Adaptive wavelet estimator for nonparametric density deconvolution
نویسندگان
چکیده
منابع مشابه
Adaptive Wavelet Estimator for Nonparametricdensity Deconvolution
Hence the problem of estimating g in (1.2) is called a deconvolution problem. The problem arises in many applications [see, e.g., Desouza (1991), Louis (1991), Zhang (1992)] and, therefore, it was studied extensively in the last decade. The most popular approach to the problem was to estimate p x by a kernel estimator and then solve equation (1.2) using a Fourier transform [see Carroll and Hall...
متن کاملPenalized contrast estimator for adaptive density deconvolution
The authors consider the problem of estimating the density g of independent and identically distributed variables Xi, from a sample Z1, . . . , Zn where Zi = Xi + σεi, i = 1, . . . , n, ε is a noise independent of X, with σε having known distribution. They present a model selection procedure allowing to construct an adaptive estimator of g and to find non-asymptotic bounds for its L2(R)-risk. T...
متن کاملOn pointwise adaptive nonparametric deconvolution
We consider estimating an unknown function f from indirect white noise observations with particular emphasis on the problem of nonparametric deconvolution. Non-parametric estimators that can adapt to unknown smoothness of f are developed. The adaptive estimators are speciied under two sets of assumptions on the kernel of the convolution transform. In particular, kernels having the Fourier trans...
متن کاملWavelet Density Estimator for Stochastic Processes
Let (X t) be a stictly stationary stochastic process (in continuous or discrete time). We are to estimate the density f of X t on the basis of discrete observations (X i); i = 1; :::; N using a \linear" wavelet estimator. For the continuous time process (X t); 0 t T those observations are the result of a regular discretization of the continuous time trajectory. We provide an adaptive version of...
متن کاملNonparametric density deconvolution by weighted kernel estimators
JSM, Denver, 4 August 2008 – 3 / 23 We observe a univariate random sample Y1, . . . , Yn from a density g, where Yi = Xi + Zi (i = 1, . . . , n). Here X1, . . . , Xn are independent and identically distributed with unknown continuous density f , and the measurement errors Z1, . . . , Zn form a random sample from the continuous density η which we assume to be known. Our goal is to obtain a nonpa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 1999
ISSN: 0090-5364
DOI: 10.1214/aos/1017939249