An alternative direct proof of Gibbard’s random dictatorship theorem

We present an alternative proof of the Gibbards random dictatorship theorem with ex post Pareto optimality. Gibbard(1977) showed that when the number of alternatives is finite and larger than two, and individual preferences are linear (strict), a strategy-proof decision scheme (a probabilistic analogue of a social choice function or a voting rule) is a convex combination of decision schemes which are, in his terms, either unilateral or duple. As a corollary of this theorem (credited to H. Sonnenschein) he showed that a decision scheme which is strategy-proof and satisfies ex post Pareto optimality is randomly dictatorial. We call this corollary the Gibbards random dictatorship theorem. We present a proof of this theorem which is direct and follows closely the original Gibbards approach. Focusing attention to the case with ex post Pareto optimality our proof is more simple and intuitive than the original Gibbards proof.Received: 15 October 2001, Accepted: 23 May 2003, JEL Classification: D71, D72Yasuhito Tanaka: The author is grateful to an anonymous referee and the Associate editor of this journal for very helpful comments and suggestions. And this research has been supported by a grant from the Zengin Foundation for Studies on Economics and Finance in Japan.     

On interpenetrating samples of unequal sizes

Summary Koop [1967] proved that interpenetrating samples of unequal sizes are more efficient than those with equal sizes for estimating a finite population total. After observing that there is a serious lacuna present in his proof, a correct proof has been suggested. The optimum choice of individual sample sizes has also been discussed for a given (i) total sample size, (ii) cost and (iii) precision, with an assumed cost structure. Finally, the resulting estimators have been compared with those based on a single sample.     

Asymptotic normality of the NPMLE of linear functionals for interval censored data, case 1

We give a new proof of the asymptotic normality of a class of linear functionals of the nonparametric maximum likelihood estimator (NPMLE) of a distribution function with "case 1" interval censored data. In particular our proof simplifies the proof of asymptotic normality of the mean given in Groeneboom and Wellner (1992). The proof relies strongly on a rate of convergence result due to van de Geer (1993), and methods from empirical process theory.     

On the unimodality of passage time densities in birth-death processes

It has been shown [2] that for any ergodic birth-death process the p.d.f. of T_on , the passage time from the reflecting state 0 to any level n is log-concave and hence strongly unimodal. It is also known (cf [2]) that the p.d.f. of T_{n, n+1} or T_{n+1, n} for such a process is completely monotone and hence unimodal. It has been conjectured that the p.d.f. for the passage time T_mn between any two states is unimodal. An analytical proof of the result is presented herein, based on underlying renewal structure and methods in the complex plane. It is further shown that the p.d.f. of T_mn can always be written as the convolution of two p.d.f.s, one completely monotone and the second PF and hence log-concave.     

Efficiency. of infinite dimensional M- estimators

It is well-known that maximum likelihood estimators are asymptotically normal with covariance equal to the inverse Fisher information in smooth, finite dimensional parametric models. Thus they are asymptotically efficient. A similar phenomenon has been observed for certain infinite dimensional parameter spaces. We give a simple proof of efficiency, starting from a theorem on asymptotic normality of infinite dimensional M -estimators. The proof avoids the explicit calculation of the Fisher information. We also address Hadamard differentiability of the corresponding M -functionals.     

Theorems related to symmetric nonlinear decomposition

Decomposition methods can provide the rescue from the curse of dimensionality, which often prevents the successful numerical solution of large scale nonlinear mathematical programming problems. A symmetric nonlinear decomposition theory has been elaborated by T.O.M. Kronsjö (4) as an extension of a theory by the same author (3). The stringent proof of the convergence of this decomposition algorithm requires some results on necessary optimality conditions for certain mathematical programming problems. In this paper we state and prove some theorems providing these results.     

中国股市对经济增长作用的实证检验

关于金融体系和经济增长之间关系的争论由来已久。本文在分析国外关于这一争论的研究成果的基础上,对中国的股票市场发展与经济增长之间的关系做了一系列实证检验,考察了金融体系的一个组成部分———股票市场与经济增长的关系。检验结果说明,中国股市发展与经济增长之间的相关性不高,回归结果也不能说明中国股市发展会推动经济增长。     

On the structure of the equilibrium manifold

An elementary proof is given of Y. Balasko's theorem that the equilibrium manifold is diffeomorphic to R^lm. Our proof includes the case (l,m)=(2,2), which the original proof does not cover.     

Afriat’s Theorem and Samuelson’s ‘Eternal Darkness’

Suppose that we have access to a finite set of expenditure data drawn from an individual consumer, i.e., how much of each good has been purchased and at what prices. Afriat (1967) was the first to establish necessary and sufficient conditions on such a data set for rationalizability by utility maximization. In this note, we provide a new and simple proof of Afriat’s Theorem, the explicit steps of which help to more deeply understand the driving force behind one of the more curious features of the result itself, namely that a concave rationalization is without loss of generality in a classical finite data setting. Our proof stresses the importance of the non-uniqueness of a utility representation along with the finiteness of the data set in ensuring the existence of a concave utility function that rationalizes the data.     

On the existence of equilibria in economies with an infinite dimensional commodity space

We prove an infinite dimensional extension of the Gale–Nikaido–Debreu lemma which includes all necessary limiting processes and allows a proof of the existence of equilibria under standard assumptions in an economy with infinitely many commodities which exactly parallels the proof of Debreu (1959) for the finite dimensional case.     

Notes on the Markowitz portfolio selection method

A proof of the validity of Markowitz's critical line method is given for a more general situation than discussed by Markowitz. Next for the Markowitz case with a positive definite covariance matrix explicit expressions are derived for all efficient portfolios. Using these expressions it can be shown that the critical line in the (μ,α²) plane is a representation of a function which is not necessarily differentiable everywhere.     

A Simple Proof of the Equivalence of the Limiting Distributions of the Continuous-Time and the Embedded Process of the Queue Size in the M/G/1 Queue*

This paper presents an extremely simple proof of the known remarkable fact that for the M/G/1 queue the continuous-time process describing the number of customers in the system has the same limiting distribution as the embedded process describing the number of customers in the system just after service completion epochs.     

A note on preference for flexibility

A result of Kreps (1979) on preference for flexibility is extended from two to three periods (formally from preferences over sets to preferences over sets of sets). An intuitively easier route to Kreps' original result is also presented, making the proof essentially ready for use in a decision theory class. Received: 23 April 2001 / Accepted: 1 September 2001 First version October 1997.     

An elementary proof that additive i-likelihood characterizes the supports of consistent assessments

I prove a convenient reformulation of Kreps and Wilson (1982, Lemma A1), whose proof has a nontrivial gap. Essentially, the support of a consistent assessment is characterized by the additive representability of the infinite-relative-likelihood relation that the support implies. My proof is unexpectedly elementary, for it relies solely on a classic result about additive representation, which in turn relies solely on Farkas’ Lemma.     

Minimum variance unbiased estimation of the parameters of the Pareto distribution

Summary This paper presents a simpler proof of some results concerning estimation of the Pareto distribution due toLike [1969].     

基于QR码应用的电子回单流程设计

有效的订单回单管理可以提高企业运作效率、加快企业资金周转。当前,很多企业都面临着订单回单返回慢、收不齐的问题,在已有二维条码技术的基础上,结合智能手机的特点,提出了基于QR码应用的电子回单流程设计,并作了成本分析和风险评价。     

由汶川大地震引起对建筑抗震设计规范的思考

文章论述了现有抗震规范抗震设计方法存在的问题，并对2008年规范的修改内容进行了详细说明，给出了概念设计的要领和做好概念设计的建议。     

Constructive identification of the mixed proportional hazards model

We give a new proof of the identifiably of the MPH model. This proof is constructive: it is a recipe for constructing the triple—regression function, base-line hazard, and distribution of the individual effect—from the observed cumulative distribution functions.
We then prove that the triples do not depend continuously on the observed cumulative distribution functions. Uniformly consistent estimators do not exist.
Finally we show that the MPH model is even identifiable from two-sided censored observations. This proof is constructive, too.     

Vague lies and lax standards of proof: On the law and economics of advice

This paper analyzes a persuasion game where a seller provides (un)biased and (im)precise advice and may be fined by an authority for misleading the buyers. In the equilibrium, biasing the advice and making it noisier are complements. The advice becomes both more biased and less precise with a stricter standard of proof employed by the authority, a larger share of credulous consumers, and a higher buyers' heterogeneity. The optimal policy of the authority is characterized in terms of a standard of proof and resources devoted to the investigation.