共查询到10条相似文献,搜索用时 15 毫秒
1.
F. Abramovich T. Sapatinas & B. W. Silverman 《Journal of the Royal Statistical Society. Series B, Statistical methodology》1998,60(4):725-749
We discuss a Bayesian formalism which gives rise to a type of wavelet threshold estimation in nonparametric regression. A prior distribution is imposed on the wavelet coefficients of the unknown response function, designed to capture the sparseness of wavelet expansion that is common to most applications. For the prior specified, the posterior median yields a thresholding procedure. Our prior model for the underlying function can be adjusted to give functions falling in any specific Besov space. We establish a relationship between the hyperparameters of the prior model and the parameters of those Besov spaces within which realizations from the prior will fall. Such a relationship gives insight into the meaning of the Besov space parameters. Moreover, the relationship established makes it possible in principle to incorporate prior knowledge about the function's regularity properties into the prior model for its wavelet coefficients. However, prior knowledge about a function's regularity properties might be difficult to elicit; with this in mind, we propose a standard choice of prior hyperparameters that works well in our examples. Several simulated examples are used to illustrate our method, and comparisons are made with other thresholding methods. We also present an application to a data set that was collected in an anaesthesiological study. 相似文献
2.
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 where a prediction of a data point is made. The residual from the prediction
is stored and can be thought of as a wavelet coefficient. This article exploits the flexibility of lifting by adaptively choosing
the kind of prediction according to a criterion. In this way the smoothness of the underlying ‘wavelet’ can be adapted to
the local properties of the function. Multiple observations at a point can readily be handled by lifting through a suitable
choice of prediction. We adapt existing shrinkage rules to work with our adaptive lifting methods.
We use simulation to demonstrate the improved sparsity of our techniques and improved regression performance when compared
to both wavelet and non-wavelet methods suitable for irregular data. We also exhibit the benefits of our adaptive lifting
on the real inductance plethysmography and motorcycle data. 相似文献
3.
Natalie Neumeyer Juan Carlos Pardo-Fernndez 《Journal of statistical planning and inference》2009,139(12):4006-4016
In this article we present a simple procedure to test for the null hypothesis of equality of two regression curves versus one-sided alternatives in a general nonparametric and heteroscedastic setup. The test is based on the comparison of the sample averages of the estimated residuals in each regression model under the null hypothesis. The test statistic has asymptotic normal distribution and can detect any local alternative of rate n-1/2. Some simulations and an application to a data set are included. 相似文献
4.
Klaus Abberger 《Statistical Papers》2006,47(1):1-15
The procedures of estimating prediction intervals for ARMA processes can be divided into model based methods and empirical
methods. Model based methods require knowledge of the model and the underlying innovation distribution. Empirical methods
are based on sample forecast errors. In this paper we apply nonparametric quantile regression to empirical forecast errors
using lead time as regressor. Using this method there is no need for a distributional assumption. But for the special data
pattern in this application a double kernel method which allows smoothing in two directions is required. An estimation algorithm
is presented and applied to some simulation examples. 相似文献
5.
E. Shirazi H. Doosti H.A. Niroumand N. Hosseinioun 《Journal of statistical planning and inference》2013
Here we consider wavelet-based identification and estimation of a censored nonparametric regression model via block thresholding methods and investigate their asymptotic convergence rates. We show that these estimators, based on block thresholding of empirical wavelet coefficients, achieve optimal convergence rates over a large range of Besov function classes, and in particular enjoy those rates without the extraneous logarithmic penalties that are usually suffered by term-by-term thresholding methods. This work is extension of results in Li et al. (2008). The performance of proposed estimator is investigated by a numerical study. 相似文献
6.
Birgitte B. Rønn 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2001,63(2):243-259
The analysis of a sample of curves can be done by self-modelling regression methods. Within this framework we follow the ideas of nonparametric maximum likelihood estimation known from event history analysis and the counting process set-up. We derive an infinite dimensional score equation and from there we suggest an algorithm to estimate the shape function for a simple shape invariant model. The nonparametric maximum likelihood estimator that we find turns out to be a Nadaraya–Watson-like estimator, but unlike in the usual kernel smoothing situation we do not need to select a bandwidth or even a kernel function, since the score equation automatically selects the shape and the smoothing parameter for the estimation. We apply the method to a sample of electrophoretic spectra to illustrate how it works. 相似文献
7.
The estimation of a multivariate function from a stationary m-dependent process is investigated, with a special focus on the case where m is large or unbounded. We develop an adaptive estimator based on wavelet methods. Under flexible assumptions on the nonparametric model, we prove the good performances of our estimator by determining sharp rates of convergence under two kinds of errors: the pointwise mean squared error and the mean integrated squared error. We illustrate our theoretical result by considering the multivariate density estimation problem, the derivatives density estimation problem, the density estimation problem in a GARCH-type model and the multivariate regression function estimation problem. The performance of proposed estimator has been shown by a numerical study for a simulated and real data sets. 相似文献
8.
《Journal of Statistical Computation and Simulation》2012,82(3):269-285
The main object of this paper is the approximate Bayes estimation of the five dimensional vector of parameters and the reliability function of a mixture of two Weibull distributions under Type-2 censoring. Under Type-2 censoring, the posterior distribution is complicated, and the integrals involved cannot be obtained in a simple closed form. In this work, Lindley's (1980) approximate form of Bayes estimation is used in the case of a mixture of two Weibull distributions under Type-2 censoring. Through Monte Carlo simulation, the root mean squared errors (RMSE's) of the Bayes estimates are computed and compared with the corresponding estimated RMSE's of the maximum likelihood estimates. 相似文献
9.
10.
This article gives a unified account of nonparametric statistics, covering testing, estimating, multiple comparisons, analysis of variance and regression, for rounded-off data, with ties handled by the average scores method. The theory is illustrated by means of numerous applications to the Biomedical, Engineering and Behavioral Sciences. 相似文献