Adaptive estimators for nonparametric heteroscedastic regression models
نویسندگان
چکیده
منابع مشابه
Asymptotically efficient estimators for nonparametric heteroscedastic regression models
This paper concerns the estimation of a function at a point in nonparametric heteroscedastic regression models with Gaussian noise or noise having unknown distribution. In those cases an asymptotically efficient kernel estimator is constructed for the minimax absolute error risk.
متن کاملNonparametric Goodness-of-fit Test for Heteroscedastic Regression Models
For the heteroscedastic nonparametric regression model Yni = m(xni)+σ(xni)2ni, i = 1, ..., n, a novel method is proposed for testing that the regression function m is constant. The test statistic is motivated by recent developments in the asymptotic theory for analysis of variance when the number of factor levels is large. Its asymptotic normality is derived under the null hypothesis and suitab...
متن کاملAdaptive Variance Function Estimation in Heteroscedastic Nonparametric Regression
We consider a wavelet thresholding approach to adaptive variance function estimation in heteroscedastic nonparametric regression. A data-driven estimator is constructed by applying wavelet thresholding to the squared first-order differences of the observations. We show that the variance function estimator is nearly optimally adaptive to the smoothness of both the mean and variance functions. Th...
متن کاملEfficient Quantile Regression for Heteroscedastic Models
Quantile regression provides estimates of a range of conditional quantiles. This stands in contrast to traditional regression techniques, which focus on a single conditional mean function. Lee et al. (2012) proposed efficient quantile regression by rounding the sharp corner of the loss. The main modification generally involves an asymmetric l2 adjustment of the loss function around zero. We ext...
متن کاملAdaptive lifting for nonparametric regression
Many wavelet shrinkage methods assume that the data are observed on an equally spaced grid of length of the form 2J for some J . These methods require serious modification or preprocessed data to cope with irregularly spaced data. The lifting scheme is a recent mathematical innovation that obtains a multiscale analysis for irregularly spaced data. A key lifting component is the “predict” step w...
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: Journal of Nonparametric Statistics
سال: 2009
ISSN: 1048-5252,1029-0311
DOI: 10.1080/10485250902993645