Robust sure independence screening for ultrahigh dimensional non-normal data

Sure independence screening（SIS） has been proposed to reduce the ultrahigh dimensionality down to a moderate scale and proved to enjoy the sure screening property under Gaussian linear models.However,the observed response is often skewed or heavy-tailed with extreme values in practice,which may dramatically deteriorate the performance of SIS.To this end,we propose a new robust sure independence screening（RoSIS） via considering the correlation between each predictor and the distribution function of the response.The proposed approach contributes to the literature in the following three folds： First,it is able to reduce ultrahigh dimensionality effectively.Second,it is robust to heavy tails or extreme values in the response.Third,it possesses both sure screening property and ranking consistency property under milder conditions.Furthermore,we demonstrate its excellent finite sample performance through numerical simulations and a real data example.     

对流占优扩散方程的一种特征差分算法

A new kind of characteristic-difference scheme for convection-diffusion equations is constructed by characteristic method and bilinear interpolation method. The convergence of the scheme is proved. The advantages of this scheme are to obtain the solutions of the convection diffusion equations with variable coefficient expediently and to reduce the numerical oscillations of the convectiondominanted diffusion equations effectively.     

ASYMPTOTICALLY ALMOST PERIODIC FUNCTIONS IN PROBABILITY

In this paper, we first study the properties of asymptotically almost periodic functions in probability and then prove the existence of almost periodic solutions in probability to some differential equations with random terms.     

A Class of Ruin Probability Mo del with Dep endent Structure

In this paper, we study a class of ruin problems, in which premiums and claims are dependent. Under the assumption that premium income is a stochastic process, we raise the model that premiums and claims are dependent, give its numerical characteristics and the ruin probability of the individual risk model in the surplus process. In addition, we promote the number of insurance policies to a Poisson process with parameter λ, using martingale methods to obtain the upper bound of the ultimate ruin probability.     

A Unified Ternary Curve Subdivision Scheme

A unified $m\,(m>2)$-point ternary scheme with some parameter is proposed. The continuity of subdivision scheme is analyzed based on the relationship between the subdivision scheme and difference scheme. Moreover, the proposed subdivision is extended to asymmetric multi-parameter subdivision and the asymmetric schemes in four cases are presented in detail. Some examples are given to show that the presented scheme has better approximating effect.     

Convolution kernels implementation of cardinalized probability hypothesis density filter

The probability hypothesis density （PHD） propagates the posterior intensity in place of the poste- rior probability density of the multi-target state. The cardinalized PHD （CPHD） recursion is a generalization of PHD recursion, which jointly propagates the posterior intensity function and posterior cardinality distribution. A number of sequential Monte Carlo （SMC） implementations of PHD and CPHD filters （also known as SMC- PHD and SMC-CPHD filters, respectively） for general non-linear non-Gaussian models have been proposed. However, these approaches encounter the limitations when the observation variable is analytically unknown or the observation noise is null or too small. In this paper, we propose a convolution kernel approach in the SMC-CPHD filter. The simuIation results show the performance of the proposed filter on several simulated case studies when compared to the SMC-CPHD filter.     

AN ADAPTIVE TRUST-REGION METHOD FOR GENERALIZED EIGENVALUES OF SYMMETRIC TENSORS

For symmetric tensors,computing generalized eigenvalues is equivalent to a homogenous polynomial optimization over the unit sphere.In this paper,we present an adaptive trustregion method for generalized eigenvalues of symmetric tensors.One of the features is that the trust-region radius is automatically updated by the adaptive technique to improve the algorithm performance.The other one is that a projection scheme is used to ensure the feasibility of all iteratives.Global convergence and local quadratic convergence of our algorithm are established,respectively.The preliminary numerical results show the efficiency of the proposed algorithm.     

带分数阶Robin边界条件的时间-空间分数阶扩散方程的有限差分方法（英文）

In this paper, an efficient numerical method is proposed to solve the Caputo-Riesz fractional diffusion equation with fractional Robin boundary conditions. We approximate the Riesz space fractional derivatives using the fractional central difference scheme with second-order accurate. A priori estimation of the solution of the numerical scheme is given, and the stability and convergence of the numerical scheme are analyzed.Finally, a numerical example is used to verify the accuracy and efficiency...     

AN ERGODIC THEOREM FOR GENERALIZED SIMPLE EXCLUSION PROCESSES WITH REVERSIBLE POSITIVE TRANSITION

Simple exclusion procosses are important infinite particle systems. This model was proposed by Spitzer (1)and studied extensively by Spitzer and Liggett (2). On the basis of the model, Yan Shi-jian and Chen Mu-fa proposed generalized exclusion processes and obtained the construction of the processes. Zheng Wen-qu obtained a necessary and sufficient condition of the reversibility and proved that the set of the reversible probability measures of such a process is equal to the set of it's Gibbs states (3). This paper is devoted to the ergodic theory of a generalized simple exclusion proess with the state space {0, 1, …, m} (m≥1, S is a countable set) and a reversible positive recurrent transition probability matrix P=(p(x, y))_(x,y)∈s Refering (4), the set of it's invariant probability measures is described and the ergodic properties of the process is obtained. We also prove that the set of it's reversible probability measures coinsides with the set of it's invariant probability measures. So the main re     

Small value probabilities for continuous state branching processes with immigration

We consider the small value probability of supercritical continuous state branching processes with immigration.From Pinsky(1972) it is known that under regularity condition on the branching mechanism and immigration mechanism,the normalized population size converges to a non-degenerate finite and positive limit W as t tends to infinity.We provide sharp estimate on asymptotic behavior of P(W≤ε) as ε→ 0+ by studying the Laplace transform of W.Without immigration,we also give a simpler proof for the small value probability in the non-subordinator case via the prolific backbone decomposition.     

A MONOTONE COMPACT IMPLICIT SCHEME FOR NONLINEAR REACTION-DIFFUSION EQUATIONS

A monotone compact implicit finite difference scheme with fourth-order accuracy in space and second-order in time is proposed for solving nonlinear reaction-diffusion equations. An accelerated monotone iterative method for the resulting discrete problem is presented. The sequence of iteration converges monotonically to the unique solution of the discrete problem, and the convergence rate is either quadratic or nearly quadratic, depending on the property of the nonlinear reaction. The numerical results illustrate the high accuracy of the proposed scheme and the rapid convergence rate of.the iteration.     

Empirical likelihood inference for semi-parametric estimating equations

Qin and Lawless (1994) established the statistical inference theory for the empirical likelihood of the general estimating equations. However, in many practical problems, some unknown functional parts h(t) appear in the corresponding estimating equations EFG(X, h(T), β) = 0. In this paper, the empirical likelihood inference of combining information about unknown parameters and distribution function through the semiparametric estimating equations are developed, and the corresponding Wilk’s theorem is established. The simulations of several useful models are conducted to compare the finite-sample performance of the proposed method and that of the normal approximation based method. An illustrated real example is also presented.     

A COMPACT UPWIND SECOND ORDER SCHEME FOR THE EIKONAL EQUATION

We present a compact upwind second order scheme for computing the viscosity solution of the Eikonal equation. This new scheme is based on： 1. the numerical observation that classical first order monotone upwind schemes for the Eikonal equation yield numerical upwind gradient which is also first order accurate up to singularities; 2. a remark that partial information on the second derivatives of the solution is known and given in the structure of the Eikonal equation and can be used to reduce the size of the stencil. We implement the second order scheme as a correction to the well known sweeping method but it should be applicable to any first order monotone upwind scheme. Care is needed to choose the appropriate stencils to avoid instabilities.     

A RepairableGeoX/G/1 Retrial Queue with Bernoulli Feedback and Impatient Customers

Abstract This paper deals with a discrete-time batch arrival retrial queue with the server subject to starting failures.Diferent from standard batch arrival retrial queues with starting failures,we assume that each customer after service either immediately returns to the orbit for another service with probabilityθor leaves the system forever with probability 1θ(0≤θ1).On the other hand,if the server is started unsuccessfully by a customer(external or repeated),the server is sent to repair immediately and the customer either joins the orbit with probability q or leaves the system forever with probability 1 q(0≤q1).Firstly,we introduce an embedded Markov chain and obtain the necessary and sufcient condition for ergodicity of this embedded Markov chain.Secondly,we derive the steady-state joint distribution of the server state and the number of customers in the system/orbit at arbitrary time.We also derive a stochastic decomposition law.In the special case of individual arrivals,we develop recursive formulae for calculating the steady-state distribution of the orbit size.Besides,we investigate the relation between our discrete-time system and its continuous counterpart.Finally,some numerical examples show the influence of the parameters on the mean orbit size.     

Two-stage local M-estimation of additive models

This paper studies local M-estimation of the nonparametric components of additive models.A two-stage local M-estimation procedure is proposed for estimating the additive components and their derivatives.Under very mild conditions,the proposed estimators of each additive component and its derivative are jointly asymptotically normal and share the same asymptotic distributions as they would be if the other components were known.The established asymptotic results also hold for two particular local M-estimations:the local least squares and least absolute deviation estimations.However,for general two-stage local M-estimation with continuous and nonlinear ψ-functions,its implementation is time-consuming.To reduce the computational burden,one-step approximations to the two-stage local M-estimators are developed.The one-step estimators are shown to achieve the same effciency as the fully iterative two-stage local M-estimators,which makes the two-stage local M-estimation more feasible in practice.The proposed estimators inherit the advantages and at the same time overcome the disadvantages of the local least-squares based smoothers.In addition,the practical implementation of the proposed estimation is considered in details.Simulations demonstrate the merits of the two-stage local M-estimation,and a real example illustrates the performance of the methodology.     

Local linear regression for data with AR errors

In many statistical applications, data are collected over time, and they are likely correlated. In this paper, we investigate how to incorporate the correlation information into the local linear regression. Under the assumption that the error process is an auto-regressive process, a new estimation procedure is proposed for the nonparametric regression by using local linear regression method and the profile least squares techniques. We further propose the SCAD penalized profile least squares method to determine the order of auto-regressive process. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed procedure, and to compare the performance of the proposed procedures with the existing one. From our empirical studies, the newly proposed procedures can dramatically improve the accuracy of naive local linear regression with working-independent error structure. We illustrate the proposed methodology by an analysis of real data set.     

A ROBUST DISCRETIZATION OF THE REISSNER-MINDLIN PLATE WITH ARBITRARY POLYNOMIAL DEGREE

A numerical scheme for the Reissner-Mindlin plate model is proposed.The method is based on a discrete Helmholtz decomposition and can be viewed as a generalization of the nonconforming finite element scheme of Arnold and Falk[SIAM J.Numer.Anal.,26(6):1276-1290,1989].The two unknowns in the discrete formulation are the in-plane rotations and the gradient of the vertical displacement.The decomposition of the discrete shear variable leads to equivalence with the usual Stokes system with penalty term plus two Poisson equations and the proposed method is equivalent to a stabilized discretization of the Stokes system that generalizes the Mini element.The method is proved to satisfy a best-approximation result which is robust with respect to the thickness parameter t.     

LOCAL MEDIAN ESTIMATION OF VARIANCE FUNCTION

This paper considers local median estimation in fixed design regression problems. The proposed method is employed to estimate the median function and the variance function of a heteroscedastic regression model. Strong convergence rates of the proposed estimators are obtained. Simulation results are given to show the performance of the proposed methods.     

A TWO-SCALE HIGHER-ORDER FINITE ELEMENT DISCRETIZATION FOR SCHROEDINGER EQUATION

In this paper, a two-scale higher-order finite element discretization scheme is proposed and analyzed for a Schroedinger equation on tensor product domains. With the scheme, the solution of the eigenvalue problem on a fine grid can be reduced to an eigenvalue problem on a much coarser grid together with some eigenvalue problems on partially fine grids. It is shown theoretically and numerically that the proposed two-scale higher-order scheme not only significantly reduces the number of degrees of freedom but also produces very accurate approximations.     

OPTIMAL POINT-WISE ERROR ESTIMATE OF A COMPACT FINITE DIFFERENCE SCHEME FOR THE COUPLED NONLINEAR SCHRODINGER EQUATIONS

In this paper, we analyze a compact finite difference scheme for computing a coupled nonlinear SchrSdinger equation. The proposed scheme not only conserves the totM mass and energy in the discrete level but also is decoupled and linearized in practical computa- tion. Due to the difficulty caused by compact difference on the nonlinear term, it is very hard to obtain the optimal error estimate without any restriction on the grid ratio. In order to overcome the difficulty, we transform the compact difference scheme into a special and equivalent vector form, then use the energy method and some important lemmas to obtain the optimal convergent rate, without any restriction on the grid ratio, at the order of O（h4 ＋r2） in the discrete L∞ -norm with time step - and mesh size h. Finally, numerical results are reported to test our theoretical results of the proposed scheme.