共查询到20条相似文献,搜索用时 78 毫秒
1.
This paper presents a kernel smoothing method for multinomial regression. A class of estimators of the regression functions is constructed by minimizing a localized power-divergence measure. These estimators include the bandwidth and a single parameter originating in the power-divergence measure as smoothing parameters. An asymptotic theory for the estimators is developed and the bias-adjusted estimators are obtained. A data-based algorithm for selecting the smoothing parameters is also proposed. Simulation results reveal that the proposed algorithm works efficiently. 相似文献
2.
Ivana Horová 《Journal of Computational Analysis and Applications》2000,2(3):253-263
Kernel smoothing provides a simple way of finding a structure in data. Oneof the most popular settings where kernel smoothing ideas can be applied isthe simple regression model. In the context of kernel estimates of aregression function, the choice of a kernel from the different points ofview can be investigated. The aim of this paper is to present constructionsof minimum variance kernels and smooth kernels by means of the Legendrepolynomials and the Gegenbauer polynomials as well. Some of these kernelshave been introduced, e.g., in [2], [3], and [5], but here another approachby using the variational calculus is presented. 相似文献
3.
In multinomial logit models, the identifiability of parameter estimates is typically obtained by side constraints that specify one of the response categories as reference category. When parameters are penalized, shrinkage of estimates should not depend on the reference category. In this paper we investigate ridge regression for the multinomial logit model with symmetric side constraints, which yields parameter estimates that are independent of the reference category. In simulation studies the results are compared with the usual maximum likelihood estimates and an application to real data is given. 相似文献
4.
Jonathan C. Marshall 《Journal of multivariate analysis》2010,101(4):949-963
In some applications of kernel density estimation the data may have a highly non-uniform distribution and be confined to a compact region. Standard fixed bandwidth density estimates can struggle to cope with the spatially variable smoothing requirements, and will be subject to excessive bias at the boundary of the region. While adaptive kernel estimators can address the first of these issues, the study of boundary kernel methods has been restricted to the fixed bandwidth context. We propose a new linear boundary kernel which reduces the asymptotic order of the bias of an adaptive density estimator at the boundary, and is simple to implement even on an irregular boundary. The properties of this adaptive boundary kernel are examined theoretically. In particular, we demonstrate that the asymptotic performance of the density estimator is maintained when the adaptive bandwidth is defined in terms of a pilot estimate rather than the true underlying density. We examine the performance for finite sample sizes numerically through analysis of simulated and real data sets. 相似文献
5.
In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure. 相似文献
6.
In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure. 相似文献
7.
Chin-Tsang Chiang Mei-Cheng Wang 《Annals of the Institute of Statistical Mathematics》2009,61(1):197-213
This article mainly considers the recurrent event process with independent censoring mechanism through a more flexible varying-coefficient
model. The smoothing estimators for the varying-coefficient functions are also proposed via maximizing the kernel weight version
of the log-partial likelihood function with respect to the coefficients at each time point. For the selection of appropriate
bandwidths and the construction of confidence intervals, the consistent empirical smoothing estimators for the covariance
functions of the estimators and a bias correction method are considered. As for the baseline effect function of recurrent
events in the population, two different smoothing estimation methods are suggested and investigated. In this study, the asymptotic
properties of the proposed smoothing estimators are derived. The finite sample properties of our methods are examined through
a Monte Carlo simulation. Moreover, the procedures are applied to a recurrent sample of AIDS link to intravenous experiences
(ALIVE) cohort study. 相似文献
8.
Shuangge Ma Michael R. Kosorok 《Annals of the Institute of Statistical Mathematics》2006,58(3):511-526
Current status data arises when a continuous response is reduced to an indicator of whether the response is greater or less
than a random threshold value. In this article we consider adaptive penalized M-estimators (including the penalized least
squares estimators and the penalized maximum likelihood estimators) for nonparametric and semiparametric models with current
status data, under the assumption that the unknown nonparametric parameters belong to unknown Sobolev spaces. The Cox model
is used as a representative of the semiparametric models. It is shown that the modified penalized M-estimators of the nonparametric
parameters can achieve adaptive convergence rates, even when the degrees of smoothing are not known in advance.
consistency, asymptotic normality and inference based on the weighted bootstrap for the estimators of the regression parameter
in the Cox model are also established. A simulation study is conducted for the Cox model to evaluate the finite sample efficacy
of the proposed approach and to compare it with the ordinary maximum likelihood estimator. It is demonstrated that the proposed
method is computationally superior.We apply the proposed approach to the California Partner Study analysis. 相似文献
9.
We consider the asymptotic analysis of penalized likelihood type estimators for generalized nonparametric regression problems in which the target parameter is a vector-valued function defined in terms of the conditional distribution of a response given a set of covariates. A variety of examples including ones related to generalized linear models and robust smoothing are covered by the theory. Linear approximations to the estimator are constructed using Taylor expansions in Hilbert spaces. An application which is treated is upper bounds on rates of convergence for the penalized likelihood-type estimators. 相似文献
10.
Chin-Tsang Chiang 《Annals of the Institute of Statistical Mathematics》2005,57(4):637-653
In this paper, we study the properties of the simultaneous and componentwise splines for the varying coefficient model with
repeatedly measured (longitudinal) dependent variable and time invariant covariates. The proposed simultaneous smoothing spline
estimators are mainly obtained from the penalized least squares with adjustment for the variations of covariates in the penalized
terms. We do this mainly to avoid the penalized terms being influenced by the scales of the covariates and the random smoothing
parameters appearing in the estimators, which complicates the derivation of the asymptotic properties of the estimators. It
is shown in this study that our estimators have smaller variances than the componentwise ones. Through a Monte Carlo simulation
and two empirical examples, the simultaneous smoothing splines are all found to be more accurate in the variances. 相似文献
11.
Basu and Basu (Statistica Sinica 8:841–860, 1998) have proposed an empty cell penalty for the minimum power-divergence estimators
which can lead to improvements in the small sample properties of these estimators. In this paper, we study the small and moderate
sample performances of the ordinary and penalized minimum power-divergence estimators in terms of efficiency and robustness
for the log-linear models in two-way contingency tables under the assumptions of multinomial sampling. Calculations made by
enumerating all possible sample combinations show that the penalized estimators are competitive with the ordinary estimators
for the moderate samples and definitely better for the smallest sample considered for both efficiency and robustness under
the considered models. The results also reveal that the bigger the main effects the more need for penalization. 相似文献
12.
《Journal of computational and graphical statistics》2013,22(1):82-100
We introduce a nonparametric time-dynamic kernel type density estimate for the situation where an underlying multivariate distribution evolves with time. Based on this time-dynamic density estimate, we propose nonparametric estimates for the time-dynamic mode of the underlying distribution. Our estimators involve boundary kernels for the time dimension so that the estimator is always centered at current time, and multivariate kernels for the spatial dimension of the time-evolving distribution. Under certain mild conditions, the asymptotic behavior of density and mode estimators, especially their uniform convergence in both time and space, is derived. A time-dynamic algorithm for mode tracking is proposed, including automatic bandwidth choices, and is implemented via a mean update algorithm. Simulation studies and real data illustrations demonstrate that the proposed methods work well in practice. 相似文献
13.
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
14.
Probability Density Function Estimation Using Gamma Kernels 总被引:6,自引:0,他引:6
Song Xi Chen 《Annals of the Institute of Statistical Mathematics》2000,52(3):471-480
We consider estimating density functions which have support on [0, ) using some gamma probability densities as kernels to replace the fixed and symmetric kernel used in the standard kernel density estimator. The gamma kernels are non-negative and have naturally varying shape. The gamma kernel estimators are free of boundary bias, non-negative and achieve the optimal rate of convergence for the mean integrated squared error. The variance of the gamma kernel estimators at a distance x away from the origin is O(n
–4/5
x
–1/2) indicating a smaller variance as x increases. Finite sample comparisons with other boundary bias free kernel estimators are made via simulation to evaluate the performance of the gamma kernel estimators. 相似文献
15.
16.
Majid Mojirsheibani 《Statistical Inference for Stochastic Processes》2006,9(1):97-107
A strong approximation of the smoothed empirical process of strictly stationary α-mixing random variables by a sequence of iid Gaussian processes will be studied.
Here, the smoothing is done via kernel density estimators. No assumptions are made on the support of the kernel; in fact,
our main results are stated for kernels with possibly an infinite support.
Received June 2003; Accepted February 2004. 相似文献
17.
Automatic model selection for partially linear models 总被引:1,自引:0,他引:1
We propose and study a unified procedure for variable selection in partially linear models. A new type of double-penalized least squares is formulated, using the smoothing spline to estimate the nonparametric part and applying a shrinkage penalty on parametric components to achieve model parsimony. Theoretically we show that, with proper choices of the smoothing and regularization parameters, the proposed procedure can be as efficient as the oracle estimator [J. Fan, R. Li, Variable selection via nonconcave penalized likelihood and its oracle properties, Journal of American Statistical Association 96 (2001) 1348–1360]. We also study the asymptotic properties of the estimator when the number of parametric effects diverges with the sample size. Frequentist and Bayesian estimates of the covariance and confidence intervals are derived for the estimators. One great advantage of this procedure is its linear mixed model (LMM) representation, which greatly facilitates its implementation by using standard statistical software. Furthermore, the LMM framework enables one to treat the smoothing parameter as a variance component and hence conveniently estimate it together with other regression coefficients. Extensive numerical studies are conducted to demonstrate the effective performance of the proposed procedure. 相似文献
18.
《Journal of computational and graphical statistics》2013,22(2):510-526
The calculation of nonparametric quantile regression curve estimates is often computationally intensive, as typically an expensive nonlinear optimization problem is involved. This article proposes a fast and easy-to-implement method for computing such estimates. The main idea is to approximate the costly nonlinear optimization by a sequence of well-studied penalized least squares-type nonparametric mean regression estimation problems. The new method can be paired with different nonparametric smoothing methods and can also be applied to higher dimensional settings. Therefore, it provides a unified framework for computing different types of nonparametric quantile regression estimates, and it also greatly broadens the scope of the applicability of quantile regression methodology. This wide applicability and the practical performance of the proposed method are illustrated with smoothing spline and wavelet curve estimators, for both uni- and bivariate settings. Results from numerical experiments suggest that estimates obtained from the proposed method are superior to many competitors. This article has supplementary material online. 相似文献
19.
Anestis Antoniadis Irène Gijbels Mila Nikolova 《Annals of the Institute of Statistical Mathematics》2011,63(3):585-615
One of the popular method for fitting a regression function is regularization: minimizing an objective function which enforces
a roughness penalty in addition to coherence with the data. This is the case when formulating penalized likelihood regression
for exponential families. Most of the smoothing methods employ quadratic penalties, leading to linear estimates, and are in
general incapable of recovering discontinuities or other important attributes in the regression function. In contrast, non-linear
estimates are generally more accurate. In this paper, we focus on non-parametric penalized likelihood regression methods using
splines and a variety of non-quadratic penalties, pointing out common basic principles. We present an asymptotic analysis of convergence rates that justifies the
approach. We report on a simulation study including comparisons between our method and some existing ones. We illustrate our
approach with an application to Poisson non-parametric regression modeling of frequency counts of reported acquired immune
deficiency syndrome (AIDS) cases in the UK. 相似文献
20.
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