一个组合分布模型及其参数估计

本文根据极值分布理论,提出了一个由原始分布和尾分布组成的组合分布模型,研究了组合分布模型中原始分布和尾分布的确定方法,建立了组合分布模型参数估计的加权最优化模型,实例计算说明,组合分布较好地反映了风险变量极值事件的风险。     

广义线性回归极大似然估计的强相合性

设有该文第1节所描述的广义线性回归模型,以$\underline{\lambda}_n$和$\overline{\lambda}_n$分别记$\sum\limits_{i=1}^{n}Z_iZ_i^{\prime}$的最小和最大特征根,$\hat{\beta}_n$记$\beta_0$的极大似然估计.在文献[1]中,当\{$Z_i,i\ge1$\}有界时得到$\hat{\beta}_n$强相合的充分条件,在自然联系和非自然联系下分别为$\underline{\lambda}_n\rightarrow\infty$, $(\overline{\lambda}_n)^{1/2+\delta}=O(\underline{\lambda}_n)$（对某$\delta>0$)以及$\underline{\lambda}_n\rightarrow\infty$, $\overline{\lambda}_n=O(\underline{\lambda}_n)$.作者将后一结果改进为只要求$(\overline{\lambda}_n)^{1/2+\delta}=O(\underline{\lambda}_n)$,从而与自然联系情况下的条件达到一致.     

Speedup estimates for some variants of the parallel implementations of the branch-and-bound method

The efficiency of parallel implementations of the branch-and-bound method in discrete optimization problems is considered. A theoretical analysis and comparison of two parallel implementations of this method is performed. A mathematical model of the computation process is constructed and used to obtain estimates of the maximum possible speedup. Examples of problems in which none of these two parallel implementations can speed up the computations are considered.     

On the construction of samples for testing approximate optimization methods for estimate calculation algorithms

To validate approximate optimization schemes for estimate calculation algorithms (ECAs), it is necessary to compute the optimal height, which cannot be done in a reasonable amount of time. A variety of samples are built for which the optimal height of the ECAs is known by construction.     

A nonlinear nonlocal mixed problem for a second order pseudoparabolic equation

We study a nonlocal mixed problem for a nonlinear pseudoparabolic equation, which can, for example, model the heat conduction involving a certain thermodynamic temperature and a conductive temperature. We prove the existence, uniqueness and continuous dependence of a strong solution of the posed problem. We first establish for the associated linear problem a priori estimate and prove that the range of the operator generated by the considered problem is dense. The technique of deriving the a priori estimate is based on constructing a suitable multiplicator. From the resulted energy estimate, it is possible to establish the solvability of the linear problem. Then, by applying an iterative process based on the obtained results for the linear problem, we establish the existence, uniqueness and continuous dependence of the weak solution of the nonlinear problem.     

On convergence of a semi-analytical method for American option pricing

We examine the valuation of American put options by a semi-analytical method, and obtain the prior estimate and the convergence of the approximate solution. Our proofs are based on the embedding theorem in Sobolev space and the theory of functional analysis, in particular, the theory of weak compactness. The results in this paper theoretically confirm empirical observations that these methods are accurate and computationally efficient.     

Local influence analysis for semiparametric reproductive dispersion nonlinear models

The present paper proposes a semiparametric reproductive dispersion nonlinear model (SRDNM) which is an extension of the nonlinear reproductive dispersion models and the semiparameter regression models. Maximum penalized likelihood estimates (MPLEs) of unknown parameters and nonparametric functions in SRDNM are presented. Assessment of local influence for various perturbation schemes are investigated. Some local influence diagnostics are given. A simulation study and a real example are used to illustrate the proposed methodologies.     

A Tikhonov-type method for solving a multidimensional inverse heat source problem in an unbounded domain

In this study we prove a stability estimate for an inverse heat source problem in the n-dimensional case. We present a revised generalized Tikhonov regularization and obtain an error estimate. Numerical experiments for the one-dimensional and two-dimensional cases show that the revised generalized Tikhonov regularization works well.     

Model-based likelihood ratio confidence intervals for survival functions

We introduce an adjusted likelihood ratio procedure for computing pointwise confidence intervals for survival functions from censored data. The test statistic, scaled by a ratio of two variance quantities, is shown to converge to a chi-squared distribution with one degree of freedom. The confidence intervals are seen to be a neighborhood of a semiparametric survival function estimator and are shown to have correct empirical coverage. Numerical studies also indicate that the proposed intervals have smaller estimated mean lengths in comparison to the ones that are produced as a neighborhood of the Kaplan-Meier estimator. We illustrate our method using a lung cancer data set.     

The characteristic finite difference streamline diffusion method for convection-dominated diffusion problems

In this paper, we consider the characteristic finite difference streamline diffusion method for two-dimensional convection-dominated diffusion problems. The scheme is combined the method of characteristics with the finite difference streamline diffusion (FDSD) method to create the characteristic FDSD (C-FDSD) procedures. Stability analysis and error estimate of the C-FDSD method are deduced. The scheme not only realizes the purpose of lowering the time-truncation error, using larger time step for solving the convection-dominated diffusion problems, but also keeps the favorable stability and high precision of the FDSD method. Finally, numerical experiments are presented to illustrate the availability of the scheme.