On a stochastic approximation procedure based on averaging

Based on the idea of averaging a new stochastic approximation algorithm has been proposed by Bather (1989), which shows a preferable performance for small to moderate sample sizes. In the present paper an almost sure representation is established for this procedure, which gives the optimal rate of convergence with minimal asymptotic variance. Work partly supported by the research grant Ku719/2-1 of the Deutsche Forschungsgemeinschaft     

Quasi-isotonic regression and stochastic approximation

Summary Mukerjee’s stochastic approximation procedure on a lattice is modified: at each stage of the procedure, a sample quasi-isotonic regression is calculated instead of the isotonic one, the former being defined as the least-squares fit of observations within the class of functions that are nonpositive on the left and nonnegative on the right of some point. An effective algorithm is given and a convergence theorem proven. A multidimensional version of the procedure is proposed, the question of its convergence being left open. Research supported by the Deutsche Forschungsgemeinschaft, SFB 72.     

Model averaging estimators for the stochastic frontier model

Journal of Productivity Analysis - Model uncertainty is a prominent feature in many applied settings. This is certainty true in the efficiency analysis realm where concerns over the proper...     

Some remarks on stochastic dominance

The present work proposes a definition of dominance (dominance in the strict sense), which is weaker than first order stochastic dominance, stating precisely that the r.v.Y dominatesX (XY) if Pr(YX)=1.Such a dominance in the strict sense is then compared with first and second order stochastic dominance and with dominance between descisions of the same decision problem summarised in a table of results, arriving at certain general remarks about decision problems and the choice between r.v.'s. Indications are also given about how it is possible to obtain simple and useful bounds for Pr(YX).

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Riassunto Nel presente lavoro si propone una definizione di dominanza (dominanza in senso stretto) più debole della dominanza stocastica del prim'ordine, precisamente dicendo che la v.a.Y dominaX (XY) se Pr(YX)=1.Si confronta poi tale dominanza in senso stretto con le dominanze stocastiche del primo e del secondo ordine e con la dominanza tra decisioni di uno stesso problema di decisione sintetizzato in una tabella dei risultati giungendo ad alcune precisazioni generali sui problemi di decisione e di scelta tra v.a. Si danno anche indicazioni su come sia possibile ottenere limitazioni per la Pr(YX).

     

Some results on general assumptions about the existence of economic equilibrium

In the present paper we maximally use the possibilities provided by the Nash approach and the Kakutani fixed point theorem for proving the existence of an economic equilibrium. We obtain a general existence theorem which does not require a special form for income distribution functions and producer's objectives, independence of consumers' tastes, ordered preference and zero degree homogeneous price dependence. The role of the non-satiation assumption becomes more clear.     

A Gaussian approximation scheme for computation of option prices in stochastic volatility models

We consider European options on a price process that follows the log-linear stochastic volatility model. Two stochastic integrals in the option pricing formula are costly to compute. We derive a central limit theorem to approximate them. At parameter settings appropriate to foreign exchange data our formulas improve computation speed by a factor of 1000 over brute force Monte Carlo making MCMC statistical methods practicable. We provide estimates of model parameters from daily data on the Swiss Franc to Euro and Japanese Yen to Euro over the period 1999–2002.     

Some new Time Sdries results

Summary Some recent work on Time Series is surveyed, and interest is focussed on Moving Average Processes, for which some new results are given. First, the background theory of the Time Domain is outlined, and then the problem of interpreting Box-Jenkins fits is discussed. Finally, we detail certain moving average properties of theoretical interest but also potentially useful in process modelling.

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Zusammenfassung Es werden einige neuere Arbeiten über Zeitreihen untersucht, wobei sich das Interesse auf Verfahren mit gleitenden Mittelwerten konzentriert, für die einige neue Ergebnisse angeführt werden. Zunächst wird der theoretische Hintergrund des Zeitbereiches umrissen, und anschließend wird das Problem der Interpretation von Box-Jenkins-Anpassungen diskutiert. Abschließend untersuchen wir detailliert bestimmte Merkmale gleitender Mittelwerte, die zwar von theoretischem Interesse sind, jedoch auch für die Erarbeitung von Verfahrensmodellen potentiell nützlich sind.

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This work was carried out while the author was with the Department of Mathematics, Nottingham University.     

谈谈英语教学中的几点心得体会

新时期的英语教学要更新观念。摒弃传统的语法教学方法,加强语言的实际操作演练,要达到这一目的,可通过对话练习、自由谈、语感的培养,多听多说,多组织英语课外活动等途径来实现。     

Some applications of stochastic analysis in financial economics: An outline

The basic features of a recent approach to the theory of continuous trading, are presented.

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Sommario Vengono presentate le linee base di un recente approccio alle opzioni in tempo continuo basato su tecniche di analisi stocastica.

     

Some general results for moments in bivariate distributions

The purpose of this paper is to present a closed formula to compute the moments of a general function from the knowledge of its bivariate survival function. The result is derived by utilizing an integration by parts formula for two variables, which is not readily available in the literature. Many of the existing results are obtained as special cases. Finally, two examples are presented to illustrate the results. In both the examples, mixed moments as well as moments for the series system and parallel system are obtained. The integration by parts formula in two variables, derived here, is of interest in its own right and we hope that it will be useful in other investigations. The integration by parts formula in two variables is derived as a special case of a general formula in n variables.     

Some results on residual entropy function

Ebrahimi and Pellerey (1995) and Ebrahimi (1996) proposed the Shannon residual entropy function as a useful dynamic measure of uncertainty. They studied the characterization problem from the residual entropy. They also used this function to define a stochastic order and two classes of distributions, DURL and IURL. In this paper, we obtain some new results on this function and we correct some mistakes in the preceding literature.Supported by Ministerio de Ciencia y Tecnologia under grant BFM2000-0362Acknowledgements. We thank two anonymous referees for some useful comments that led to an improvement in the presentation of this paper.     

Some theoretical results on forecast combinations

This paper proposes a framework for the analysis of the theoretical properties of forecast combination, with the forecast performance being measured in terms of mean squared forecast errors (MSFE). Such a framework is useful for deriving all existing results with ease. In addition, it also provides insights into two forecast combination puzzles. Specifically, it investigates why a simple average of forecasts often outperforms forecasts from single models in terms of MSFEs, and why a more complicated weighting scheme does not always perform better than a simple average. In addition, this paper presents two new findings that are particularly relevant in practice. First, the MSFE of a forecast combination decreases as the number of models increases. Second, the conventional approach to the selection of optimal models, based on a simple comparison of MSFEs without further statistical testing, leads to a biased selection.     

品牌建设之我见

文章从从基层做起,保证安全生产规范管理,提高效率贵在坚持,搞好宣传3个方面,结合电力企业实际对品牌建设的重要性和不可替代的作用进行了阐述,具有较好的指导意义。     

关于信用标准化的若干问题

1 信用标准化的必要性 信用，作为履行人们之间约定而取得的信任，是建立市场秩序的基础。信用标准化之所以必要，是由标准的特性决定的。根据1997年ISO／IEC导则对“标准”的最新定义，“标准”的四大特性为：     

可靠性工作中的若干问题

一．引言 可靠性工程是提高产品质量的一种十分有效的技术和方法，已经形成了一门独立的学科。可靠性工程是“战争的产物”。二次世界大战中，伴随电子管等电子元器件的广泛使用，大大提高了武器装备的作战效能，但出厂检验“合格”的装备在使用中却故障频繁；其后在朝鲜战场上这一问题变得更为严重。     

品牌建设之我见

文章从＂从基层做起,保证安全生产＂＂规范管理,提高效率＂＂贵在坚持,搞好宣传＂3个方面,结合电力企业实际对品牌建设的重要性和不可替代的作用进行了阐述,具有较好的指导意义。     

Gradient dynamics in population games: Some basic results

When each player in a population game continuously adjusts her action to move up the payoff gradient, then the state variable (the action distribution) obeys a nonlinear partial differential equation. We find conditions that render gradient adjustment myopically optimal and analyze two broad classes of population games. For one class, we use known results to establish the existence and uniqueness of solutions to the PDE. In some cases, these solutions exhibit shock waves or rarefaction waves. For a second class, we use a local form of Nash equilibrium to characterize the steady state solutions of the PDE and find sufficient conditions for asymptotic convergence.     

Some results on an additive hazards model

In the present paper, we study the analytical properties of an addictive hazards model. The ageing properties of the baseline random variable and the induced random variable are compared. Various stochastic orders that relate these two variables are also explored.     

Some results on discrete a–monotonicity

Some characterizations and preservation properties of a–monotonicity are investigated. In particular it is shown that a mixture of binomial or Poisson distributions preserves the a–monotonicity of the mixing distribution. Also, a characterization of a class of infinitely divisible distributions, within the discrete α–unimodal class, is given. This characterization is the discrete version of that of ALAMATSAZ (1985) and KOTZ and STEUTEL (1988) in the continuous case.     

关于食品安全问题的几点思考

食品安全从社会层面来看,不仅是公共卫生问题,而是社会问题、政治问题,甚至是社会安定团结问题。因此,食品安全问题科学管治意义重大。针对目前的治理现状,笔者从立法、市场行为价值取向、执法监管及媒介引导四个角度进行了思考,并对这些问题提出了建议性意见。