共查询到20条相似文献,搜索用时 15 毫秒
1.
Irène Gijbels Alexandre Lambert Peihua Qiu 《Annals of the Institute of Statistical Mathematics》2007,59(2):235-272
This paper deals with nonparametric estimation of a regression curve, where the estimation method should preserve possible
jumps in the curve. At each point x at which one wants to estimate the regression function, the method chooses in an adaptive way among three estimates: a local
linear estimate using only datapoints to the left of x, a local linear estimate based on only datapoints to the right of x, and finally a local linear estimate using data in a two-sided neighbourhood around x. The choice among these three estimates is made by looking at differences of the weighted residual mean squares of the three
fits. The resulting estimate preserves the jumps well and in addition gives smooth estimates of the continuity parts of the
curve. This property of compromise between local smoothing and jump-preserving is what distinguishes our method from most
previously proposed methods, that mainly focused on local smoothing and consequently blurred possible jumps, or mainly focused
on jump-preserving and hence led to rather noisy estimates in continuity regions of the underlying regression curve. Strong
consistency of the estimator is established and its performance is tested via a simulation study. This study also compares
the current method with some existing methods. The current method is illustrated in analyzing a real dataset. 相似文献
2.
A great deal of effort has been devoted to the inference of additive model in the last decade. Among existing procedures,
the kernel type are too costly to implement for high dimensions or large sample sizes, while the spline type provide no asymptotic
distribution or uniform convergence. We propose a one step backfitting estimator of the component function in an additive
regression model, using spline estimators in the first stage followed by kernel/local linear estimators. Under weak conditions,
the proposed estimator’s pointwise distribution is asymptotically equivalent to an univariate kernel/local linear estimator,
hence the dimension is effectively reduced to one at any point. This dimension reduction holds uniformly over an interval
under assumptions of normal errors. Monte Carlo evidence supports the asymptotic results for dimensions ranging from low to
very high, and sample sizes ranging from moderate to large. The proposed confidence band is applied to the Boston housing
data for linearity diagnosis.
Supported in part by NSF awards DMS 0405330, 0706518, BCS 0308420 and SES 0127722. 相似文献
3.
Varying coefficient error-in-covariables models are considered with surrogate data and validation sampling. Without specifying any error structure equation, two estimators for the coefficient function vector are suggested by using the local linear kernel smoothing technique. The proposed estimators are proved to be asymptotically normal. A bootstrap procedure is suggested to estimate the asymptotic variances. The data-driven bandwidth selection method is discussed. A simulation study is conducted to evaluate the proposed estimating methods. 相似文献
4.
Muhammad Hanif 《随机分析与应用》2013,31(6):956-974
This article addresses the problem of nonparametric estimation of the first and second infinitesimal moments by using the local linear method of the underlying jump-diffusion models. The motivation behind the study is to use the asymmetric kernels instead of standard kernel smoothing. The basic idea relies on replacing the symmetric kernel by asymmetric kernel and provides a new way of obtaining the nonparametric estimation for jump-diffusion models. We prove that the estimators based on the local linear method for jump-diffusion models are consistent and asymptotically follow normal distribution under the condition of recurrence and stationarity. 相似文献
5.
The effects of moderate levels of serial correlation on one-sided and ordinary cross-validation in the context of local linear and kernel smoothing is investigated. It is shown both theoretically and by simulation that one-sided cross-validation is much less adversely affected by correlation than is ordinary cross-validation. The former method is a reliable means of window width selection in the presence of moderate levels of serial correlation, while the latter is not. It is also shown that ordinary cross-validation is less robust to correlation when applied to Gasser-Müller kernel estimators than to local linear ones. 相似文献
6.
In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective. 相似文献
7.
Anne van Delft Michael Eichler 《Journal of computational and graphical statistics》2019,28(2):244-255
This article introduces a data-adaptive nonparametric approach for the estimation of time-varying spectral densities from nonstationary time series. Time-varying spectral densities are commonly estimated by local kernel smoothing. The performance of these nonparametric estimators, however, depends crucially on the smoothing bandwidths that need to be specified in both time and frequency direction. As an alternative and extension to traditional bandwidth selection methods, we propose an iterative algorithm for constructing localized smoothing kernels data-adaptively. The main idea, inspired by the concept of propagation-separation, is to determine for a point in the time-frequency plane the largest local vicinity over which smoothing is justified by the data. By shaping the smoothing kernels nonparametrically, our method not only avoids the problem of bandwidth selection in the strict sense but also becomes more flexible. It not only adapts to changing curvature in smoothly varying spectra but also adjusts for structural breaks in the time-varying spectrum. Supplementary materials, including the R package tvspecAdapt containing an implementation of the routine, are available online. 相似文献
8.
9.
A sequential asymptotically efficient procedure is constructed for estimating the drift coefficient at a given state point
in ergodic diffusion processes. Sequential kernel estimators are used. The optimal convergence rate with the sharp constant
is given for a local minimax risk. 相似文献
10.
Burkhardt Seifert Michael Brockmann Joachim Engel Theo Gasser 《Journal of computational and graphical statistics》2013,22(2):192-213
Abstract Naive implementations of local polynomial fits and kernel estimators require almost O(n 2) operations. In this article two fast O(n) algorithms for nonparametric local polynomial fitting are presented. They are based on updating normal equations. Numerical stability is guaranteed by controlling ill-conditioned situations for small bandwidths and data-tuned restarting of the updating procedure. Restarting at every output point results in a moderately fast but highly stable O(n 7/5) algorithm. Applicability of algorithms is evaluated for estimation of regression curves and their derivatives. The idea is also applied to kernel estimators of regression curves and densities. 相似文献
11.
12.
Summary We consider nonparametric estimation of hazard functions and their derivatives under random censorship, based on kernel smoothing of the Nelson (1972) estimator. One critically important ingredient for smoothing methods is the choice of an appropriate bandwidth. Since local variance of these estimates depends on the point where the hazard function is estimated and the bandwidth determines the trade-off between local variance and local bias, data-based local bandwidth choice is proposed. A general principle for obtaining asymptotically efficient data-based local bandwiths, is obtained by means of weak convergence of a local bandwidth process to a Gaussian limit process. Several specific asymptotically efficient bandwidth estimators are discussed. We propose in particular an, asymptotically efficient method derived from direct pilot estimators of the hazard function and of the local mean squared error. This bandwidth choice method has practical advantages and is also of interest in the uncensored case as well as for density estimation.Research supported by UC Davis Faculty Research Grant and by Air Force grant AFOSR-89-0386Research supported by Air Force grant AFOSR-89-0386 相似文献
13.
Jianqing Fan Theo Gasser Irène Gijbels Michael Brockmann Joachim Engel 《Annals of the Institute of Statistical Mathematics》1997,49(1):79-99
We consider local polynomial fitting for estimating a regression function and its derivatives nonparametrically. This method possesses many nice features, among which automatic adaptation to the boundary and adaptation to various designs. A first contribution of this paper is the derivation of an optimal kernel for local polynomial regression, revealing that there is a universal optimal weighting scheme. Fan (1993, Ann. Statist., 21, 196-216) showed that the univariate local linear regression estimator is the best linear smoother, meaning that it attains the asymptotic linear minimax risk. Moreover, this smoother has high minimax risk. We show that this property also holds for the multivariate local linear regression estimator. In the univariate case we investigate minimax efficiency of local polynomial regression estimators, and find that the asymptotic minimax efficiency for commonly-used orders of fit is 100% among the class of all linear smoothers. Further, we quantify the loss in efficiency when going beyond this class. 相似文献
14.
Jib Huh 《Journal of multivariate analysis》2010,101(7):1681-1700
In this paper, we consider the regression function or its νth derivative in generalized linear models which may have a change/discontinuity point at an unknown location. The location and its jump size are estimated with the local polynomial fits based on one-sided kernel weighted local-likelihood functions. Asymptotic distributions of the proposed estimators of location and jump size are established. The finite-sample performances of the proposed estimators with practical aspects are illustrated by simulated and beetle mortality examples. 相似文献
15.
Numerical discretization-based kernel type estimation methods for ordinary differential equation models
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We consider the problem of parameter estimation in both linear and nonlinear ordinary differential equation(ODE) models. Nonlinear ODE models are widely used in applications. But their analytic solutions are usually not available. Thus regular methods usually depend on repetitive use of numerical solutions which bring huge computational cost. We proposed a new two-stage approach which includes a smoothing method(kernel smoothing or local polynomial fitting) in the first stage, and a numerical discretization method(Eulers discretization method, the trapezoidal discretization method,or the Runge–Kutta discretization method) in the second stage. Through numerical simulations, we find the proposed method gains a proper balance between estimation accuracy and computational cost.Asymptotic properties are also presented, which show the consistency and asymptotic normality of estimators under some mild conditions. The proposed method is compared to existing methods in term of accuracy and computational cost. The simulation results show that the estimators with local linear smoothing in the first stage and trapezoidal discretization in the second stage have the lowest average relative errors. We apply the proposed method to HIV dynamics data to illustrate the practicability of the estimator. 相似文献
16.
Zhan-Qian Lu 《Journal of multivariate analysis》1996,59(2):187-205
Nonparametric regression estimator based on locally weighted least squares fitting has been studied by Fan and Ruppert and Wand. The latter paper also studies, in the univariate case, nonparametric derivative estimators given by a locally weighted polynomial fitting. Compared with traditional kernel estimators, these estimators are often of simpler form and possess some better properties. In this paper, we develop current work on locally weighted regression and generalize locally weighted polynomial fitting to the estimation of partial derivatives in a multivariate regression context. Specifically, for both the regression and partial derivative estimators we prove joint asymptotic normality and derive explicit asymptotic expansions for their conditional bias and conditional convariance matrix (given observations of predictor variables) in each of the two important cases of local linear fit and local quadratic fit. 相似文献
17.
Likelihood estimation of the extremal index 总被引:1,自引:0,他引:1
Mária Süveges 《Extremes》2007,10(1-2):41-55
The article develops the approach of Ferro and Segers (J.R. Stat. Soc., Ser. B 65:545, 2003) to the estimation of the extremal index, and proposes the use of a new variable decreasing the bias of the likelihood based
on the point process character of the exceedances. Two estimators are discussed: a maximum likelihood estimator and an iterative
least squares estimator based on the normalized gaps between clusters. The first provides a flexible tool for use with smoothing
methods. A diagnostic is given for condition , under which maximum likelihood is valid. The performance of the new estimators were tested by extensive simulations. An
application to the Central England temperature series demonstrates the use of the maximum likelihood estimator together with
smoothing methods.
相似文献
18.
Suppose we want to estimate a density at a point where we know the values of its first or higher order derivatives. In this case a given kernel estimator of the density can be modified by adding appropriately weighted kernel estimators of these derivatives. We give conditions under which the modified estimators are asymptotically normal. We also determine the optimal weights. When the highest derivative is known to vanish at a point, then the bias is asymptotically negligible at that point and the asymptotic variance of the kernel estimator can be made arbitrarily small by choosing a large bandwidth. 相似文献
19.
Frederico Caeiro Lígia Henriques‐Rodrigues 《Mathematical Methods in the Applied Sciences》2019,42(17):5867-5880
In this paper, we deal with the semi‐parametric estimation of the extreme value index, an important parameter in extreme value analysis. It is well known that many classic estimators, such as the Hill estimator, reveal a strong bias. This problem motivated the study of two classes of kernel estimators. Those classes generalize the classical Hill estimator and have a tuning parameter that enables us to modify the asymptotic mean squared error and eventually to improve their efficiency. Since the improvement in efficiency is not very expressive, we also study new reduced bias estimators based on the two classes of kernel statistics. Under suitable conditions, we prove their asymptotic normality. Moreover, an asymptotic comparison, at optimal levels, shows that the new classes of reduced bias estimators are more efficient than other reduced bias estimator from the literature. An illustration of the finite sample behaviour of the kernel reduced‐bias estimators is also provided through the analysis of a data set in the field of insurance. 相似文献