动态投资分配模型及其优化

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Characterization of continuous distributions in terms of moments of extremal statistics

We give characterizations of continuous distributions in terms of moments of order statistics when the sample size is random. In particular, we characterize uniform, exponential, Pareto, and logistic distributions. Special cases of a random sample size (logarithmic series, geometrical, truncated binomial, truncated negative binomial, and truncated Poisson distribution) are also considered. Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part I.     

Matrix scaling,entropy minimization,and conjugate duality (II): The dual problem

We present a matrix scaling problem calledtruncated scaling and describe applications arising in economics, urban planning, and statistics. We associate a dual pair of convex optimization problems to the scaling problem and prove that the existence of a solution for the truncated scaling problem is characterized by the attainment of the infimum in the dual optimization problem. We show that optimization problems used by Bacharach (1970), Bachem and Korte (1979), Eaves et al. (1985), Marshall and Olkin (1968) and Rothblum and Schneider (1989) to study scaling problems can be derived as special cases of the dual problem for truncated scaling. We present computational results for solving truncated scaling problems using dual coordinate descent, thereby showing that truncated scaling provides a framework for modeling and solving large-scale matrix scaling problems.Research supported in part by NSF grants ECS 8718971 and ECS 8943458.     

Empirical Likelihood Ratio With Arbitrarily Censored/Truncated Data by EM Algorithm

The empirical likelihood is a general nonparametric inference procedure with many desirable properties. Recently, theoretical results for empirical likelihood with certain censored/truncated data have been developed. However, the computation of empirical likelihood ratios with censored/truncated data is often nontrivial. This article proposes a modified self-consistent/EM algorithm to compute a class of empirical likelihood ratios for arbitrarily censored/truncated data with a mean type constraint. Simulations show that the chi-square approximations of the log-empirical likelihood ratio perform well. Examples and simulations are given in the following cases: (1) right-censored data with a mean parameter; and (2) left-truncated and right-censored data with a mean type parameter.     

The truncatedSVD as a method for regularization

The truncated singular value decomposition (SVD) is considered as a method for regularization of ill-posed linear least squares problems. In particular, the truncated SVD solution is compared with the usual regularized solution. Necessary conditions are defined in which the two methods will yield similar results. This investigation suggests the truncated SVD as a favorable alternative to standard-form regularization in cases of ill-conditioned matrices with well-determined numerical rank.This work was carried out while the author visited the Dept. of Computer Science, Stanford University, California, U.S.A., and was supported in part by National Science Foundation Grant Number DCR 8412314, by a Fulbright Supplementary Grant, and by the Danish Space Board.     

Tableaux and plane partitions of truncated shapes

We consider a new kind of straight and shifted plane partitions/Young tableaux – ones whose diagrams are no longer of partition shape, but rather Young diagrams with boxes erased from their upper right ends. We find formulas for the number of standard tableaux in certain cases, namely a shifted staircase without the box in its upper right corner, i.e. truncated by a box, a rectangle truncated by a staircase and a rectangle truncated by a square minus a box. The proofs involve finding the generating function of the corresponding plane partitions using interpretations and formulas for sums of restricted Schur functions and their specializations. The number of standard tableaux is then found as a certain limit of this function.     

Some General Characterizations of the Bivariate Gumbel Distribution and the Bivariate Lomax Distribution Based on Truncated Expectations

Recently attempts have been made to characterize probability distributions via truncated expectations in both univariate and multivariate cases. In this paper we will use a well known theorem of Lau and Rao (1982) to obtain some characterization results, based on the truncated expectations of a functionh, for the bivariate Gumbel distribution, a bivariate Lomax distribution, and a bivariate power distribution. The results of the paper subsume some earlier results appearing in the literature.     

Approximation theorems for a general class of truncated operators

In this paper we give direct approximation theorems for a general family of truncated operators. We discuss the linear and nonlinear cases.     

Estimation of the number of failures in the Weibull model using the ordinary differential equation

In estimating the number of failures using right truncated grouped data, we often encounter cases that the estimate is smaller than the true one when we use the likelihood principle to conditional probability. In infectious disease spread predictions, the SIR model described by simultaneous ordinary differential equations is commonly used, and it can predict reasonably well the number of infected patients even when the size of observed data is small. We have investigated whether the ordinary differential equation model can estimate the number of failures more accurately than does the likelihood principle under the condition of right truncated grouped data. The positive results are obtained in the Weibull model, similarly to the cases of the SARS, A(H1N1), and FMD.     

Study of cut-set distributions in the fuzzy reliability evaluation models

The performances of the cut-set distributions in the fuzzy reliability evaluation are studied based on cut-set method. Firstly, a theorem is proved to indicate the convergence defect of the model with the three commonly used cut-set distributions, including uniform distribution, linear distribution and truncated normal distribution. Secondly, a general method is proposed to construct a new family of cut-set distributions named intrinsic cut-set distributions, and three specific intrinsic cut-set distributions are obtained based on this method, including modified truncated normal distribution, truncated lognormal distribution and truncated Weibull distribution. Thirdly, numerical examples are carried out to verify the above theoretical results. It is shown that, compared with the three commonly used cut-set distributions, the proposed intrinsic cut-set distributions make the evaluation more stable and the fuzzy reliability model achieve good convergence at the boundary cases, which could effectively improve the evaluation accuracy and broaden the application of the model. Finally, some recommendations are given to show how to choose a suitable cut-set distribution in practice.     

Positivity of Riesz functionals and solutions of quadratic and quartic moment problems

We employ positivity of Riesz functionals to establish representing measures (or approximate representing measures) for truncated multivariate moment sequences. For a truncated moment sequence y, we show that y lies in the closure of truncated moment sequences admitting representing measures supported in a prescribed closed set K⊆Rn if and only if the associated Riesz functional Ly is K-positive. For a determining set K, we prove that if Ly is strictly K-positive, then y admits a representing measure supported in K. As a consequence, we are able to solve the truncated K-moment problem of degree k in the cases: (i) (n,k)=(2,4) and K=R²; (ii) n?1, k=2, and K is defined by one quadratic equality or inequality. In particular, these results solve the truncated moment problem in the remaining open cases of Hilbert's theorem on sums of squares.