Confidence intervals for nonparametric regression functions with missing data: Multiple design case

This paper considers two estimators of θ = g (x) in a nonparametric regression model Y = g (x) + ɛ (x ∈ (0, 1) ^p ) with missing responses: Imputation and inverse probability weighted estimators. Asymptotic normality of the two estimators is established, which is used to construct normal approximation based confidence intervals on θ.     

Discriminant analysis based on statistical depth

<正> In the past two decades,many statistical depth functions seemed as powerful exploratoryand inferential tools for multivariate data analysis have been presented.In this paper,a new depthfunction family that meets four properties mentioned in Zuo and Serfling(2000)is proposed.Then aclassification rule based on the depth function family is proposed.The classification parameter b couldbe modified according to the type-Ⅰ error α,and the estimator of b has the consistency and achievesthe convergence rate n~(-1/2).With the help of the proper selection for depth family parameter c,theapproach for discriminant analysis could minimize the type-Ⅱ error β.A simulation study and a realdata example compare the performance of the different discriminant methods.     

CONVERGENCE PROPERTIES OF THE DEPENDENT PRP CONJUGATE GRADIENT METHODS

In this paper, a new region of βk with respect to ;βk^PRP is given. With two Armijo-type line searches, the authors investigate the global convergence properties of the dependent PRP conjugate gradient methods, which extend the global convergence results of PRP conjugate gradient method proved by Grippo and Lucidi （1997） and Dai and Yuan （2002）.     

Solutions for singular p-Laplacian equation in R n

In this paper, the authors study the existence and non-existence of positive solutions for singular p-Laplacian equation −∆ _p u = f(x)u ^−α + λg(x)u ^β in R ^N ; where N ≥ 3, 1 < p < N, λ > 0, 0 < α < 1, max(p, 2) < β + 1 < p* = \fracN_pN - p \frac{{{N_p}}}{{N - p}} . We prove that there exists a critical value ¤ such that the problem has at least two solutions if 0 < λ < Λ; at least one solution if λ = Λ; and no solutions if λ > Λ.     

The limit theorem for dependent random variables with applications to autoregression models

This paper studies the autoregression models of order one, in a general time series setting that allows for weakly dependent innovations. Let {X _t } be a linear process defined by X _t = Σ _k=0^∞ψ _k ɛ _t−k , where {ψ _k , k ≥ 0} is a sequence of real numbers and {ɛ _k , k = 0, ±1, ±2, …} is a sequence of random variables. Two results are proved in this paper. In the first result, assuming that {ɛ _k , k ≥ 1} is a sequence of asymptotically linear negative quadrant dependent (ALNQD) random variables, the authors find the limiting distributions of the least squares estimator and the associated regression t statistic. It is interesting that the limiting distributions are similar to the one found in earlier work under the assumption of i.i.d. innovations. In the second result the authors prove that the least squares estimator is not a strong consistency estimator of the autoregressive parameter α when {ɛ _k , k ≥ 1} is a sequence of negatively associated (NA) random variables, and ψ ₀ = 1, ψ _k = 0, k ≥ 1.     

Global stability of an epidemic model for vector-borne disease

<正> This paper considers an epidemic model of a vector-borne disease which has the vectormediatedtransmission only.The incidence term is of the bilinear mass-action form.It is shown that theglobal dynamics is completely determined by the basic reproduction number R_0.If R_01,the diseasefreeequilibrium is globally stable and the disease dies out.If R_01,a unique endemic equilibrium isglobally stable in the interior of the feasible region and the disease persists at the endemic equilibrium.Numerical simulations are presented to illustrate the results.     

Single-Index Quantile Regression with Left Truncated Data

The purpose of this paper is two fold. First, the authors investigate quantile regression(QR) estimation for single-index QR models when the response is subject to random left truncation.The random weights are introduced to deal with left truncated data and the associated iteration estimation method is proposed. The asymptotic properties for the proposed QR estimates of the index parameter and unknown link function are both obtained. Further, by combining the QR loss function and the adaptive LA...     

Asymptotic normality of wavelet estimator in heteroscedastic model with <Emphasis Type="Italic">α</Emphasis>-mixing errors

Consider heteroscedastic regression model Y _ni = g(x _ni ) + σ _ni ɛ _ni (1 ≤ i ≤ n), where σ _ni ² = f(u _ni ), the design points (x _ni , u _ni ) are known and nonrandom, g(·) and f(·) are unknown functions defined on closed interval [0, 1], and the random errors {ɛ _ni , 1 ≤ i ≤ n} are assumed to have the same distribution as {ξ _i , 1 ≤ i ≤ n}, which is a stationary and α-mixing time series with Eξ _i = 0. Under appropriate conditions, we study asymptotic normality of wavelet estimators of g(·) and f(·). Finite sample behavior of the estimators is investigated via simulations, too.     

Adjusted Empirical Likelihood Estimation of Distribution Function and Quantile with Nonignorable Missing Data

This paper considers the estimation problem of distribution functions and quantiles with nonignorable missing response data. Three approaches are developed to estimate distribution functions and quantiles, i.e., the Horvtiz-Thompson-type method, regression imputation method and augmented inverse probability weighted approach. The propensity score is specified by a semiparametric exponential tilting model. To estimate the tilting parameter in the propensity score, the authors propose an adjusted empirical likelihood method to deal with the over-identified system. Under some regular conditions, the authors investigate the asymptotic properties of the proposed three estimators for distribution functions and quantiles, and find that these estimators have the same asymptotic variance. The jackknife method is employed to consistently estimate the asymptotic variances. Simulation studies are conducted to investigate the finite sample performance of the proposed methodologies.     

H ∞ filtering for continuous-time systems with pointwise time-varying delay

The problem of H_∞filtering for continuous-time systems with pointwise time-varying delay is investigated in this paper.By applying an innovation analysis in Krein space,a necessary and sufficient condition for the existence of an H_∞filter is derived in two methods:One is the partial differential equation approach,the other is the reorganized innovation analysis approach.The former gives a solution to the proposed H_∞filtering problem in terms of the solution of a partial differential equation with boundary conditions.The later gives an analytical solution to the proposed H_∞filtering problem in terms of the solutions of Riccati and matrix differential equations.     

Sliding mode H∞ control for a class of uncertain nonlinear state-delayed systems

A new proportional-integral (PI) sliding surface is designed for a class of uncertain nonlinear state-delayed systems. Based on this, an adaptive sliding mode controller (ASMC) is synthesized, which guarantees the occurrence of sliding mode even when the system is undergoing parameter uncertainties and external disturbance. The resulting sliding mode has the same order as the original system, so that it becomes easy to solve the H_∞ control problem by designing a memoryless H_∞ state feedback controller. A delay-dependent sufficient condition is proposed in terms of linear matrix inequalities (LMIs), which guarantees the sliding mode robust asymptotically stable and has a noise attenuation level γ in an H_∞ sense. The admissible state feedback controller can be found by solving a sequential minimization problem subject to LMI constraints by applying the cone complementary linearization method. This design scheme combines the strong robustness of the sliding mode control with the H_∞ norm performance. A numerical example is given to illustrate the effectiveness of the proposed scheme.     

基于加权l1范数优化的双基地ISAR稀疏成像算法

针对低信噪比条件下实现双基地逆合成孔径雷达(inverse synthetic aperture radar, ISAR)稀疏孔径成像时重构质量较差的问题, 提出了一种基于加权l₁范数优化的高分辨成像算法。首先, 假设各像元稀疏非同分布, 利用贝叶斯准则和最大后验概率估计将双基地ISAR稀疏孔径成像问题转化为加权l₁范数约束问题, 建立成像模型; 然后, 利用柯西-牛顿算法进行加权l₁范数约束最优化问题的求解, 实现目标图像重构。由于假设各像元独立非同分布, 故通过像元加权的方式更好地利用了目标的能量聚集和结构特性, 提高了成像质量。最后, 仿真实验验证了算法的有效性和优越性。     

A NEW FAMILY OF TRIVALENT CAYLEY NETWORKS ON WREATH PRODUCT Zm ～ Sn

We propose a new family of interconnection networks （WGn^m） with regular degree three. When the generator set is chosen properly, they are isomorphic to Cayley graphs on the wreath product Zm ～ Sn. In the case of m ≥ 3 and n ≥3, we investigate their different algebraic properties and give a routing algorithm with the diameter upper bounded by [m/2]（3n^2- 8n ＋ 4） - 2n ＋ 1. The connectivity and the optimal fault tolerance of the proposed networks are also derived. In conclusion, we present comparisons of some familiar networks with constant degree 3.     

New HB-weighted time delay estimation algorithm under impulsive noise environment

The traditional HB-weighted time-delay estimation （TDE） method degenerates under the impulsive noise environment. Two new time-delay estimation methods are proposed based on fractional lower order statistics （FLOS） according to the impulsive characteristics of fractional lower order α-stable noises. Theoretic analysis and computer simulations indicate that the proposed covariation based HB weighted （COV-HB） algorithm can suppress impulsive noises in one received signal for 1 ≤α≤ 2, whereas the other proposed fractional lower order eovariancebased HB weighted （FLOC-HB） algorithm has robust performance under arbitrary impulsive noise conditions for the whole range of 0 〈α≤ 2.     

Nonconforming finite element method for nonlinear parabolic equations

<正> A nonconforming finite element method for the nonlinear parabolic equations is studied inthis paper.The convergence analysis is presented and the optimal error estimate in L~2(‖·‖_h)norm isobtained through Ritz projection technique,where ‖·‖_h is a norm over the finite element space.     

IMPROVED ROBUST H-INFINITY ESTIMATION FOR UNCERTAIN CONTINUOUS-TIME SYSTEMS

The design of full-order robust estimators is investigated for continuous-time polytopic uncertain systems. The main purpose is to obtain a stable linear estimator such that the estimation error system remains robustly stable with a prescribed H∞ attenuation level. Firstly, a simple alternative proof is given for an improved LMI representation of H∞ performance proposed recently. Based on the performance criterion which keeps the Lyapunov matrix out of the product of the system dynamic matrices, a sufficient condition for the existence of the robust estimator is provided in terms of linear matrix inequalities. It is shown that the proposed design strategy allows the use of parameterdependent Lyapunov functions and hence it is less conservative than the earlier results. A numerical example is employed to illustrate the feasibility and advantage of the proposed design.     

Model checking for general linear error-in-covariables model with validation data

In this paper, model checking problem is considered for general linear model when covariables are measured with error and an independent validation data set is available. Without assuming any error model structure between the true variable and the surrogate variable, the author first apply nonparametric method to model the relationship between the true variable and the surrogate variable with the help of the validation sample. Then the author construct a score-type test statistic through model adjustment. The large sample behaviors of the score-type test statistic are investigated. It is shown that the test is consistent and can detect the alternative hypothesis close to the null hypothesis at the rate n ^−r with 0 ≤ r ≤ 1/2. Simulation results indicate that the proposed method works well.     

Empirical likelihood for partially linear models under negatively associated errors

This paper proposes to use the blockwise empirical likelihood(EL) method to construct the confidence regions for the regression vector β in a partially linear model under negatively associated errors. It is shown that the blockwise EL ratio statistic for β is asymptotically χ~2 distributed. The result is used to obtain an EL-based confidence region for β. Results of a simulation study on the finite sample performance of the proposed confidence regions are reported.     

Global stability of endemic equilibrium point of basic virus infection model with application to HBV infection

In this paper, the authors first show that if R ₀ ≤ 1, the infection free steady state is globally attractive by using approaches different from those given by Min, et al.(2008). Then the authors prove that if R ₀ > 1, the endemic steady state is also globally attractive. Finally, based on a patient’s clinical HBV DNA data of anti-HBV infection with drug lamivudine, the authors establish an ABVIM. The numerical simulations of the ABVIM are good in agreement with the clinical data.