Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove mod...Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove moderate deviations and large deviations for the statistic sup ｜fn（x） - fn（-x） ｜.展开更多
This paper develops the theory of the kth power expectile estimation and considers its relevant hypothesis tests for coefficients of linear regression models.We prove that the asymptotic covariance matrix of kth power...This paper develops the theory of the kth power expectile estimation and considers its relevant hypothesis tests for coefficients of linear regression models.We prove that the asymptotic covariance matrix of kth power expectile regression converges to that of quantile regression as k converges to one and hence promise a moment estimator of asymptotic matrix of quantile regression.The kth power expectile regression is then utilized to test for homoskedasticity and conditional symmetry of the data.Detailed comparisons of the local power among the kth power expectile regression tests,the quantile regression test,and the expectile regression test have been provided.When the underlying distribution is not standard normal,results show that the optimal k are often larger than 1 and smaller than 2,which suggests the general kth power expectile regression is necessary.Finally,the methods are illustrated by a real example.展开更多
Suppose that Y1 , Y2 , , Yn are independent and identically distributed n observations from convolution model Y = X ＋ ε, where X is an unobserved random variable with unknown density f X,and ε is the measurement er...Suppose that Y1 , Y2 , , Yn are independent and identically distributed n observations from convolution model Y = X ＋ ε, where X is an unobserved random variable with unknown density f X,and ε is the measurement error with a known density function. Set f n （ x ）to be a nonparametric kernel density estimator of f X,and the pointwise and uniform moderate deviations of statistic sup x∈ R ｜ f n （ x ） f n（ x） ｜are given by Gine and Guillou＇s exponential inequality.展开更多
基金Research supported by the National Natural Science Foundation of China (10271091)
文摘Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove moderate deviations and large deviations for the statistic sup ｜fn（x） - fn（-x） ｜.
文摘This paper develops the theory of the kth power expectile estimation and considers its relevant hypothesis tests for coefficients of linear regression models.We prove that the asymptotic covariance matrix of kth power expectile regression converges to that of quantile regression as k converges to one and hence promise a moment estimator of asymptotic matrix of quantile regression.The kth power expectile regression is then utilized to test for homoskedasticity and conditional symmetry of the data.Detailed comparisons of the local power among the kth power expectile regression tests,the quantile regression test,and the expectile regression test have been provided.When the underlying distribution is not standard normal,results show that the optimal k are often larger than 1 and smaller than 2,which suggests the general kth power expectile regression is necessary.Finally,the methods are illustrated by a real example.
文摘Suppose that Y1 , Y2 , , Yn are independent and identically distributed n observations from convolution model Y = X ＋ ε, where X is an unobserved random variable with unknown density f X,and ε is the measurement error with a known density function. Set f n （ x ）to be a nonparametric kernel density estimator of f X,and the pointwise and uniform moderate deviations of statistic sup x∈ R ｜ f n （ x ） f n（ x） ｜are given by Gine and Guillou＇s exponential inequality.
