共查询到20条相似文献,搜索用时 31 毫秒
1.
The dependence orderings, more associated and more regression dependent, due to Schriever (1986, Order Dependence, Centre for Mathematics and Computer Sciences, Amsterdam; 1987, Ann. Statist., 15, 1208–1214) and Yanagimoto and Okamoto (1969, Ann. Inst. Statist. Math., 21, 489–505) respectively, are studied in detail for continuous bivariate distributions. Equivalent forms of the orderings under some conditions are given so that the orderings are more easily checkable for some bivariate distributions. For several parametric bivariate families, the dependence orderings are shown to be equivalent to an ordering of the parameter. A study of functionals that are increasing with respect to the more associated ordering leads to inequalities, measures of dependence as well as a way of checking that this ordering does not hold for two distributions.This research has been supported by NSERC Canada grants and a Scientific Grant of the University of Science and Technology of China. 相似文献
2.
We have studied the numerical integration 2D based on bivariate C
1 local polynomial splines with a criss–cross triangulation of nonuniform rectangular partition. We have constructed the cubature formula and proved the convergence properties and error bounds. The paper includes some numerical tests that illustrate the performance of the corresponding algorithm. In the appendix there are explicit expressions of the quadratic polynomial restrictions of the B-splines related to every triangular cell. 相似文献
3.
Motivated by the notion of regression depth (Rousseeuw and Hubert, 1996) we introduce thecatline, a new method for simple linear regression. At any bivariate data setZn={(xi, yi);i=1, …, n} its regression depth is at leastn/3. This lower bound is attained for data lying on a convex or concave curve, whereas for perfectly linear data the catline attains a depth ofn. We construct anO(n log n) algorithm for the catline, so it can be computed fast in practice. The catline is Fisher-consistent at any linear modely=βx+α+ein which the error distribution satisfies med(e | x)=0, which encompasses skewed and/or heteroscedastic errors. The breakdown value of the catline is 1/3, and its influence function is bounded. At the bivariate gaussian distribution its asymptotic relative efficiency compared to theL1line is 79.3% for the slope, and 88.9% for the intercept. The finite-sample relative efficiencies are in close agreement with these values. This combination of properties makes the catline an attractive fitting method. 相似文献
4.
William P. Alexander Scott D. Grimshaw 《Journal of computational and graphical statistics》2013,22(2):156-175
Abstract Given a data set consisting of n observations on p independent variables and a single dependent variable, treed regression creates a binary tree with a simple linear regression function at each of the leaves. Each node of the tree consists of an inequality condition on one of the independent variables. The tree is generated from the training data by a recursive partitioning algorithm. Treed regression models are more parsimonious than CART models because there are fewer splits. Additionally, monotonicity in some or all of the variables can be imposed. 相似文献
5.
Let Ω be a rectangular bounded domain of a plane equipped with a rectangular partition Δ. Assume a piecewise bivariate function
that is differentiable up to order (k,l) except at the knots of Δ, where it is less differentiable. In this paper, we introduce a new method for smoothing the above
function at the knots. More precisely, we describe algorithms allowing one to transform it into another function that will
be differentiable up to order (k,l) in the whole domain Ω. Then, as an application of this method, we give a recursive computation of tensor product Hermite
spline interpolants. To illustrate our results, some numerical examples are presented.
AMS subject classification (2000) 41A05, 41A15, 65D05, 65D07, 65D10 相似文献
6.
《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
7.
Semi inherited bivariate interpolation 总被引:1,自引:0,他引:1
The bivariate interpolation in two dimensional space R2 is more complicated than that in one dimensional space R, because there is no Haar space of continuous functions in R2. Therefore, the bivariate interpolation has not a unique solution for a set of arbitrary distinct pairwise points. In this work, we suggest a type of basis which depends on the points such that the bivariate interpolation has the unique solution for any set of distinct pairwise points. In this case, the matrix of bivariate interpolation has the semi inherited factorization. 相似文献
8.
Daniel R. Eno George R. Terrell 《Journal of computational and graphical statistics》2013,22(3):413-425
Abstract We present a method for graphically displaying regression data with Bernoulli responses. The method, which is based on the use of grayscale graphics to visualize contributions to a likelihood function, provides an analog of a scatterplot for logistic regression, as well as probit analysis. Furthermore, the method may be used in place of a traditional scatterplot in situations where such plots are often used. 相似文献
9.
Kenneth Lange Janet S. Sinsheimer 《Journal of computational and graphical statistics》2013,22(2):175-198
Abstract Maximum likelihood estimation with nonnormal error distributions provides one method of robust regression. Certain families of normal/independent distributions are particularly attractive for adaptive, robust regression. This article reviews the properties of normal/independent distributions and presents several new results. A major virtue of these distributions is that they lend themselves to EM algorithms for maximum likelihood estimation. EM algorithms are discussed for least Lp regression and for adaptive, robust regression based on the t, slash, and contaminated normal families. Four concrete examples illustrate the performance of the different methods on real data. 相似文献
10.
11.
In this paper, an interpolating method for bivariate cubic splines with C
2-join on type-II triangular at a rectangular domain is given, and the approximation degree, interpolating existence and uniqueness
of the cubic splines are studied.
Supported by NSFC General Projects(60473130). 相似文献
12.
Kernel regression estimation for continuous spatial processes 总被引:1,自引:0,他引:1
We investigate here a kernel estimate of the spatial regression function r(x) = E(Y
u | X
u = x), x ∈ ℝd, of a stationary multidimensional spatial process { Z
u = (X
u, Y
u), u ∈ ℝ
N
}. The weak and strong consistency of the estimate is shown under sufficient conditions on the mixing coefficients and the
bandwidth, when the process is observed over a rectangular domain of ℝN. Special attention is paid to achieve optimal and suroptimal strong rates of convergence. It is also shown that this suroptimal
rate is preserved by using a suitable spatial sampling scheme.
相似文献
13.
14.
Abstract When estimating a regression function or its derivatives, local polynomials are an attractive choice due to their flexibility and asymptotic performance. Seifert and Gasser proposed ridging of local polynomials to overcome problems with variance for random design while retaining their advantages. In this article we present a data-independent rule of thumb and a data-adaptive spatial choice of the ridge parameter in local linear regression. In a framework of penalized local least squares regression, the methods are generalized to higher order polynomials, to estimation of derivatives, and to multivariate designs. The main message is that ridging is a powerful tool for improving the performance of local polynomials. A rule of thumb offers drastic improvements; data-adaptive ridging brings further but modest gains in mean square error. 相似文献
15.
AndreasChristmann 《应用数学学报(英文版)》2005,21(2):193-208
The goals of this paper are twofold: we describe common features in data sets from motor vehicle insurance companies and we investigate a general strategy which exploits the knowledge of such features. The results of the strategy are a basis to develop insurance tariffs. We use a nonparametric approach based on a combination of kernel logistic regression and ε-support vector regression which both have good robustness properties. The strategy is applied to a data set from motor vehicle insurance companies. 相似文献
16.
Charles Kooperberg 《Journal of computational and graphical statistics》2013,22(3):322-341
Abstract A procedure for estimating a bivariate density based on data that may be censored is described. After the data are transformed to the unit square, the bivariate density is estimated using linear splines and their tensor products. The combined procedure yields an estimate of the bivariate density on the original scale, which may provide insight about the dependence structure. The procedure can also be used to estimate densities that are known to be symmetric and to test for independence. 相似文献
17.
It is shown that bivariate interpolatory splines defined on a rectangleR can be characterized as being unique solutions to certain variational problems. This variational property is used to prove the uniform convergence of bivariate polynomial splines interpolating moderately smooth functions at data which includes interpolation to values on a rectangular grid. These results are then extended to bivariate splines defined on anL-shaped region.This research was supported by a University of Kansas General Research Grant. 相似文献
18.
Wei Pan 《Journal of computational and graphical statistics》2013,22(4):687-698
Abstract Akaike's information criterion (AIC), derived from asymptotics of the maximum likelihood estimator, is widely used in model selection. However, it has a finite-sample bias that produces overfitting in linear regression. To deal with this problem, Ishiguro, Sakamoto, and Kitagawa proposed a bootstrap-based extension to AIC which they called EIC. This article compares model-selection performance of AIC, EIC, a bootstrap-smoothed likelihood cross-validation (BCV) and its modification (632CV) in small-sample linear regression, logistic regression, and Cox regression. Simulation results show that EIC largely overcomes AIC's overfitting problem and that BCV may be better than EIC. Hence, the three methods based on bootstrapping the likelihood establish themselves as important alternatives to AIC in model selection with small samples. 相似文献
19.
We treat with the r-k class estimation in a regression model, which includes the ordinary least squares estimator, the ordinary ridge regression estimator and the principal component regression estimator as special cases of the r-k class estimator. Many papers compared total mean square error of these estimators. Sarkar (1989, Ann. Inst. Statist. Math., 41, 717–724) asserts that the results of this comparison are still valid in a misspecified linear model. We point out some confusions of Sarkar and show additional conditions under which his assertion holds. 相似文献
20.
二元切触有理插值是有理插值的一个重要内容,而降低其函数的次数和解决其函数的存在性是有理插值的一个重要问题.二元切触有理插值算法的可行性大都是有条件的,且计算复杂度较大,有理函数的次数较高.利用二元Hermite(埃米特)插值基函数的方法和二元多项式插值误差性质,构造出了一种二元切触有理插值算法并将其推广到向量值情形.较之其它算法,有理插值函数的次数和计算量较低.最后通过数值实例说明该算法的可行性是无条件的,且计算量低. 相似文献