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
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.
