共查询到20条相似文献,搜索用时 15 毫秒
1.
Stephan Derbort Holger Dette Axel Munk 《Annals of the Institute of Statistical Mathematics》2002,54(1):60-82
A simple consistent test of additivity in a multiple nonparametric regression model is proposed, where data are observed on a lattice. The new test is based on an estimator of the L
2-distance between the (unknown) nonparametric regression function and its best approximation by an additive nonparametric regression model. The corresponding test-statistic is the difference of a classical ANOVA style statistic in a two-way layout with one observation per cell and a variance estimator in a homoscedastic nonparametric regression model. Under the null hypothesis of additivity asymptotic normality is established with a limiting variance which involves only the variance of the error of measurements. The results are extended to models with an approximate lattice structure, a heteroscedastic error structure and the finite sample behaviour of the proposed procedure is investigated by means of a simulation study. 相似文献
2.
Gerlind Plonka 《Advances in Computational Mathematics》1995,3(1):1-22
The Fourier transforms of B-splines with multiple integer knots are shown to satisfy a simple recursion relation. This recursion
formula is applied to derive a generalized two-scale relation for B-splines with multiple knots. Furthermore, the structure
of the corresponding autocorrelation symbol is investigated.
In particular, it can be observed that the solvability of the cardinal Hermite spline interpolation problem for spline functions
of degree 2m+1 and defectr, first considered by Lipow and Schoenberg [9], is equivalent to the Riesz basis property of our B-splines with degreem and defectr. In this way we obtain a new, simple proof for the assertion that the cardinal Hermite spline interpolation problem in [9]
has a unique solution. 相似文献
3.
The purpose of this article is to show how naturally recurrence relations for most general Chebyshevian B-splines emerge from blossoms. In particular, this work gives a new insight into previous results by Lyche [A recurrence relation for Chebyshevian B-splines, Constr. Approx. 1 (1985) 155–178], the importance of which it underlines. 相似文献
4.
A general method for constructing quasi-interpolation operators based on B-splines is developed. Given a B-spline ? in Rs, s≥1, normalized by ∑i∈Zs?(⋅−i)=1, the classical structure Q(f)?∑i∈Zsλf(⋅+i)?(⋅−i), for a quasi-interpolation operator Q is considered. A minimization problem is derived from an estimate of the quasi-interpolation error associated with Q when λf is a linear combination of values of f at points in some neighbourhood of the support of ?; or a linear combination of values of f and some of its derivatives at some points in this set; or a linear combination of weighted mean values of the function to be approximated. That linear functional is defined to produce a quasi-interpolant exact on the space of polynomials of maximal total degree included in the space spanned by the integer translates of ?. The solution of that minimization problem is characterized in terms of specific splines which do not depend on λ but only on ?. 相似文献
5.
In this article, using the likelihood score theory extended to nuisance parameters we derive a new homogeneity score test for comparing linage disequilibrium across several strata. Power and sample size formulae are also obtained. 相似文献
6.
回归信度模型在保险研究中具有重要的作用。本文讨论了具有线性趋势回归信度模型自相关性的score检验问题。首先推导出模型中自相关存在性检验的score检验统计量,然后利用Monte-Carlo方法模拟了此种检验统计量的功效。最后利用文中所得到的检验方法对旅客意外身体伤害保险数据进行了实例分析。 相似文献
7.
Marie-Laurence Mazure 《Numerical Algorithms》2009,51(4):401-428
This works complements a recent article (Mazure, J. Comp. Appl. Math. 219(2):457–470, 2008) in which we showed that T. Lyche’s recurrence relations for Chebyshevian B-splines (Lyche, Constr. Approx. 1:155–178, 1985) naturally emerged from blossoms and their properties via de Boor type algorithms. Based on Chebyshevian divided differences,
T. Lyche’s approach concerned splines with all sections in the same Chebyshev space and with ordinary connections at the knots.
Here, we consider geometrically continuous piecewise Chebyshevian splines, namely, splines with sections in different Chebyshev
spaces, and with geometric connections at the knots. In this general framework, we proved in (Mazure, Constr. Approx. 20:603–624,
2004) that existence of B-spline bases could not be separated from existence of blossoms. Actually, the present paper enhances
the powerfulness of blossoms in which not only B-splines are inherent, but also their recurrence relations. We compare this
fact with the work by G. Mühlbach and Y. Tang (Mühlbach and Tang, Num. Alg. 41:35–78, 2006) who obtained the same recurrence relations via generalised Chebyshevian divided differences, but only under some total positivity
assumption on the connexion matrices. We illustrate this comparison with splines with four-dimensional sections. The general
situation addressed here also enhances the differences of behaviour between B-splines and the functions of smaller and smaller
supports involved in the recurrence relations. 相似文献
8.
9.
Yongge Tian 《Linear and Multilinear Algebra》2005,53(1):45-65
Some results on the Moore-Penrose inverse for sums of matrices under rank additivity conditions are revisited and some new consequences are presented. Their extensions to the weighted Moore-Penrose inverse of sums of matrices under rank additivity conditions are also considered. 相似文献
10.
This paper considers the problem for designing optimal smoothing and interpolating splines with equality and/or inequality constraints. The splines are constituted by employing normalized uniform B-splines as the basis functions, namely as weighted sum of shifted B-splines of degree k. Then a central issue is to determine an optimal vector of the so-called control points. By employing such an approach, it is shown that various types of constraints are formulated as linear function of the control points, and the problems reduce to quadratic programming problems. We demonstrate the effectiveness and usefulness by numerical examples including approximation of probability density functions, approximation of discontinuous functions, and trajectory planning. 相似文献
11.
Dione M. Valença Heleno Bolfarine 《Annals of the Institute of Statistical Mathematics》2006,58(1):115-129
We discuss properties of the score statistics for testing the null hypothesis of homogeneity in a Weibull mixing model in
which the group effect is modelled as a random variable and some of the covariates are measured with error. The statistics
proposed are based on the corrected score approach and they require estimation only under the conventional Weibull model with
measurement errors and does not require that the distribution of the random effect be specified. The results in this paper
extend results in Gimenez, Bolfarine, and Colosimo (Annals of the Institute of Statistical Mathematics, 52, 698–711, 2000) for the case of independent Weibull models. A simulation study is provided.
An erratum to this article can be found at 相似文献
12.
Lin Jinguan Wei Bocheng Zhang Nansong Dept.of Math.& Comput.Sci. Jiangsu Institute of Education Jiangsu China. Dept of Math. Southeast Univ. Jiangsu China. Dept of Math. Zhejiang Univ. Zhejiang China. 《高校应用数学学报(英文版)》2003,18(3):294-302
§ 1 Introduction and modelsThe general form of exponential family nonlinear models isg(μi) =f(xi,﹀) , (1 )where,g(· ) is a monotonic link function,f is a known differentiable nonlinear functionand﹀ is a p-vectoroffixed population parameters;μi=E(yi) and the density of response yiisp(yi) =exp{[yiθi -b(θi) -c(yi) ] -12 a(yi,) } ,(2 )whereθi is the natural parameter, is the dispersion parameter.From [1 1 ] ,μi=b(θi) ,Vi=Var(yi) =- 1 b(θi) .If f(xi,β) =x Ti ﹀,then mod… 相似文献
13.
在多项选择题测验分数等于真实分数和猜测分数之和的假设模型下,本文得到了一个多项选择题测验信度的理论公式,并由此给出了测验信度的估计方法。最后,通过两个例子,说明了本文提出的方法在测验信度分析中的应用,并将这种方法与教育测量中常用的库德——理查逊方法(Kuder-Richardson)进行了比较 相似文献
14.
15.
This paper proposes a new statistic to test independence of high-dimensional data. The simulation results suggest that the performance of the test based on our statistic is comparable to the existing ones, and under some circumstances it may have higher power. Therefore, the new statistic can be employed in practice as an alternative choice. 相似文献
16.
Guido Walz 《BIT Numerical Mathematics》1997,37(1):189-201
In this paper we investigate some properties of trigonometric B-splines. We establish a complex integral representation for
these functions, which is in certain analogy to the polynomial case, but the proof of which has to be done in a different
and more complicated way. Using this integral representation, we can prove some identities concerning the evaluation of a
trigonometric B-spline, its derivative and its partial derivative w.r.t. the knots. Finally we show that—in the case of equidistant
knots—the trigonometric B-splines of odd order form a partition of a constant, and therefore the corresponding B-spline curve
possesses the convex-hull property. This is illustrated by a numerical example. 相似文献
17.
《Journal of computational and graphical statistics》2013,22(4):870-891
The goal of our article is to provide a transparent, robust, and computationally feasible statistical platform for restricted likelihood ratio testing (RLRT) for zero variance components in linear mixed models. This problem is nonstandard because under the null hypothesis the parameter is on the boundary of the parameter space. Our proposed approach is different from the asymptotic results of Stram and Lee who assumed that the outcome vector can be partitioned into many independent subvectors. Thus, our methodology applies to a wider class of mixed models, which includes models with a moderate number of clusters or nonparametric smoothing components. We propose two approximations to the finite sample null distribution of the RLRT statistic. Both approximations converge weakly to the asymptotic distribution obtained by Stram and Lee when their assumptions hold. When their assumptions do not hold, we show in extensive simulation studies that both approximations outperform the Stram and Lee approximation and the parametric bootstrap. We also identify and address numerical problems associated with standard mixed model software. Our methods are motivated by and applied to a large longitudinal study on air pollution health effects in a highly susceptible cohort. Relevant software is posted as an online supplement. 相似文献
18.
Sándor Csörgő 《Statistics & probability letters》1985,3(1):45-49
A nonparametric large sample test is proposed for testing the linearity of a regression model with independent and identically distributed errors satisfying only a very mild tail condition. The statistic is based on the functional least squares estimator of the slope vector. The test is applied to the stack loss data. 相似文献
19.
讨论了具有AR(1)误差的线性均值漂移模型,研究了自相关性的检验问题,导出了关于误差相关性的Score检验统计量和似然比检验统计量,并把它推广到误差项为AR(1)非线性均值漂移模型.本文还给出了一个数值例子说明检验方法的实用性. 相似文献