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针对响应变量随机缺失的强混合函数型时间序列数据,首次提出了非参数回归模型的k近邻估计,并在一些正则条件下建立了k近邻回归算子的几乎完全一致收敛速度.此研究不仅推进了函数型非参数模型的理论研究,也为函数型数据的实际应用领域提供了理论支撑. 相似文献
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本文主要研究非参数异方差回归模型的局部多项式估计问题.首先利用局部线性逼近的技巧,得到了回归均值函数的局部极大似然估计.然后,考虑到回归方差函数的非负性,利用局部对数多项式拟合,得到了方差函数的局部多项式估计,保证了估计量的非负性,并证明了估计量的渐近性质.最后,通过对农村居民消费与收入的实证研究,说明了非参数异方差回归模型的局部多项式方法比普通最小二乘估计法的拟合效果更好,并且预测的精度更高. 相似文献
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针对函数型非参数回归模型,基于相依数据场合,研究了模型中响应变量随机缺失的回归算子核估计问题.在一定的条件下,采用Kolmogorov熵得到了核估计量的几乎一致完全收敛速度. 相似文献
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传统函数型回归模型变量选择方法,忽略了对稀疏函数型数据的讨论.提出了稀疏函数型数据情形下函数型回归模型的变量选择方法,基于条件期望对稀疏函数型自变量进行函数型主成分分析,并以估计的正交特征函数作为基函数对模型进行展开.这种方法可以有效解决对稀疏函数型变量的选择.作为实证分析,选取2002年到2011年全国34个气象观测站的年降水量,月度平均气温,光照时长,湿度,最高气温和最低气温数据,分别比较讨论了密集和稀疏情形下,原始样本和Bootstrap样本的函数型回归模型变量选择的结果,结果显示新方法具有较好的选择效果. 相似文献
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Philip T. Reiss Lei Huang Yin-Hsiu Chen Lan Huo Thaddeus Tarpey Maarten Mennes 《Journal of computational and graphical statistics》2013,22(1):232-248
A penalized approach is proposed for performing large numbers of parallel nonparametric analyses of either of two types: restricted likelihood ratio tests of a parametric regression model versus a general smooth alternative, and nonparametric regression. Compared with naïvely performing each analysis in turn, our techniques reduce computation time dramatically. Viewing the large collection of scatterplot smooths produced by our methods as functional data, we develop a clustering approach to summarize and visualize these results. Our approach is applicable to ultra-high-dimensional data, particularly data acquired by neuroimaging; we illustrate it with an analysis of developmental trajectories of functional connectivity at each of approximately 70,000 brain locations. Supplementary materials, including an appendix and an R package, are available online. 相似文献
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There is a recent interest in developing new statistical methods to predict time series by taking into account a continuous set of past values as predictors. In this functional time series prediction approach, we propose a functional version of the partial linear model that allows both to consider additional covariates and to use a continuous path in the past to predict future values of the process. The aim of this paper is to present this model, to construct some estimates and to look at their properties both from a theoretical point of view by means of asymptotic results and from a practical perspective by treating some real data sets. Although the literature on the use of parametric or nonparametric functional modeling is growing, as far as we know, this is the first paper on semiparametric functional modeling for the prediction of time series. 相似文献
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This paper studies estimation in functional partial
linear composite quantile regression model in which the dependent variable
is related to both a function-valued random variable in linear form and a
real-valued random variable in nonparametric form. The functional principal
component analysis and regression splines are employed to estimate the slope
function and the nonparametric function respectively, and the convergence
rates of the estimators are obtained under some regularity conditions.
Simulation studies and a real data example are presented for illustration
of the performance of the proposed estimators. 相似文献
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We consider the problem of estimation in semiparametric varying coefficient models where the covariate modifying the varying coefficients is functional and is modeled nonparametrically. We develop a kernel-based estimator of the nonparametric component and a profiling estimator of the parametric component of the model and derive their asymptotic properties. Specifically, we show the consistency of the nonparametric functional estimates and derive the asymptotic expansion of the estimates of the parametric component. We illustrate the performance of our methodology using a simulation study and a real data application. 相似文献
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In this paper, we introduce a semi-functional linear model in which a scalar response variable is explained by a linear operator of a random function and a nonparametric function of a real-valued random variable. We study the spline estimators of the functional coefficient and nonparametric function and obtain the rates of convergence of the spline estimators. Finally, we present some simulation results that illustrate the performance of our estimation method. 相似文献
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Philip T. Reiss David L. Miller Pei-Shien Wu Wen-Yu Hua 《Journal of computational and graphical statistics》2017,26(3):569-578
A number of classical approaches to nonparametric regression have recently been extended to the case of functional predictors. This article introduces a new method of this type, which extends intermediate-rank penalized smoothing to scalar-on-function regression. In the proposed method, which we call principal coordinate ridge regression, one regresses the response on leading principal coordinates defined by a relevant distance among the functional predictors, while applying a ridge penalty. Our publicly available implementation, based on generalized additive modeling software, allows for fast optimal tuning parameter selection and for extensions to multiple functional predictors, exponential family-valued responses, and mixed-effects models. In an application to signature verification data, principal coordinate ridge regression, with dynamic time warping distance used to define the principal coordinates, is shown to outperform a functional generalized linear model. Supplementary materials for this article are available online. 相似文献
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The additive–multiplicative hazards (AMH) regression model specifies an additive and multiplicative form on the hazard function for the counting process associated with a multidimensional covariate process, which contains the Cox proportional hazards model and the additive hazards model as its special cases. In this paper, we study the AMH model with current status data, where the cumulative hazard hazard function is assumed to be nonparametric and is estimated using B-splines with monotonicity constraint on the functional, while a simultaneous sieve maximum likelihood estimation is proposed to estimate regression parameters. The proposed estimator for the parameter vector is shown to be asymptotically normal and semiparametric efficient. The B-splines estimator of the functional of the cumulative hazard function is shown to achieve the optimal nonparametric rate of convergence. A simulation study is conducted to examine the finite sample performance of the proposed estimators and algorithm, and a real data example is presented for illustration. 相似文献
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In the research it is frequently assumed
that the growth curve is a polynomial in time. In practice,
researchers mainly use higher-order polynomials to obtain more
precise estimates. But this method has many defects, such as the
model can be easily affected by outliers and the polynomial
hypothesis may be much strong in practice. So in this paper we first
proposed nonparametric approach, local polynomial, instead of
parametric method for estimation in growth curve model. We give the
nonparametric growth curve model, and its nonparametric estimation.
Then discuss the large sample character of local polynomial
estimate. The ideal theoretical choice of a local bandwidth is also
discussed in detail in this paper. Finally, through the simulation
study, from the fitting curve and average square error box plot we
can clearly see that the performance of nonparametric approach is
much better than parametric technique. 相似文献
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Because of its orthogonality, interpretability and best representation, functional principal component analysis approach has been extensively used to estimate the slope function in the functional linear model. However, as a very popular smooth technique in nonparametric/semiparametric regression, polynomial spline method has received little attention in the functional data case. In this paper, we propose the polynomial spline method to estimate a partial functional linear model. Some asymptotic results are established, including asymptotic normality for the parameter vector and the global rate of convergence for the slope function. Finally, we evaluate the performance of our estimation method by some simulation studies. 相似文献
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首次利用短期利率模型,分析香港银行同业拆借利率(Hibor),揭示了最近十年内香港银行同业拆借利率的基本特征.初步分析表明,Hibor数据的平稳性不能保证,因此采用了非参数统计方法.利用bandi文章中的方法,给出了函数的漂移项和扩散项的非参数估计,同时还得到了过程的局部时估计.通过实证分析,发现香港银行间同业拆借利率在2006至2015年间,以2009年为界,前后两个时间段的数据表现出不同的特征,样本数据的局部时函数也表现为双峰分布. 相似文献