261-286.
[12]Zhao P X,Xue L G.Variable selection for semiparametric varying coefficient partially linear models[J].Statistics and Probability Letters,2009,79:2148-2157.
[13]Schumaker L L.Spline functions:basic theory[M].New Jersey:John Wiley &Sons,Inc.,1981.
[14]Li J,Ray S,Lindsay B G.A nonparametric statistical approach to clustering via mode identification[J].Journal of Machine Learning Research,2007,8:1687-1723.
[15]Fan J Q,Li R Z.Variable selection via nonconcave penalized likelihood and its oracle properties[J].Journal of the American Statistical Association,2001,96:1348-1360.
[16]Nierenberg D W,Stukel T A,Baron J A,et al.Determinants of plasma levels of beta-carotene and retinol[J].American Journal of Epidemiology,1989,130(3):511-521.
[2] Hastie T J,Tibshirani R J.Generalized additive models[M].London:Chapman and Hall/CRC,1990.
[3] Robinson P M.Root-N-consistent semiparametric regression[J].Econometrica,1988,56:931-954.
[4] Heckman N E.Spline smoothing in a partly linear model[J].Journal of the Royal Statistical Society:Series B,1986,48(2):244-248.
[5] Chen G L,Wang Z J.The multivariate partially linear model with B-spline[J].应用概率统计,2010,26(2):138-150.
[6] Lv X F,Li R.Smoothed empirical likelihood analysis of partially linear quantile regression models with missing response variables[J].AStA-Advances in Statistical Analysis,2013,97(4):317-347.
[7] Zhu L P,Li R Z,Cui H G.Robust estimation for partially linear models with large-dimensional covariates[J].Science China Mathematics,2013,56(10):2069-2088.
[8] Yao W X,Lindsay B G,Li R Z.Local modal regression[J].Journal of Nonparametric Statistics,2012,24(3):647-663.
[9] Zhao W H,Zhang R Q,Liu J C,et al.Robust and efficient variable selection for semiparametric partially linear varying coefficient model based on modal regression[J].Annals of the Institute of Statistical Mathematics,2014,66(1):165-191.
[10]Yao W X,Li L H.A new regression model:modal linear regression[J].Scandinavian Journal of Statistics,2014,41:656-671.
[11]Li R Z,Liang H.Variable selection in semiparametric regression modeling[J].The Annals of Statistics,2008,36(1):261-286.
[12]Zhao P X,Xue L G.Variable selection for semiparametric varying coefficient partially linear models[J].Statistics and Probability Letters,2009,79:2148-2157.
[13]Schumaker L L.Spline functions:basic theory[M].New Jersey:John Wiley &Sons,Inc.,1981.
[14]Li J,Ray S,Lindsay B G.A nonparametric statistical approach to clustering via mode identification[J].Journal of Machine Learning Research,2007,8:1687-1723.
[15]Fan J Q,Li R Z.Variable selection via nonconcave penalized likelihood and its oracle properties[J].Journal of the American Statistical Association,2001,96:1348-1360.
[16]Nierenberg D W,Stukel T A,Baron J A,et al.Determinants of plasma levels of beta-carotene and retinol[J].American Journal of Epidemiology,1989,130(3):511-521.