An objective function for simulation based inference on exchange rate data

The assessment of models of financial market behaviour requires evaluation tools. When complexity hinders a direct estimation approach, e.g., for agent based microsimulation models, simulation based estimators might provide an alternative. In order to apply such techniques, an objective function is required, which should be based on robust statistics of the time series under consideration. Based on the identification of robust statistics of foreign exchange rate time series in previous research, an objective function is derived. This function takes into account stylized facts about the unconditional distribution of exchange rate returns and properties of the conditional distribution, in particular, autoregressive conditional heteroscedasticity and long memory. A bootstrap procedure is used to obtain an estimate of the variance-covariance matrix of the different moments included in the objective function, which is used as a base for the weighting matrix. Finally, the properties of the objective function are analyzed for two different agent based models of the foreign exchange market, a simple GARCH-model and a stochastic volatility model using the DM/US-$ exchange rate as a benchmark. It is also discussed how the results might be used for inference purposes. Research has been supported by the DFG grant WI 20024/2-1/2. We are indebted to two anonymous referees of this journal, Leigh Tesfatsion, Patrick Burns and other participants of the CEF’06 conference in Limassol for helpful comments on preliminary versions of this paper.     

Conditional nonparametric frontier models for convex and nonconvex technologies: a unifying approach

The explanation of productivity differentials is very important to identify the economic conditions that create inefficiency and to improve managerial performance. In the literature two main approaches have been developed: one-stage approaches and two-stage approaches. Daraio and Simar (2005, J Prod Anal 24(1):93–121) propose a fully nonparametric methodology based on conditional FDH and conditional order-m frontiers without any convexity assumption on the technology. However, convexity has always been assumed in mainstream production theory and general equilibrium. In addition, in many empirical applications, the convexity assumption can be reasonable and sometimes natural. Lead by these considerations, in this paper we propose a unifying approach to introduce external-environmental variables in nonparametric frontier models for convex and nonconvex technologies. Extending earlier contributions by Daraio and Simar (2005, J Prod Anal 24(1):93–121) as well as Cazals et al. (2002, J Econometrics 106:1–25), we introduce a conditional DEA estimator, i.e., an estimator of production frontier of DEA type conditioned to some external-environmental variables which are neither inputs nor outputs under the control of the producer. A robust version of this conditional estimator is proposed too. These various measures of efficiency provide also indicators of convexity which we illustrate using simulated and real data. Cinzia Daraio received Research support from the Italian Ministry of Education Research on Innovation Systems Project (iRis) “The reorganization of the public system of research for the technological transfer: governance, tools and interventions” and from the Italian Ministry of Educational Research Project (MIUR 40% 2004) “System spillovers on the competitiveness of Italian economy: quantitative analysis for sectoral policies” which are acknowledged. Léopold Simar received Research support from the “Interuniversity Attraction Pole”, Phase V (No. P5/24) from the Belgian Government (Belgian Science Policy) is acknowledged.     

Minimax estimation of a cumulative distribution function by converting to a parametric problem

Let X = (X ₁,...,X _n ) be a sample from an unknown cumulative distribution function F defined on the real line . The problem of estimating the cumulative distribution function F is considered using a decision theoretic approach. No assumptions are imposed on the unknown function F. A general method of finding a minimax estimator d(t;X) of F under the loss function of a general form is presented. The method of solution is based on converting the nonparametric problem of searching for minimax estimators of a distribution function to the parametric problem of searching for minimax estimators of the probability of success for a binomial distribution. The solution uses also the completeness property of the class of monotone decision procedures in a monotone decision problem. Some special cases of the underlying problem are considered in the situation when the loss function in the nonparametric problem is defined by a weighted squared, LINEX or a weighted absolute error.     

Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach

This paper proposes a general formulation of a nonparametric frontier model introducing external environmental factors that might influence the production process but are neither inputs nor outputs under the control of the producer. A representation is proposed in terms of a probabilistic model which defines the data generating process. Our approach extends the basic ideas from Cazals et al. (2002) to the full multivariate case. We introduce the concepts of conditional efficiency measure and of conditional efficiency measure of order-m. Afterwards we suggest a practical way for computing the nonparametric estimators. Finally, a simple methodology to investigate the influence of these external factors on the production process is proposed. Numerical illustrations through some simulated examples and through a real data set on Mutual Funds show the usefulness of the approach.JEL Classification: C13, C14, D20     

Estimating regression coefficients from survey data by asymptotic design-cum-model based approach

Postulating a linear regression of a variable of interest on an auxiliary variable with values of the latter known for all units of a survey population, we consider appropriate ways of choosing a sample and estimating the regression parameters. Recalling Thomsen’s (1978) results on non-existence of ‘design-cum-model’ based minimum variance unbiased estimators of regression coefficients we apply Brewer’s (1979) ‘asymptotic’ analysis to derive ‘asymptotic-design-cummodel’ based optimal estimators assuming large population and sample sizes. A variance estimation procedure is also proposed.     

A general framework for frontier estimation with panel data

The main objective of the paper is to present a general framework for estimating production frontier models with panel data. A sample of firms i = 1, ..., N is observed on several time periods t = 1, ... T. In this framework, nonparametric stochastic models for the frontier will be analyzed. The usual parametric formulations of the literature are viewed as particular cases and the convergence of the obtained estimators in this general framework are investigated. Special attention is devoted to the role of N and of T on the speeds of convergence of the obtained estimators. First, a very general model is investigated. In this model almost no restriction is imposed on the structure of the model or of the inefficiencies. This model is estimable from a nonparametric point of view but needs large values of T and of N to obtain reliable estimates of the individual production functions and estimates of the frontier function. Then more specific nonparametric firm effect models are presented. In these cases, only NT must be large to estimate the common production function; but again both large N and T are needed for estimating individual efficiencies and for estimating the frontier. The methods are illustrated through a numerical example with real data.     

Exponential deconvolution: two asymptotically equivalent estimators

Two isotonic estimators for the distribution function in a specific deconvolution model, the exponential deconvolution model, are considered. The first estimator is a least squares projection of a naive estimator for the distribution function on the set of distribution functions. The second estimator is the well known maximum likelihood estimator. The two estimators are shown to be first order asymptotically equivalent at a fixed point.     

CENTRAL LIMIT THEORMS IN C[0,1] FOR A CLASS OF ESTIMATORS OF A DISTRIBUTION FUNCTION

As non–parametric estimates of an unknown distribution function (d.f.) F based on i.i.d. observations X ₁ X_n with this d.f.

are used, where H _n is a sequence of d.f.'s converging weakly to the unit mass at zero. Under regularity conditions on F and the sequence ( H _n) it is shown that √_n( F _n– F ) and √_n( R _n – F ) in C [0,1] converge in distribution to a process G with G( t ) = W° ( F ( t )), where W ° is a Brownian bridge in C [0,1]. Further the a.s. uniform convergence of R., is considered and some examples are given.     

Decomposing productivity patterns in a conditional convergence framework

In this study we examine regional data on per worker GDP, disaggregated at sectoral level, by focusing our interest on the role of differences in the sectoral composition of activities, and in productivity gaps that are uniform across sectors, in explaining the catching-up process, which is realized through physical and human capital as well as technological knowledge accumulation. Our objective is to investigate how much of the interregional inequality in aggregate productivity per worker is imputable to each component. A methodology for identifying and analyzing sources of inequality from a decomposed perspective is developed in the growth framework by combining a shift-share based technique and a SUR model specification for the conditional-convergence analysis. The proposed approach is employed to analyze aggregate interregional inequality of per worker productivity levels in Italy over the period 1970–2000. With respect to the existing empirical results, our approach provides a more comprehensive and detailed examination of the contribution of each identified component in explaining the regional productivity gaps in Italy. It is argued that region-specific productivity differentials, uniform across sectors, explain a quite large share of differences in productivity per worker. However, sectoral composition plays a non negligible role, although decreasing since the end of 1980s, and very different productivity patterns emerge within geographical areas.

On Limits of Uniquely Best Linear Estimators

In a general linear model, it is shown that all admissible linear estimators are limits of linear estimators that are uniquely best at some point in an extended parameter set. The principal result shows that a linear estimator that is uniquely best at a pointW ₂ among multiple linear estimators that are best at a pointW ₁ is the limit of uniquely best estimators at points approachingW ₁ along the line joiningW ₁ andW ₂. Research supported in part by U.S.A.F. Aerospace Research Laboratories under contract F33615-71-C-1463, summer 1973, and in part by Grant DMS-9104811 from the National Science Foundation.     

Asymptotic comparison at optimal levels of reduced‐bias extreme value index estimators

In this article we are interested in the asymptotic comparison, at optimal levels, of a set of semi‐parametric reduced‐bias extreme value (EV) index estimators, valid for a wide class of heavy‐tailed models, underlying the available data. Again, as in the classical case, there is not any estimator that can always dominate the alternatives, but interesting clear‐cut patterns are found. Consequently, and in practice, a suitable choice of a set of EV index estimators will jointly enable us to better estimate the EV index γ, the primary parameter of extreme events.     

On a local uniform bootstrap validity

Some relations between smoothness of statistical functionals and locally uniform validity of Efron's bootstrap for the estimators generated by the functionals are studied. It is shown that the Fréchet differentiability easily implies the locally uniform bootstrap validity. In an important example of empirical median it is indicated that indeed stronger regularity conditions are necessary to make the bootstrap a very reliable tool. It is also shown that a smoothing method based on Huber's M-estimation applied to the median may lead to an improved simple bootstrap there.     

The life-length of banknotes*

Abstract With the aid of the Bank's banknote sorting system the issue and subsequent withdrawal of f 25–banknotes on three varieties of paper have been recorded for two-and-a-half years. The aim was to measure the durability of the three paper varieties in circulation. The results of this second trial with f 25–banknotes confirm the statistical model developed previously for the first trial with f 100–banknotes. GRESHAM's Law is equally not applicable, neither to f 25–banknotes nor to f 100–banknotes. A two-parameter gamma distribution fits the cumulative fraction of banknotes withdrawn reasonably well.     

如何加强在设计阶段的工程造价管理

分析我国设计阶段工程造价管理的现状,并就如何合理地确定投资估算和设计概算提出一些见解。     

VAN DE HULST ON ROBUST STATISTICS: A HISTORICAL NOTE

This paper provides a discussion of an unpublished set of notes written in 1942 by the Dutch astronomer H.C. VAN DE HULST. In these notes VAN DE HULST derives the asymptotic variances of M– estimators as well as trimmed means and concludes that the asymptotic variance of what is now called HUBER'S estimator is the same as that of a trimmed mean. This conclusion is usually ascribed to BICKEL (1965). A letter written by D. VAN DANTZIG in 1943 providing a critical evaluation of. VAN DE HULST'S results, adds interest to this suprisingly early contribution to the theory of robust statistics.     

Statistics for the contact process

A d -dimensional contact process is a simplified model for the spread of an infection on the lattice Z ^d . At any given time t ≥ 0 , certain sites x ∈ Z ^d are infected while the remaining once are healthy. Infected sites recover at constant rate 1, while healthy sites are infected at a rate proportional to the number of infected neighboring sites. The model is parametrized by the proportionality constant λ. If λ is sufficiently small, infection dies out (subcritical process), whereas if λ is sufficiently large infection tends to be permanent (supercritical process).
In this paper we study the estimation problem for the parameter λ of the supercritical contact process starting with a single infected site at the origin. Based on an observation of this process at a single time t , we obtain an estimator for the parameter λ which is consistent and asymptotically normal as t →∞     

鱼雷效能及效费评估方法

鱼雷的效能是鱼雷研制和使用关心的首要问题,而效能又与费用存在着矛盾的关系,需在这两者之间进行权衡。分别对鱼雷效能评估方法和效费评估方法作了综合评述,对比了各种方法的适用范围以及不同方法的优劣;讨论了效能评估方法急需解决的主要问题,并对其今后的发展方向做了展望,为鱼雷进行效能以及效费评估提供有效的方法论支持。