熵指数的可分解特性及其在多元化测度中的应用

熵是对不确定性的度量,被广泛应用于多个学科领域。可分解特性是熵统计量的良好品质,它使事件的总体熵可以分解为类间熵和平均的类内熵。这种特性应用到公司多元化水平的测度中,可以有效地解决多元化指数在统计分析中的多重共线性问题。     

Two-sample rank tests with truncated populations

LetX ₁,…,X _m andY ₁,…,Y _n be two independent samples from continuous distributionsF andG respectively. Using a Hoeffding (1951) type theorem, we obtain the distributions of the vector S=(S ₍₁₎,…,S _(n)), whereS _(j)=# (X _i ’s≤Y _(j)) andY _(j) is thej-th order statistic ofY sample, under three truncation models: (a)G is a left truncation ofF orG is a right truncation ofF, (b)F is a right truncation ofH andG is a left truncation ofH, whereH is some continuous distribution function, (c)G is a two tail truncation ofF. Exploiting the relation between S and the vectorR of the ranks of the order statistics of theY-sample in the pooled sample, we can obtain exact distributions of many rank tests. We use these to compare powers of the Hajek test (Hajek 1967), the Sidak Vondracek test (1957) and the Mann-Whitney-Wilcoxon test. We derive some order relations between the values of the probagility-functions under each model. Hence find that the tests based onS ₍₁₎ andS _(n) are the UMP rank tests for the alternative (a). We also find LMP rank tests under the alternatives (b) and (c).     

A note on the projection properties of Hadamard matrices obtained by the first Payley construction

We show that the projections on four factors of an arbitrary orthogonal array of strength 2 allow the estimation of main effects and two-factor interactions when all other effects are assumed to be zero, if those projections satisfy the bounds given by Weils theorem. The only exceptions are the Hadamard matrices of orders 16 and 24. A consequence is again the estimability of main effects and two-factor interactions for the projections on four factors of the first Payley construction for arbitrary run size.     

Exceptional Convergence of the Sample Variance

The case is investigated when Hoeffding's one sample U–statistic theorem for the sample variance S² is not applicable. It is shown that this occurs only when the parent distribution is the two–point distribution with jumps of equal magnitude. For this exceptional case the standardised S² is shown to converge in distribution to (1 – V )√2, where V has chi–square distribution with one degree of freedom.     

Extensive-form games and strategic complementarities

I prove the subgame-perfect equivalent of the basic result for Nash equilibria in normal-form games of strategic complements: the set of subgame-perfect equilibria is a nonempty, complete lattice—in particular, subgame-perfect Nash equilibria exist. For this purpose I introduce a device that allows the study of the set of subgame-perfect equilibria as the set of fixed points of a correspondence. My results are limited because extensive-form games of strategic complementarities turn out—surprisingly—to be a very restrictive class of games.     

论传统外部性理论解决环境代际外部性的失效

代际外部性问题主要是人类代际之间行为的相互影响,尤其是前代对后代、当代对后代的影响。在解决代际外部性上,施害者、受害者和政府生活在不同的时空中,新古典方法几乎就无能为力。产权的界定是在产权主体存在的前提下进行的,所以产权在代际进行界定是不可能实现的,所以通过科斯定理来消除代际的外部性也行不通。     

Advertising, Its Determinants, and Market Structure

This study derives a formal model of firm advertising behavior and applies it to the industry level to figure out the relationship between advertising and market structure. The firm advertising model shows that both consumer preference andfirm-specific advertising competence jointly determineprofit-maximizing advertising intensity. At the industry level, advertising intensity is represented multiplicatively by consumer preference and a measure of market structure, which reflects the joint distribution of the levels of advertising competence and market shares among firms. The new market structure measure suggests that those single-dimensional measures of market structure such as seller concentration and the Herfindahl index are inadequate in explaining interindustry differences in advertising intensity, and that the long-debated advertising-concentration relationship differs depending primarily on the appropriability of advertising. An empirical analysis of 426 five-digit Korean manufacturing industries shows that an inverted U-shaped relationship between the Herfindahl index and industry advertising intensity is observed for consumer goods industries but a lazy J-shaped relationship for producer goods industries.     

The power of dimensional analysis in production systems design

Dimensional Analysis (DA) is a well-known methodology in physics, chemistry and other traditional engineering areas. In its simplest form, DA is used to check the meaningfulness of a set of equations (dimensional homogeneity). In the last century, the dimensional theory has been profoundly investigated: its highest achievement is the Buckingham theorem (or pi-theorem), which states that any equation modelling a physical problem can be rearranged in terms of dimensionless ratios, thus saving variables to be handled, and especially enriching the inner physical knowledge of the studied phenomenon.In this paper we investigate how DA can be applied to Operations Management (OM) topics and which benefits it can bring to researchers in this area. A literature review is performed to clarify the main operative issues regarding DA application (assumptions and limitations); then existing applications of DA to OM are explored, pointing out that few researchers have tried to apply this methodology in the OM research field.Stemming from this analysis, we applied the pi-theorem to the design of a Flexible Manufacturing System. A complex problem, requiring 13 dimensional quantities to be expressed, is first studied via simulation; then DA is applied, reducing the number of variables to 9 dimensionless ratios. The reduced problem has a suitable size to be analytically explored and a regression model is formulated which, compared with the simulation study, offers the same precision in analysing the FMS behaviour, being more compact and powerful. This application shows the potential of DA in OM research, and will hopefully draw the attention of researches to this powerful, but unfamiliar and therefore neglected, methodology.     

将数学建模引入高等数学教学中的典型案例

首先阐述了将数学建模思想融入高等数学教学内容中的意义,接着从高等数学中的基本概念和基本定理出发,通过具体案例说明如何将数学建模案例融入在高等数学教学中。最后给出了根据高等数学内容选编的典型建模案例。     

Solvability of perturbation solutions in DSGE models

We prove that the undetermined Taylor series coefficients of local approximations to the policy function of arbitrary order in a wide class of discrete time dynamic stochastic general equilibrium (DSGE) models are solvable by standard DSGE perturbation methods under regularity and saddle point stability assumptions on first order approximations. Extending the approach to nonstationary models, we provide necessary and sufficient conditions for solvability, as well as an example in the neoclassical growth model where solvability fails. Finally, we eliminate the assumption of solvability needed for the local existence theorem of perturbation solutions, complete the proof that the policy function is invariant to first order changes in risk, and attribute the loss of numerical accuracy in progressively higher order terms to the compounding of errors from the first order transition matrix.