共查询到20条相似文献,搜索用时 15 毫秒
1.
Gordon J Johnston 《Journal of multivariate analysis》1982,12(3):402-414
Let (X, Y) have regression function m(x) = E(Y | X = x), and let X have a marginal density f1(x). We consider two nonparameteric estimates of m(x): the Watson estimate when f1 is known and the Yang estimate when f1 is known or unknown. For both estimates the asymptotic distribution of the maximal deviation from m(x) is proved, thus extending results of Bickel and Rosenblatt for the estimation of density functions. 相似文献
2.
Harro Walk 《Annals of the Institute of Statistical Mathematics》2005,57(4):665-685
The paper deals with kernel estimates of Nadaraya-Watson type for a regression function with square integrable response variable.
For usual bandwidth sequences and smooth nonnegative kernels, e.g., Gaussian and quartic kernels, strongL
2-consistency is shown without any further condition on the underlying distribution. The proof uses a Tauberian theorem for
Cesàro summability. 相似文献
3.
Michael Kohler Adam Krzyżak Harro Walk 《Annals of the Institute of Statistical Mathematics》2003,55(2):287-308
Regression function estimation from independent and identically distributed bounded data is considered. TheL
2 error with integration with respect to the design measure is used as an error criterion. It is shown that the kernel regression
estimate with an arbitrary random bandwidth is weakly and strongly consistent forall distributions whenever the random bandwidth is chosen from some deterministic interval whose upper and lower bounds satisfy
the usual conditions used to prove consistency of the kernel estimate for deterministic bandwidths. Choosing discrete bandwidths
by cross-validation allows to weaken the conditions on the bandwidths.
Research supported by DAAD, NSERC and Alexander von Humboldt Foundation.
The research of the second author was completed during his stay at the Technical University of Szczecin, Poland. 相似文献
4.
Jean-Paul Penot Constantin Zalinescu 《Proceedings of the American Mathematical Society》2006,134(7):1937-1946
We study the convergence of maximal monotone operators with the help of representations by convex functions. In particular, we prove the convergence of a sequence of sums of maximal monotone operators under a general qualification condition of the Attouch-Brezis type.
5.
Sanghyuk Lee 《Proceedings of the American Mathematical Society》2003,131(5):1433-1442
We consider the problem of endpoint estimates for the circular maximal function defined by
where is the normalized surface area measure on . Let be the closed triangle with vertices . We prove that for , there is a constant such that Furthermore, .
where is the normalized surface area measure on . Let be the closed triangle with vertices . We prove that for , there is a constant such that Furthermore, .
6.
田茂茜 《纯粹数学与应用数学》2011,27(5):622-627
利用齐型空间中的覆盖引理及其有界区域的二进方体分解得到了分数次Orlicz极大算子在齐型空间(X,d,μ)中的有界区域Ω上的局部加权端点估计.该工作为分数次积分交换子[b,Iα】在欧式空间R^n中的有界区域上的加权端点弱型估计推广到齐型空间奠定了基础. 相似文献
7.
L. C. Zhao 《Journal of multivariate analysis》1989,29(2)
Let (X, Y), (X1, Y1), …, (Xn, Yn) be i.d.d. Rr × R-valued random vectors with E|Y| < ∞, and let Qn(x) be a kernel estimate of the regression function Q(x) = E(Y|X = x). In this paper, we establish an exponential bound of the mean deviation between Qn(x) and Q(x) given the training sample Zn = (X1, Y1, …, Xn, Yn), under conditions as weak as possible. 相似文献
8.
The aim of this paper is to control the rate of convergence for central limit theorems of sojourn times of Gaussian fields in both cases: the fixed and the moving level. Our main tools are the Malliavin calculus and the Stein method, developed by Nualart, Peccati and Nourdin. We also extend some results of Berman to the multidimensional case. 相似文献
9.
Liliana Forzani Roberto Scotto Peter Sjö gren Wilfredo Urbina 《Proceedings of the American Mathematical Society》2002,130(1):73-79
The purpose of this paper is to prove the boundedness, for 1$">, of the non-centered Hardy-Littlewood maximal operator associated with the Gaussian measure .
10.
We prove endpoint estimates for maximal commutators for a class of singular integral operators related to the real analysis of the Monge Ampere equation. 相似文献
11.
This paper proposes a prior near-ignorance model for regression based on a set of Gaussian Processes (GP). GPs are natural prior distributions for Bayesian regression. They offer a great modeling flexibility and have found widespread application in many regression problems. However, a GP requires the prior elicitation of its mean function, which represents our prior belief about the shape of the regression function, and of the covariance between any two function values.In the absence of prior information, it may be difficult to fully specify these infinite dimensional parameters. In this work, by modeling the prior mean of the GP as a linear combination of a set of basis functions and assuming as prior for the combination coefficients a set of conjugate distributions obtained as limits of truncate exponential priors, we have been able to model prior ignorance about the mean of the GP. The resulting model satisfies translation invariance, learning and, under some constraints, convergence, which are desirable properties for a prior near-ignorance model. Moreover, it is shown in this paper how this model can be extended to allow for a weaker specification of the GP covariance between function values, by letting each basis function to vary in a set of functions.Application to hypothesis testing has shown how the use of this model induces the capability of automatically detecting when a reliable decision cannot be made based on the available data. 相似文献
12.
Consider the nonparametric regression modelY=go(T)+u, whereY is real-valued,u is a random error,T is a randomd-vector of explanatory variables ranging over a nondegenerated-dimensional compact setC, andgo(·) is the unknown smooth regression function, which ism (0) times continuously differentiable and itsmth partial derivatives
satisfy the Hölder condition with exponent(0,1], wherei
1, ...,i
d
are nonnegative integers satisfying
k
=1/d
i
k
=m. The piecewise polynomial estimator ofgo based onM-estimates is considered. It is proved that the rate of convergence of the underlying estimator is
under certain regular conditions, which is the optimal global rate of convergence of least square estimates for nonparametric regression studied in [10–11].This work is partly supported by the National Natural Science Foundation of China. 相似文献
13.
Several iterative methods for maximal correlation problems (MCPs) have been proposed in the literature. This paper deals with the convergence of these iterations and contains three contributions. Firstly, a unified and concise proof of the monotone convergence of these iterative methods is presented. Secondly, a starting point strategy is analysed. Thirdly, some error estimates are presented to test the quality of a computed solution. Both theoretical results and numerical tests suggest that combining with this starting point strategy these methods converge rapidly and are more likely converging to a global maximizer of MCP. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
14.
Robust estimation procedures for linear and mixture linear errors-in-variables regression models are proposed based on the relationship between the least absolute deviation criterion and maximum likelihood estimation in a Laplace distribution. The finite sample performance of the proposed procedures is evaluated by simulation studies. 相似文献
15.
16.
FANG Yixin JIN Man & ZHAO Lincheng Department of Statistics Finance University of Science Technology of China Hefei China 《中国科学A辑(英文版)》2005,48(2):155-168
A regression model with a nonnegativity constraint on the dependent variable, known as censored median regression model, is considered. Under some mild conditions, the LAD estimate of the regression coefficient is shown to be strongly consistent. Furthermore, its convergence rate and Bahadur strong representation are also obtained. 相似文献
17.
18.
Wen Hsiang Wei 《Annals of the Institute of Statistical Mathematics》2009,61(2):291-308
A class of regression model selection criteria for the data with correlated errors is proposed. The proposed class of selection
criteria is an estimator of weighted prediction risk. In addition, the proposed selection criteria are the generalizations
of several commonly used criteria in statistical analysis. The theoretical and asymptotic properties for the class of criteria
are established. Further, in the medium-sample case, the results based on a simulation study are quite consistent with the
theoretical ones. The proposed criteria perform well in the simulations. Several applications are also given for a variety
of statistical models. 相似文献
19.
Pu Zhang 《数学学报(英文版)》2015,31(6):973-994
Let M be the multilinear maximal function and b =(b1,..., bm) be a collection of locally integrable functions. Denote by M b and [ b, M] the maximal commutator and the commutator of M with b, respectively. In this paper, the multiple weighted strong and weak type estimates for operators M b and [ b, M] are studied. Some characterizations of the class of functions bj are given, for which these operators satisfy some strong or weak type estimates. 相似文献
20.
Trace regression models are widely used in applications involving panel data, images, genomic microarrays, etc., where high-dimensional covariates are often involved. However, the existing research involving high-dimensional covariates focuses mainly on the condition mean model. In this paper, we extend the trace regression model to the quantile trace regression model when the parameter is a matrix of simultaneously low rank and row (column) sparsity. The convergence rate of the penalized estimator is derived under mild conditions. Simulations, as well as a real data application, are also carried out for illustration. 相似文献