An operative extension of the likelihood ratio test from fuzzy data

In the present paper we are going to extend the likelihood ratio test to the case in which the available experimental information involves fuzzy imprecision (more precisely, the observable events associated with the random experiment concerning the test may be characterized as fuzzy subsets of the sample space, as intended by Zadeh, 1965). In addition, we will approximate the immediate intractable extension, which is based on Zadeh’s probabilistic definition, by using the minimum inaccuracy principle of estimation from fuzzy data, that has been introduced in previous papers as an operative extension of the maximum likelihood method.     

对函数sin(kx+)一个性质的探讨

本文探讨如何找最小正实数k,使f(x)=sin(kx+)在任意两个整数间至少有一个最大值1与一个最小值-1,导出了函数f(x)的周期T与f(x)具有上述性质的关系,然后把问题简化为在0≤φ≤π/2的范围内讨论,并得出了φ为0,π/2,q/p·π/2(q/p为既约真分数)及其它四种情况的最小正实数k。     

Theory of optimal blocking of nonregular factorial designs

The authors introduce the notion of split generalized wordlength pattern (GWP), i.e., treatment GWP and block GWP, for a blocked nonregular factorial design. They generalize the minimum aberration criterion to suit this type of design. Connections between factorial design theory and coding theory allow them to obtain combinatorial identities that govern the relationship between the split GWP of a blocked factorial design and that of its blocked consulting design. These identities work for regular and nonregular designs. Furthermore, the authors establish general rules for identifying generalized minimum aberration (GMA) blocked designs through their blocked consulting designs. Finally they tabulate and compare some GMA blocked designs from Hall's orthogonal array OA(16,2¹5,2) of type III.     

Estimation of the MSE matrix of the stein estimator

Uniformly minimum-variance unbiased (UMVU) estimators of the total risk and the mean-squared-error (MSE) matrix of the Stein estimator for the multivariate normal mean with unknown covariance matrix are proposed. The estimated MSE matrix is helpful in identifying the components which contribute most to the total risk. It also contains information about the performance of the shrinkage estimator with respect to other quadratic loss functions.     

DELAY ESTIMATION BY A HILBERT TRANSFORM METHOD

This paper describes an estimation of the time delay between two stationary time series signals, in which an input signal is measured with little noise and an output signal is the sum of a noise and the response from a linear system. We use the Hilbert transform relation for minimum delay systems to estimate the time delay. Some computer simulation results are given to evaluate the performance of the proposed method.     

“The Motherhood Wage Gap for Women in the United States: The Importance of College and Fertility Delay”

One of the stylized facts from the past 30 years has been the declining rate of first births before age 30 for all women and the increase rate of first births after age 30 among women with four-year college degrees (Steven P. Martin, Demography, 37(4), 523–533, 2000). What are some of the factors behind womens decision to postpone their childbearing? We hypothesize that the wage difference often observed between like-educated mothers and non-mothers (Jane Waldfogel, Journal of Labor Economics, 16, 505–545, 1998a; Journal of Economic Perspectives 12(1) 137–156, 1998b) may be affected by the postponement of childbearing until after careers are fully established. Hence, we focus on college-educated women because they are typically more career-oriented than their non-college educated counterparts and also the group most often observed postponing maternity. We use individual-level data on women from the 1979 National Longitudinal Survey of Youth (NLSY79) in order to control for individual-level unobserved heterogeneity as well as human capital characteristics, such as actual work experience, in our empirical analysis. We estimate wage equations, first producing base-line results to compare to the existing literature. Then, we expand the basic wage equation model to address fundamental econometric issues and the education/fertility issue at hand. Our empirical findings are two-fold. First, we find that college-educated mothers do not experience a motherhood wage penalty at all. In fact, they enjoy a wage boost when compared to college-educated childless women. Second, fertility delay enhances this wage boost even further. Our results provide an explanation for the observed postponement of maternity for educated women. We argue that the wage boost experienced by college-educated mothers may be the result of their search for family–friendly work environments, which, in turn, yields job matches with more female-friendly firms offering greater opportunities for advancement.JEL Codes: J13 and J3     

The Effect of a Family Policy Reform on Mother’s Pay: A Natural Experiment Approach

All parents in Norway with children aged one to three, who do not attend publicly subsidised day care, are entitled to a cash-for-care (CFC) subsidy. Studies have shown that the reform has reduced mothers labour supply. In this paper we analyse wage effects of the reform. We put forward a framework for evaluating reforms when reforms are uniformly and equally accessible nation-wide. First, running a simple Difference in differences (DD) analysis, results suggest that the CFC reform has reduced the mothers wages. However, after controlling for the age of the child effect, by running a triple difference approach, we no longer find any evidence of negative wage effects.This revised version was published online in May 2005 with corrections to the authors name and to the heading of table A2.     

Two Variations of the Minimum Steiner Problem

Given a set S of starting vertices and a set T of terminating vertices in a graph G = (V,E) with non-negative weights on edges, the minimum Steiner network problem is to find a subgraph of G with the minimum total edge weight. In such a subgraph, we require that for each vertex s S and t T, there is a path from s to a terminating vertex as well as a path from a starting vertex to t. This problem can easily be proven NP-hard. For solving the minimum Steiner network problem, we first present an algorithm that runs in time and space that both are polynomial in n with constant degrees, but exponential in |S|+|T|, where n is the number of vertices in G. Then we present an algorithm that uses space that is quadratic in n and runs in time that is polynomial in n with a degree O(max {max {|S|,|T|}–2,min {|S|,|T|}–1}). In spite of this degree, we prove that the number of Steiner vertices in our solution can be as large as |S|+|T|–2. Our algorithm can enumerate all possible optimal solutions. The input graph G can either be undirected or directed acyclic. We also give a linear time algorithm for the special case when min {|S|,|T|} = 1 and max {|S|,|T|} = 2.The minimum union paths problem is similar to the minimum Steiner network problem except that we are given a set H of hitting vertices in G in addition to the sets of starting and terminating vertices. We want to find a subgraph of G with the minimum total edge weight such that the conditions required by the minimum Steiner network problem are satisfied as well as the condition that every hitting vertex is on a path from a starting vertex to a terminating vertex. Furthermore, G must be directed acyclic. For solving the minimum union paths problem, we also present algorithms that have a time and space tradeoff similar to algorithms for the minimum Steiner network problem. We also give a linear time algorithm for the special case when |S| = 1, |T| = 1 and |H| = 2.An extended abstract of part of this paper appears in Hsu et al. (1996).Supported in part by the National Science Foundation under Grants CCR-9309743 and INT-9207212, and by the Office of Naval Research under Grant No. N00014-93-1-0272.Supported in part by the National Science Council, Taiwan, ROC, under Grant No. NSC-83-0408-E-001-021.     

Multiparameter estimation of discrete exponential distributions

Let X₁, …, X_p be independent random variables, all having the same distribution up to a possibly varying unspecified parameter, where each of the p distributions belongs to the family of one parameter discrete exponential distributions. The problem is to estimate the unknown parameters simultaneously. Hudson (1978) shows that the minimum variance unbiased estimator (MVUE) of the parameters is inadmissible under squared error loss, and estimators better than the MVUE are proposed. Essentially, these estimators shrink the MVUE towards the origin. In this paper, we indicate that estimators shifting the MVUE towards a point different from the origin or a point determined by the observations can be obtained.     

农村最低生活保障制度存在问题及对策——基于甘肃省的调查分析

对甘肃省农村最低生活保障制度进行了相关调查,对该制度实施的现状和存在的问题进行了分析,研究表明：甘肃省农村最低生活保障制度在实施中存在的问题主要有经费缺乏,保障水平低,覆盖面窄,低保对象的确定和界定标准困难,缺乏法律保障,下级部门执行不力等,因此要科学确定农村居民最低生活保障标准,提高保障标准;完善最低生活保障对象的甄别机制;大力推行政府主导与多元复合的农村低保救助模式;运用专业技术,提高管理水平;建立健全综合性的低保制度体系;加强法制建设,实现最低生活保障的法制化、规范化管理。