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...     

Estimation in the first-order moving average model through the finite autoregressive approximation: Some asymptotic results

To estimate α in the model y_t = u_t+αu_t?1, we consider a proposal by Durbin (Biometrika, 1969). It consists in fitting an autoregression of order k to the data, and deriving from there an estimate α^. The probability limit and the variance of the limiting normal distribution of α^ are presented and discussed in detail, when the sample size T → ∞, but k remains fixed. The differences between the resulting values and those corresponding to the maximum likelihood estimator are exponentially decreasing functions of k. Several modifications of the estimator are discussed and found consistent, but asymptotically inefficient.     

Variational Bayes approximation of factor stochastic volatility models

Estimation and prediction in high dimensional multivariate factor stochastic volatility models is an important and active research area, because such models allow a parsimonious representation of multivariate stochastic volatility. Bayesian inference for factor stochastic volatility models is usually done by Markov chain Monte Carlo methods (often by particle Markov chain Monte Carlo methods), which are usually slow for high dimensional or long time series because of the large number of parameters and latent states involved. Our article makes two contributions. The first is to propose a fast and accurate variational Bayes methods to approximate the posterior distribution of the states and parameters in factor stochastic volatility models. The second is to extend this batch methodology to develop fast sequential variational updates for prediction as new observations arrive. The methods are applied to simulated and real datasets, and shown to produce good approximate inference and prediction compared to the latest particle Markov chain Monte Carlo approaches, but are much faster.     

Convergence of stochastic approximation algorithms under irregular conditions

We consider a class of stochastic approximation (SA) algorithms for solving a system of estimating equations. The standard condition for the convergence of the SA algorithms is that the estimating functions are locally Lipschitz continuous. Here, we show that this condition can be relaxed to the extent that the estimating functions are bounded and continuous almost everywhere. As a consequence, the use of the SA algorithm can be extended to some problems with irregular estimating functions. Our theoretical results are illustrated by solving an estimation problem for exponential power mixture models.     

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.     

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).

     

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.     

关于城市化的几个问题

一、城市化的实质是经济发展城市化是一个很复杂的问题 ,涉及的方面很多 ,但城市化首先是一个经济问题。城市化的实质是经济发展 ,它是一个国家或地区产业结构大调整的反映。城市化到底是什么 ?城市化是人类生产方式和生活方式由乡村型向城市型转化的历史过程 ,它表现为城市人口的增长、城市数量和规模的发展以及城市现代化水平的提高。城市化的核心是为农村剩余劳力提供大量非农就业岗位。没有这个前提就无所谓城市化。过去为什么我们的城市化推进得慢 ,就是因为我们的经济发展落后 ,我们是一个农业大国 ,吃饭问题长期没有得到解决。今年全…     

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。     

“物流”的几点思考

首先从较具有代表性的美国关于物流的定义入手,分析物流的本质及内涵,结合《物流术语》中的提法,作简要分析,提出了在物流概念认知时几个关键问题,最后提出如何推动物流概念的正确传播。     

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.

     

Plug‐in bandwidth selector for recursive kernel regression estimators defined by stochastic approximation method

In this paper, we propose an automatic selection of the bandwidth of the recursive kernel estimators of a regression function defined by the stochastic approximation algorithm. We showed that, using the selected bandwidth and the stepsize which minimize the mean weighted integrated squared error, the recursive estimator will be better than the non‐recursive one for small sample setting in terms of estimation error and computational costs. We corroborated these theoretical results through simulation study and a real dataset.     

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.     

关于自相似空间的一些讨论

本文通过定义距离空间(X,d)上的自相似空间的概念,给出相关命题的同时证E(kk=1,2,…,m)多于两个点的紧致距离空间(X,d)中的压缩Lipschitz道路,且X=km=1Ek。如果存在非扩张Lipschitz满射gi:X→[0,1(]1燮i燮m),则X为自相似空间;作为应用得知:有限个有公共交点的Lipschitz道路之并是自相似空间;平面上任一连通图与树都是自相似空间。     

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。