一类非参数回归函数导数估计的渐近分布

设y_1,…,y_n是在固定点x_1,…,x_n的n个观察值,适合模型y_i=g(x_i)+ε_i,1≤i≤n,这里g是R~1上的未知函数,{ε_i}为零均值、有限方差的i.i.d.序列,设O=x_o≤x_l≤…≤x_(n-1)≤x_n=1我们用作为g~(p)(x)的估计. 本文给出了的渐近分布,其中x~(1),…,x~(m)为(0,1)内的相异点。     

非参数回归函数估计的一个结果

这里g是[0,1]上的未知函数,ε_i是具有零均值的i.i.d随机变量,且假定0≤x_1≤…≤x_n≤1,我们要估计g(x),Priestley and Chao提出了一种加权核估计法,即用     

相依样本一类非参数回归函数估计的强相合性

设Y_1,Y_2,…,Y_n是在固定点x_1,x_2,…,x_n的n个观察值,适合模型 Y_1=g(x_1)+ε_x,1≤i≤n (1) 这里g是R上的未知函数,{ε_1}为零均值的平稳、φ-混合过程,假定0=x_0≤x_1≤…≤x_(n-1)≤X_n=1。用 g_n(x)=sum from n-1 to ∞n Y_1H_n~(-1)(x_1-x_(x-x)K((x-x_1)/h_n) (2) 作为g(x)[x∈(0.1)]的估计。 本文讨论了g_n(x)的强相合性。     

二次插值样条函数的积分性质

已知区间[a,b]的一个分划△:a=x_0相似文献   

B值随机变量阵列加权和完全收敛性的某结果

设{Xnii≥1,n≥1}为行间独立的B值r.v.阵列,g(x)是指数为1/p的正则变化函数,r＞1,{αnii≥1,n≥1}为实数阵列,本文得到了使∞∑n=1nr-2P(‖∞∑i=1αniXni‖＞εg(n))＜∞[]ε＞0成立的条件.     

一类半线性波动方程解的渐近理论

研究了三维空间中如下半线性波动方程的初值问题　　 utt =Δu - b24 u+εF(u ,ε) ,　　t >0 ,x∈R3,u(0 ,x ,ε) =u0 (x ,ε) ,ut(0 ,x ,ε) =u1(x ,ε) ,x∈R3,解的渐近理论。其中Δ = 3i=1 2 x2 i,常数b≥ 0。在古典空间C2 中得到了形式近似解的合理性在长时间t∈〔0 ,｜ε｜- 12 -k( p- 1) 〕(ε充分小 ,0 <2 -k(p- 1) <1,0 3)内成立     

穿孔区域中非线性波动方程解的存在性与齐次化

本文研究如下非线性波动方程的齐次化问题 uε'div(AεΔuε) g(uε') = fε in Ωε× (0,T),在Ωε× (0,T) 内,这里Ωε为一周期穿孔区域,g为一非降标量函数,我们首先证明该问题解的存在性与唯一性,然后论证该解收敛于其齐次化问题的解。     

图中具有分数(g,f)-因子的若干充分条件

设g和f分别是定义在图G的顶点集合V(G)上的整数值函数且对每个x∈V(G)有0≤g(x)≤f(x)。本文给出了一个图有分数(g,f)-因子的若干充分条件。     

关于半相依回归方程组的一类两步Minimax估计的优良性

本文考虑半相依回归方程系统Y_i=X_iβ_i+ε_i,i=1,2,其中Eε_i=0,Gov(ε_i,ε_j)=σ_(ij)I_n,β_i∈R~(pi),∑=(σ_(ij))_(2×2)>0未知。在矩阵损失函数L(β,δ)=(δ-β)(δ-β)'下,我们证明了Zellner的两步估计是不可容许的,本文提出了参数β_i的一类两步Minimax估计,证明了这一类两步Minimax估计较Zellner的两步估计具有更优良的性质。     

不可微多目标规划的局部真有效性(为庆贺游兆永教授60寿辰而作)

一 定义及其注记 本文考虑多目标规划问题 (VP) 其中f:k~n→k~p,g:R~n→R~m,f(x)=f_1(x),…,f_p(x)),g(x)=(g_1(x),…,g_m(x)).记(VP)的可行集为D={x∈R~n:g(x)≦0}。 设a=(a_1,…,a_n)~T,b=(b_1,…,b_n)~T,文中a≧b表示a_i≥b_i(i=1,…,n);a≥b表示a≧b但a≠b;a>b表示a_i>b_i(i=1,…,n)。 定义1 称(VP)的局部有效解x~*为广义KT真有效解,如果下述不等式组无解     

Sub-actions for weakly hyperbolic one-dimensional systems

Let f be an expanding map of degree 2 in the unitary interval [0,1], with an indifferent fixed point at x = 0 (i. e. (0) = 1), increasing, surjective and C 1 in each injective branch [0, c ] and ( c ,1], with inf{ f ' ( x ) | x ] [ g , 1)\{ c }} > 1 for all g > 0. Let A : [0,1] M be a function f -Hölder in each injective branch, monotone in a small neighbourhood of the origin, with A (0)< m and A (1)< m, where m is the maximum value of Z A d w over all invariant probability measures of f. Our main result is to prove that there exists a f -Hölder function S : [0,1] M , which satisfies the subcohomology equation Using S we prove that, if A admits a unique measure which maximizes Z , then this measure is uniquely ergodic. If A =log f ' , we are analysing the measure of maximal Lyapunov exponent. We also use the function f to define a bidimensional bijective function B in the unitary square [0,1) 2 [0,1), which is a modification of the Baker's Map, having an indifferent fixed point at the origin. If A : [0,1) 2     

Efficient estimation for marginal generalized partially linear single-index models with longitudinal data

We consider marginal generalized partially linear single-index models for longitudinal data. A profile generalized estimating equations (GEE)-based approach is proposed to estimate unknown regression parameters. Within a wide range of bandwidths for estimating the nonparametric function, our profile GEE estimator is consistent and asymptotically normal even if the covariance structure is misspecified. Moreover, if the covariance structure is correctly specified, the semiparametric efficiency can be achieved under heteroscedasticity and without distributional assumptions on the covariates. Simulation studies are conducted to evaluate the finite sample performance of the proposed procedure. The proposed methodology is further illustrated through a data analysis.     

Phase II Monitoring of Nonlinear Profile Variance Using Wavelet

In some statistical process control applications, the quality of a process or a product can be characterized by a nonlinear relationship between a response variable and one or more explanatory variables. Monitoring nonlinear profiles using nonlinear regression has been proposed by several researchers as a potential area for research. To avoid disadvantages of parameter estimation in nonlinear regression, we used nonparametric regression with wavelets for monitoring nonlinear profiles. In nonparametric regression framework, traditional variance estimator is not proper; other estimators should be used instead. Parametric or nonparametric control charts in phase II are proposed to monitor error term variance when nonparametric regression with wavelet is used. Multivariate control chart based on regression coefficients (approximate wavelet coefficients) is added to variance control chart to check stability in the process mean. It is well known that the performance of control schemes in detecting shifts in multivariate control charts deteriorates as the dimension of regression coefficient increases. To improve the performance of control schemes, we considered decomposition level as a smoothing parameter, which determines the form of regression function (size of approximate wavelet coefficients vector) in nonparametric regression with wavelet. A method based on an analysis of variance is proposed to determine the optimal decomposition level. The statistical performances of the proposed methods are evaluated using average run length criterion using vertical density profile data. Numerical results indicate that the proposed methods perform satisfactorily. Copyright © 2012 John Wiley & Sons, Ltd.     

Random and deterministic perturbation of a class of skew-product systems

Abstract. This paper is concerned with the stability properties of skew-products T (x,y) = (f(x), g(x,y)) in which (f,X,mu) is an ergodic map of a compact metric space X and g: Xx Rn Rn is continuous. We assume that the skew-product has a negative maximal Lyapunov exponent in the fibre. We study the orbit stability and stability of mixing of T(x,y) = (f(x), g(x,y)) under deterministic and random perturbation of g. We show that such systems are stable in the sense that for any > 0 there is a pairing of orbits of the perturbed and unperturbed system such that paired orbits stay within a distance of each other except for a fraction of the time. Furthermore, we show that the invariant measure for the perturbed system is continuous (in the Hutchinson metric) as a function of the size of the perturbation to g (Lipschitz topology) and the noise distribution. Our results have applications to the stability of Iterated Function Systems which 'contract on average'.     

Series Estimation of a Probability Density Function

A class of nonparametric estimators of f(x) based on a set of n observations has been proved by Parzen [l] to be consistent and asymptotically normal subject to certain conditions. Although quite useful for a wide variety of practical problems, these estimators have two serious disadvantages when n is large: 1. All n observations must be stored in rapid-access storage.

2. Evaluation of f(x) for a particular value of x requires a long computation involving each of the observations.

The Parzen estimator, which has n terms, can be replaced by a series approximation which has a number of terms determined by the accuracy required in the estimate rather than by the number of observations in the sample. The summation over all of the observations is performed only to establish the value of the coefficients in the series.

Although no member of the class of estimators has been proved “best” for estimating an unknown density from a finite sample, a power series expansion for a particular member of the class was singled out because of computational simplicity. A comparison is made between the proposed estimator and the Gram–Charlier Series of Type A. A multidimensional counterpart of the proposed estimator has also been derived.     

Methods of Multivariate Analysis

Nonparametric estimation of abrupt changes in a regression function involves choosing smoothing (bandwidth) parameters. The performance of estimation procedures depends heavily on this choice. So far, little attention has been paid to the crucial issue of choosing appropriate bandwidth parameters in practice. In this article we propose a bootstrap procedure for selecting the bandwidth parameters in a nonparametric two-step estimation method. This method results in a fully data-driven procedure for estimating a finite (but possibly unknown) number of changepoints in a regression function. We evaluate the performance of the data-driven procedure via a simulation study, which reveals that the fully automatic procedure performs quite well. As an illustration, we apply the procedure to some real data.     

Model checks for parametric regression models

In the paper we deal with the problem of model selection among fixed-design regression models. We establish a new test that indicates whether or not the model fits the data. The test statistic is based on the difference between a parametric estimator for the model variance and a nonparametric difference-based estimator, see Hall et al. (Biometrika 77:521–528, 1990). The weights in the nonparametric estimator depend on n, and they are chosen by solving an optimisation problem in order to obtain a test with high power.     

Nonparametric density estimation in presence of bias and censoring

We consider projection estimator methods for the nonparametric estimation of the density of i.i.d. biased observations with a general known bias function w and under right censoring. Adaptive procedures to catch the optimal estimator among a collection by contrast penalization are investigated and proved to give efficient estimators with optimal nonparametric rates of convergence. Monte-Carlo experiments complete the study and illustrate the method.     

Local polynomial regression smoothers with AR-error structure

Consider the fixed regression model with random observation error that follows an AR(1) correlation structure. In this paper, we study the nonparametric estimation of the regression function and its derivatives using a modified version of estimators obtained by weighted local polynomial fitting. The asymptotic properties of the proposed estimators are studied: expressions for the bias and the variance/covariance matrix of the estimators are obtained and the joint asymptotic normality is established. In a simulation study, a better behavior of the Mean Integrated Squared Error of the proposed regression estimator with respect to that of the classical local polynomial estimator is observed when the correlation of the observations is large. This work has been partially supported by grants PB98-0182-C02-01, PGIDT01PXI10505PR and MCyT Grant BFM2002-00265 (European FEDER support included).