Asymptotic Normality for Deconvolving Kernel Density Estimators
نویسنده
چکیده
Suppose that we have 11 observations from the convolution model Y = X + £, where X and £ are the independent unobservable random variables, and £ is measurement error with a known distribution. We will discuss the asymptotic normality for deconvolving kernel density estimators of the unknown density f x 0 of X by assuming either the tail of the characteristic function of £ behaves as II I~Oexp(11.1 13/1) as I ~ 00 (which is called supersmooth error), or the tail of the characteristic function is of order 0 (113) (called ordinary smooth error). Asymptotic normality of estimating the funcI tional T if) =L aj f (j l(;e 0) is also addressed. I
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