极值分布下联合位置与散度模型的变量选择
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摘要
极值分布在地震、洪灾和其它自然灾害的预测中是非常有用的.在许多应用方面,很有必要对散度建模.本文推广经典极值回归模型,研究了联合位置与散度模型,并提出了一种同时对位置模型和散度模型的变量选择方法.同时证明了惩罚极大似然估计具有相合性和oracle性质,通过随机模拟研究了所提出方法的有限样本性质.
The extreme-value distribution is very useful in predicting the probability that an extreme earthquake,flood or other natural disaster will occur.In many applications,there is a great need to model the dispersion.In this paper,a unified procedure is proposed to simultaneously select significant variables in joint location and dispersion models which provide a useful extension of the general extreme-value regression model.It is further shown that the presented penalized maximum likelihood estimator enjoys the consistency and the oracle property.Numerical simulation is conducted to examine the finite sample properties of the proposed method.
The extreme-value distribution is very useful in predicting the probability that an extreme earthquake,flood or other natural disaster will occur.In many applications,there is a great need to model the dispersion.In this paper,a unified procedure is proposed to simultaneously select significant variables in joint location and dispersion models which provide a useful extension of the general extreme-value regression model.It is further shown that the presented penalized maximum likelihood estimator enjoys the consistency and the oracle property.Numerical simulation is conducted to examine the finite sample properties of the proposed method.
引文
[1]史道济.实用极值统计方法[M].天津:天津科学技术出版社,2006Shi D J.Practical Statistical Method of Extreme Value[M].Tianjin:Tianjin Press of Science and Technol-ogy,2006
[2]韦博成,林金官,吕庆哲.回归模型中的异方差或变离差检验问题综述[J].应用概率统计,2003,19(2):210-220Wei B C,Lin J G,Lv Q Z.Summary of tests for heteroscedasticity or dispersion in regression models[J].Chinese Journal of Applied Probability and Statistics,2003,19(2):210-220
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[4]Engel J,Huele A F.A generalized linear modeling approach to robust design[J].Technometrics,1996,38(4):365-373
[5]Smyth G K.Generalized linear models with varying dispersion[J].Journal of the Royal Statistical SocietySeries B,1989,51(1):47-60
[6]Lee Y,Nelder J A.Generalized linear models for the analysis of quality improvement experiments[J].Canadian Journal of Statistics,1998,26(1):95-105
[7]Taylor J T,Verbyla A P.Joint modelling of location and scale parameters of the t distribution[J].StatisticalModelling,2004,4(2):91-112
[8]杨宜平,薛留根,程维虎.纵向数据下部分线性EV模型的变量选择[J].工程数学学报,2011,28(2):211-219Yang Y P,Xue L G,Cheng W H.Variable selection in partially linear EV models with longitudinal data[J].Chinese Journal of Engineering Mathematics,2011,28(2):211-219
[9]Fan J Q,Lv J C.A selective overview of variable selection in high dimensional feature space[J].StatisticaSinica,2010,20(1):101-148
[10]Fan J Q,Li R.Variable selection via nonconcave penalized likelihood and its oracle properties[J].Journalof the American Statistical Association,2001,96(456):1348-1360
[11]Tibshirani R.Regression shrinkage and selection via the LASSO[J].Journal of the Royal Statistical SocietySeries B,1996,58(1):267-288
[12]Antoniadis A.Wavelets in statistics:a review(with discussion)[J].Journal of the Italian Statistical Asso-ciation,1997,6(2):97-144
[13]Wang H,Li R,Tsai C.Tuning parameter selectors for the smoothly clipped absolute deviation method[J].Biometrika,2007,94(3):553-568
[14]Li R,Liang H.Variable selection in semiparametric regression modeling[J].The Annals of Statistics,2008,36(1):261-286
[15]Zhao P X,Xue L G.Variable selection for semiparametric varying coeffcient partially linear errors-in-variables models[J].Journal of Multivariate Analysis,2010,101(8):1872-1883
[16]刘强,薛留根.核实数据下单指标EV模型的经验似然推断[J].工程数学学报,2010,27(2):321-332Liu Q,Xue L G.Empirical likelihood-based inference for single-index EV models with validation data[J].Chinese Journal of Engineering Mathematics,2010,27(2):321-332
[2]韦博成,林金官,吕庆哲.回归模型中的异方差或变离差检验问题综述[J].应用概率统计,2003,19(2):210-220Wei B C,Lin J G,Lv Q Z.Summary of tests for heteroscedasticity or dispersion in regression models[J].Chinese Journal of Applied Probability and Statistics,2003,19(2):210-220
[3]Aitkin M.Modelling variance heterogeneity in normal regression using GLIM[J].Journal of the RoyalStatistical Society Series C,1987,36(3):332-339
[4]Engel J,Huele A F.A generalized linear modeling approach to robust design[J].Technometrics,1996,38(4):365-373
[5]Smyth G K.Generalized linear models with varying dispersion[J].Journal of the Royal Statistical SocietySeries B,1989,51(1):47-60
[6]Lee Y,Nelder J A.Generalized linear models for the analysis of quality improvement experiments[J].Canadian Journal of Statistics,1998,26(1):95-105
[7]Taylor J T,Verbyla A P.Joint modelling of location and scale parameters of the t distribution[J].StatisticalModelling,2004,4(2):91-112
[8]杨宜平,薛留根,程维虎.纵向数据下部分线性EV模型的变量选择[J].工程数学学报,2011,28(2):211-219Yang Y P,Xue L G,Cheng W H.Variable selection in partially linear EV models with longitudinal data[J].Chinese Journal of Engineering Mathematics,2011,28(2):211-219
[9]Fan J Q,Lv J C.A selective overview of variable selection in high dimensional feature space[J].StatisticaSinica,2010,20(1):101-148
[10]Fan J Q,Li R.Variable selection via nonconcave penalized likelihood and its oracle properties[J].Journalof the American Statistical Association,2001,96(456):1348-1360
[11]Tibshirani R.Regression shrinkage and selection via the LASSO[J].Journal of the Royal Statistical SocietySeries B,1996,58(1):267-288
[12]Antoniadis A.Wavelets in statistics:a review(with discussion)[J].Journal of the Italian Statistical Asso-ciation,1997,6(2):97-144
[13]Wang H,Li R,Tsai C.Tuning parameter selectors for the smoothly clipped absolute deviation method[J].Biometrika,2007,94(3):553-568
[14]Li R,Liang H.Variable selection in semiparametric regression modeling[J].The Annals of Statistics,2008,36(1):261-286
[15]Zhao P X,Xue L G.Variable selection for semiparametric varying coeffcient partially linear errors-in-variables models[J].Journal of Multivariate Analysis,2010,101(8):1872-1883
[16]刘强,薛留根.核实数据下单指标EV模型的经验似然推断[J].工程数学学报,2010,27(2):321-332Liu Q,Xue L G.Empirical likelihood-based inference for single-index EV models with validation data[J].Chinese Journal of Engineering Mathematics,2010,27(2):321-332
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