共查询到20条相似文献,搜索用时 31 毫秒
1.
设X为p维随机向量,对于未知的投影方向θo(‖θo‖=1),本文利用θo的估计与核密度估计相结合的方法给出了θ^T0X的密度(方向密度)的核型密度估计,获得了此估计的逐点渐近正态性,逐点精确强收敛率,一致精确强收敛率以及均方误差收敛率,所得结果与最优性与已知方向上的核密度估计完全一致。作为例子,对θo为X协方差阵的最大特征值所对应的特征方向,我们给出了θo的满足条件的估计极其方向密度估计。 相似文献
2.
T. I. Savyolova M. V. Sypchenko 《Computational Mathematics and Mathematical Physics》2007,47(6):970-982
Kernel and projection methods for recovering the density function on the rotation group SO(3) are considered. Numerical examples are presented in which the density function is estimated depending on the sample size, a smoothing parameter (in the case of kernel methods), the approximation kernel, and the error in the input data. A set of orientations is specified by normally distributed rotations on SO(3) derived by the Monte Carlo method. 相似文献
3.
Dianne Cook Andreas Buja Javier Cabrera Catherine Hurley 《Journal of computational and graphical statistics》2013,22(3):155-172
Abstract The grand tour and projection pursuit are two methods for exploring multivariate data. We show how to combine them into a dynamic graphical tool for exploratory data analysis, called a projection pursuit guided tour. This tool assists in clustering data when clusters are oddly shaped and in finding general low-dimensional structure in high-dimensional, and in particular, sparse data. An example shows that the method, which is projection-based, can be quite powerful in situations that may cause grief for methods based on kernel smoothing. The projection pursuit guided tour is also useful for comparing and developing projection pursuit indexes and illustrating some types of asymptotic results. 相似文献
4.
5.
投影寻踪模型在国民经济综合评价中的应用 总被引:10,自引:0,他引:10
文章针对区域国民经济发展的多属性,采用投影寻踪评价模型,用加速遗传算法寻找最佳投影方向,将多维属性指标转换为一维投影值.在此基础上,通过建立单属性指标的分类等级区间,给出区域国民经济发展水平分类的投影值区间,从而实现对区域国民经济发展水平的分类.应用表明,它是国民经济评价的一种计算过程简单、直观的新方法. 相似文献
6.
在损失分布方法的基础上,本文基于非参数方法对商业银行操作风险的度量进行了研究。非参数方法对损失额的分布不作过多的设定,避免了由于分布误设可能出现的偏差。古典的核密度估计对损失额拟合的效果不太好,特别是尾部的拟合效果更差。变换后的核密度估计的拟合效果比古典的核密度估计改善很多.基于变换后的核密度估计对商业银行操作风险损失度量可以得到不同置信水平的VaR与ES,并且不同置信水平的差距比较大。基于非参数与基于参数方法得到的各个置信水平的VaR与ES有一定差距。 相似文献
7.
Gérard Kerkyacharian Oleg Lepski Dominique Picard 《Probability Theory and Related Fields》2001,121(2):137-170
In the framework of denoising a function depending of a multidimensional variable (for instance an image), we provide a nonparametric
procedure which constructs a pointwise kernel estimation with a local selection of the multidimensional bandwidth parameter.
Our method is a generalization of the Lepski's method of adaptation, and roughly consists in choosing the “coarsest” bandwidth
such that the estimated bias is negligible. However, this notion becomes more delicate in a multidimensional setting. We will
particularly focus on functions with inhomogeneous smoothness properties and especially providing a possible disparity of
the inhomogeneous aspect in the different directions. We show, in particular that our method is able to exactly attain the
minimax rate or to adapt to unknown degree of anisotropic smoothness up to a logarithmic factor, for a large scale of anisotropic
Besov spaces.
Received: 11 November 1999 / Revised version: 14 November 2000 / Published online: 24 July 2001 相似文献
8.
《International Journal of Approximate Reasoning》2014,55(4):989-1010
Non-parametric density estimation is an important technique in probabilistic modeling and reasoning with uncertainty. We present a method for learning mixtures of polynomials (MoPs) approximations of one-dimensional and multidimensional probability densities from data. The method is based on basis spline interpolation, where a density is approximated as a linear combination of basis splines. We compute maximum likelihood estimators of the mixing coefficients of the linear combination. The Bayesian information criterion is used as the score function to select the order of the polynomials and the number of pieces of the MoP. The method is evaluated in two ways. First, we test the approximation fitting. We sample artificial datasets from known one-dimensional and multidimensional densities and learn MoP approximations from the datasets. The quality of the approximations is analyzed according to different criteria, and the new proposal is compared with MoPs learned with Lagrange interpolation and mixtures of truncated basis functions. Second, the proposed method is used as a non-parametric density estimation technique in Bayesian classifiers. Two of the most widely studied Bayesian classifiers, i.e., the naive Bayes and tree-augmented naive Bayes classifiers, are implemented and compared. Results on real datasets show that the non-parametric Bayesian classifiers using MoPs are comparable to the kernel density-based Bayesian classifiers. We provide a free R package implementing the proposed methods. 相似文献
9.
1.IntroductionLinearregressionmodelsarewidelyusedinstatisticalanalysisofexperimentalandobservationaldata,thatis,oneoftenemploysastandardlinearmodely=or K: E,a.s.,(1.1)todostatisticalanalysis,whereydenotesascalaroutcomevariableand2denotesaP-dimensionalcolumnvectorofregressorvariables.Thismodelmeansthattheprojectionofthepdimensionalexplanatory2ontotheone-dimensionalsubspaceadZcapturesalltheinformationweneedtoknowabouttheoutcomevariabley.Thisisadimension-reductionmodel.Hencewemayreachthegoalofd… 相似文献
10.
Dmitri Pavlov Svetla Slavova Richard J. Kryscio 《Methodology and Computing in Applied Probability》2009,11(2):249-265
This paper considers a non-parametric method for identifying intervals on the line where the relative risk of cases to controls
exceeds a pre-specified level. The method is based on the kth nearest neighbor (kNN) approach for density estimation. An asymptotic result is presented that yields an explicit formula
for constructing a confidence interval for the relative risk at a given point. Numerical simulations are used to compare this
approach with a kernel density estimation procedure. An application is made to a case-control study in which the relative
risk of motor vehicle crashes caused by female drivers is compared to male drivers in the state of Kentucky as a function
of age and then by time of day.
相似文献
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Peter Hall 《Probability Theory and Related Fields》1988,80(1):51-77
Summary Estimation of orientation is a key operation at each step in projection pursuit. Since projection pursuit is a nonparametric algorithm, and since even low-dimensional approximations to the target function must converge to their limits at rates considerably slower than n
-1
2
(where n is sample size), then it might be thought that the same is true of orientation estimates. It is shown in the present paper that this is not the case, and that estimation of orientation is a parametric operation, in the sense that, under mild nonparametric assumptions, correctly-chosen kernel-type orientation estimates converge to their limits at rate n
-1
2
. This property is not enjoyed by standard projection pursuit orientation estimates, which converge at a slower rate than n
-1
2
. Most attention in the present paper is focussed on the case of projection pursuit density approximation, but it is pointed out that our arguments hold generally. An important practical conclusion is that data should be smoothed less when estimating orientation than when constructing the final projection pursuit approximation. 相似文献
13.
Dianne Cook Andreas Buja Javier Cabrera 《Journal of computational and graphical statistics》2013,22(3):225-250
Abstract Projection pursuit describes a procedure for searching high-dimensional data for “interesting” low-dimensional projections via the optimization of a criterion function called the projection pursuit index. By empirically examining the optimization process for several projection pursuit indexes, we observed differences in the types of structure that maximized each index. We were especially curious about differences between two indexes based on expansions in terms of orthogonal polynomials, the Legendre index, and the Hermite index. Being fast to compute, these indexes are ideally suited for dynamic graphics implementations. Both Legendre and Hermite indexes are weighted L 2 distances between the density of the projected data and a standard normal density. A general form for this type of index is introduced that encompasses both indexes. The form clarifies the effects of the weight function on the index's sensitivity to differences from normality, highlighting some conceptual problems with the Legendre and Hermite indexes. A new index, called the Natural Hermite index, which alleviates some of these problems, is introduced. A polynomial expansion of the data density reduces the form of the index to a sum of squares of the coefficients used in the expansion. This drew our attention to examining these coefficients as indexes in their own right. We found that the first two coefficients, and the lowest-order indexes produced by them, are the most useful ones for practical data exploration because they respond to structure that can be analytically identified, and because they have “long-sighted” vision that enables them to “see” large structure from a distance. Complementing this low-order behavior, the higher-order indexes are “short-sighted.” They are able to see intricate structure, but only when they are close to it. We also show some practical use of projection pursuit using the polynomial indexes, including a discovery of previously unseen structure in a set of telephone usage data, and two cautionary examples which illustrate that structure found is not always meaningful. 相似文献
14.
Denis Belomestny 《Stochastic Processes and their Applications》2011,121(6):1217-1244
The problem of estimating the Lévy density of a partially observed multidimensional affine process from low-frequency and mixed-frequency data is considered. The estimation methodology is based on the log-affine representation of the conditional characteristic function of an affine process and local linear smoothing in time. We derive almost sure uniform rates of convergence for the estimated Lévy density both in mixed-frequency and low-frequency setups and prove that these rates are optimal in the minimax sense. Finally, the performance of the estimation algorithms is illustrated in the case of the Bates stochastic volatility model. 相似文献
15.
K. P. Aganin T. I. Savyolova 《Computational Mathematics and Mathematical Physics》2008,48(6):1024-1038
The orientation density function is recovered from a sample of orientations on the rotation group SO(3) of the three-dimensional Euclidean space. Sufficient conditions for the consistency of kernel and projection estimates in L 2, L 1, and C are considered. Numerical results concerning the error estimation of projection methods over the basis of generalized spherical functions are given for normal distributions on SO(3). 相似文献
16.
《Journal of computational and graphical statistics》2013,22(1):101-120
In high-dimensional classification problems, one is often interested in finding a few important discriminant directions in order to reduce the dimensionality. Fisher's linear discriminant analysis (LDA) is a commonly used method. Although LDA is guaranteed to find the best directions when each class has a Gaussian density with a common covariance matrix, it can fail if the class densities are more general. Using a likelihood-based interpretation of Fisher's LDA criterion, we develop a general method for finding important discriminant directions without assuming the class densities belong to any particular parametric family. We also show that our method can be easily integrated with projection pursuit density estimation to produce a powerful procedure for (reduced-rank) nonparametric discriminant analysis. 相似文献
17.
In this paper, we discuss the estimation of a density function based on censored data by the kernel smoothing method when the survival and the censoring times form a stationary α-mixing sequence. A Berry-Esseen type bound is derived for the kernel density estimator at a fixed point x. For practical purposes, a randomly weighted estimator of the density function is also constructed and investigated. 相似文献
18.
V. Fakoor 《Statistics & probability letters》2010,80(5-6):318-323
Problems with censored data arise frequently in survival analyses and reliability applications. The estimation of the density function of the lifetimes is often of interest. In this paper, the estimation of the density function by the kernel method is considered, when censored data show some kind of dependence. We apply the strong Gaussian approximation technique for studying the strong uniform consistency for kernel estimators of the density function under a censored dependent model. 相似文献
19.
Summary We study the estimation of a density and a hazard rate function based on censored data by the kernel smoothing method. Our technique is facilitated by a recent result of Lo and Singh (1986) which establishes a strong uniform approximation of the Kaplan-Meier estimator by an average of independent random variables. (Note that the approximation is carried out on the original probability space, which should be distinguished from the Hungarian embedding approach.) Pointwise strong consistency and a law of iterated logarithm are derived, as well as the mean squared error expression and asymptotic normality, which is obtain using a more traditional method, as compared with the Hajek projection employed by Tanner and Wong (1983). 相似文献
20.
This paper studies the estimation of change point in mean and variance function of a non-parametric regression model based on kernel estimation and wavelet method. First, kernel estimation of mean function is developed and it is used to estimate the position and jump size of mean change. Second, wavelet methods are applied to derive the variance estimator which is used to estimate the location and jump size of the change point in variance. The asymptotic properties of these estimators are proved. Finally, the results from a numerical simulations and comparison study show that validate the effectiveness of our method. 相似文献