A Sufficient and Necessary Condition for the Solvability of General Total Least Squares Problem

Abstract:

It is given that a simplistic proof for the solvability of Total Least Squares problem, extending this idea for General Total Least Squares problem, establishes a sufficient and necessary condition for solvability, proves the uniqueness of the amendment matrix and gives it's expression.

Key words:

general total least squares problem; SVD decomposition; singular values; singular vectors

Weak Convergence for Distribution Functions of Induced Maximum

Abstract:

Let{(X_n,Y_n)} be i.i.d. random vectors with common d.f. F. Under weaker conditions, it is shown in this paper that A_n^-1(Y_{(n,n )}-B_n)¡úI holds for some nondecreasing function I. Therefore the Nagaraja and David's result is generalized. Moreover, We prove that our conditions are not only sufficient, but also necessary for weak convergence of the sequence (a_n^-1(X_n,n-b_n), A_n^-1(Y_(n,n)-B_n)). At last, we show that the weak convergences of bivariate extreme values and (a_n^-1 (X_n,n-b_n), A_n^-1(Y_(n,n)-B_n)) are closely related.

Key words:

induced maximum; weak convergence for distribution functions; bivariate extremes

Numerical Approximation of Interface Problems for Elliptic Differential Equations

Abstract:

It is discussed that the numerical approximation of interface problems for elliptic partial differential equations. For the interface problems with variable coefficients, it is introduced that a particular finite element method combined with the infinite element method to approach the singular solution in the neighborhood of the singular points, and it is proved that the method possesses the same accuracy as the finite element method to the regular solution. Numerical examples are also given.

Key words:

infinite element method; interface problem; singularity

On the Maximal Solution of the Matrix Equation X+A^TX^-1A=I

Abstract:

An elegant property of the maximal solution to the matrix equation X+A^TX^-1A=I is presented. The property shows that the maximal solution is well-conditioned. Two new iteration methods for finding the maximal solution are proposed. Of these two methods, one is a linearly convergent iteration without matrix inversion, and one is related to Newton's method and quadratically convergent. The convergence analysis is also given. Comparisons have been made with other known methods. In all test problems the new quadratically convergent method appeared to be far superior to the other methods.

Key words:

matrix equation; maximal solution; numerical methods

Random Independence and Regressive Independence

Abstract:

Regressive independence means that conditional expectation E(Y|X) of two random variables X and Y does not depend on X. The relation between regressive independence and random independence is discussed, and several necessary and sufficient conditions are presented.

Key words:

Conditional expectation; random independence; weak association

Weak Convergence of Distribution of Concomitants of Fixed Rank Order Statistics

Abstract:

A Sufficient and necessary condition on weak convergence of joint distribution of fixed rank order statistics and its concomitants is obtained, also a sufficient condition on weak convergence of distribution of the maxima of concomitants of selected order statistics is obtained.

Key words:

concomitant of order statistics; extreme-value distribution laws; weak convergence of distribution

Improvement on the Natural Dictionary-ordering Method in Reliability Growth Tests

Abstract:

In a m-stage reliability growth test, to estimate the lower confidence limit of the reliability of the system in the final stage, randomization is introduced to improve the exsiting natural chain method. Simulation study shows that when the number of stages is one, the randomization method is ideal.

Key words:

reliability; lower confidence limit; sample space ordering; ML ordering method; NATURAL dictionary ordering method

Statistical Modeling of J-effect and Policy Experiments

Abstract:

The main purpose of this paper is to investigate the statistical analysis of J-effect in trade balance of Mexico in 1989-1995.Sparse coefficients modeling has been successfully introduced for the model construction of J-effect. Based on the model, the recovery period index is easy to define and the policy experiment also may be carried out by orthogonal experiment design. The results show that the devaluation of Pesos and the short interest rate are over adjusted but the economic and financial policy during that period were basically correct. Finally, J-effects between Mexico and Japan are compared, it seems that the recovery period of developing countries will be longer than the industry countries.

Key words:

J-effect; international trade balance; sparse coefficients modeling

Generalized Pareto Distribution and Analysis of Stock Price Returns

Abstract:

Some properties of the generalized Pareto distribution are discussed.Then GP model is used to analyze the returns to Shanghai stock index,Shenzhen stock index and the stock prices of two specific companies.A quantitative indicator of extreme changes in stock index and stock price is mentioned.The estimation of Value-at-Risk is also discussed.

Key words:

Generalized Pareto distribution; returns; tail index; value at risk; capital-loss coefficient

A Model of Attention-based Image Recognition and Its Application in Face Detection

Abstract:

An attention-based image recognition model is proposed.When analyze complex visual field or pattern,visual attention mechanism is used to detect saliency features in the image and drive the fixation point to scan the saliency features sequentially.During each fixation,the local pattern at the fixation point is memorized or matched.There are two parts in the memory of a complex pattern,the memory of local patterns that constitute the complex pattern and the memory of space relations between local patterns.Corresponding to memory process,the recognition process also contains two parts,the matching of local patterns and the matching of space relations between local patterns.An object is recognized only when there are enough numbers of local patterns is matched and the space relations between these local patterns are correct. This model is used in face detection in complex background.The results shows that the model can solves the problem of invariant recognition with respect to shift,rotation and scale,and the computing is fast and robust.This model likes human's vision system and is applicable.

Key words:

visual attention; visual model; face detection; invariant recognition

An Edgeworth Expansion of A Sum of Extreme Values

Abstract:

Under the condition of second order generalized regular variation,the asymptotic expansions for the distribution of the sums of extreme values are obtained.

Key words:

sum of extreme values; regular variation; asymptotic expansion

Difference Sets in Groups of Order 4p⁴

Abstract:

Let G be a group of order 4p⁴,N be a normal subgroup of G and D be a hypothetical Menon difference set in G, by investigating the intersection numbers, some necessary conditions are gotten.

Key words:

difference sets; intersection numbers; complete cyclic basis

¦Ð₁-finite-index Maps from 3-manifolds Covered by Torus Bundles over S^£±

Abstract:

It is proved that any ¦Ð₁-finite-index map from a closed orientable 3-manifold covered by a torus bundle over S¹ to a closed aspherical orientable irreducible 3-manifold is homotopic to a covering map,and is of non-zero degree.This verifies a special case of the conjecture that any ¦Ð₁-surjective map between closed aspherical 3-manifolds having the same rank on ¦Ð₁ must be of non-zero degree.

Key words:

¦Ð₁-finite-index map; torus bundle over S¹; aspherical 3-manifold; covering map; non-zero degree

Some Results on MLE of the Parameter of the Exponential Distribution from Randomly Censored Data

Abstract:

Key words:

asymptotic minimax efficiency; interative logarithm law; mean error

Limit of Perturbed Discontinuous Dynamical System

Abstract:

The author uses comparison theorem for stochastic differential equations to explore the limit behavior of one-dimentional discontinuous dynamical system with small random perturbations.

Key words:

stochastic differential equations; comparison theorem; weak convergence

Automatic Segmentation of Moving Objects for
Head-shoulder Video Sequence

Abstract:

Introducing and comparing the difference within the conception of area segmentation,motion segmentation and moving object segmentation (VOP extraction),and their application in content-based video sequence image coding.Analysis the relationship between the frame difference image and its relative frame gray level image.Then a new automatic moving object edge tracking and extracting method,based on the high correlation between the edge of frame difference and the edge of gray level image,was proposed.Using the close of moving object edge to get the real moving object.

Key words:

segmentation; video object; area segmentation; motion segmentation; object segmentation; object tracking

q-Zero-covariance Portfolio Frontier

Abstract:

Unlike the literature.this paper mainly discusses the characteristics of the portfolio which isn't on the portfolio frontier.A more general concept¡ªq-zero-covariance portfolio frontier is proposed, and its geometric configuration is depicted in the ¦Ò₂(r)¡ªE£Ûr£Ý space.The usual zero covariance portfolio of the frontier portfolio is its degenerate case,and the portfolio frontier is the envelope of our q-zero-covariance portfolio frontier as q moves.

Key words:

portfolio frontier; frontier portfolio; q-zero-covariance portfolio frontier

Optimum BMS Designs with Dependent Risks

Abstract:

The bivariate Poisson models of contingent claim times about the homogeneous portfolios are studied, and an independent condition of the two variables is proved, and then the Mixed bivariate Poisson models of contingent claim times about the heterogeneous portfolios with dependent risks are studied, and the last, the optimum BMS formula about the heterogeneous portfolios with dependent risks are reached.

Key words:

risk dependence; bivariate Poisson; mixed Poisson; BMS

A New Definition of Fuzzy Partition and Its Application

Abstract:

In this paper, we pointed out that the Ruspini's definition of fuzzy partition has a shortcoming, which does not always coincide with our intuition. So we proposed a new definition for fuzzy partition and proved the new definition of fuzzy partition has a desired property consistent with our intuition and applications of fuzzy partition (e.g., fuzzy decision making, fuzzy clustering, fuzzy control, etc.). It can follow Ruspini's definition of fuzzy partition, which are cited frequently in current papers. According to the new definition of fuzzy partition, we defined the relative clearness of fuzzy sets and the mean clearness of fuzzy partition. The latter is proved effective for evaluating the performance of FCM algorithm by the experiments.

Key words:

fuzzy sets; fuzzy partition; FCM algorithm

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