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
This paper addresses estimation and its asymptotics of mean transformation θ = E[h（X）] of a random variable X based on n lid. observations from errors-in-variables model Y = X＋ v, where v is a measurement error wi...This paper addresses estimation and its asymptotics of mean transformation θ = E[h（X）] of a random variable X based on n lid. observations from errors-in-variables model Y = X＋ v, where v is a measurement error with a known distribution and h（.） is a known smooth function. The asymptotics of deconvolution kernel estimator for ordinary smooth error distribution and expectation extrapolation estimator are given for normal error distribution respectively. Under some mild regularity conditions, the consistency and asymptotically normality are obtained for both type of estimators. Simulations show they have good performance.展开更多
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.
基金This research is supported by the National Natural Science Foundation of China(Grant No. 19771011 and 10071009) the RFDP (No. 20020027010) of MOE.
文摘This paper addresses estimation and its asymptotics of mean transformation θ = E[h（X）] of a random variable X based on n lid. observations from errors-in-variables model Y = X＋ v, where v is a measurement error with a known distribution and h（.） is a known smooth function. The asymptotics of deconvolution kernel estimator for ordinary smooth error distribution and expectation extrapolation estimator are given for normal error distribution respectively. Under some mild regularity conditions, the consistency and asymptotically normality are obtained for both type of estimators. Simulations show they have good performance.
