On model selection in Bayesian regression

We discuss the problem of constructing a suitable regression model from a nonparametric Bayesian viewpoint. For this purpose, we consider the case when the error terms have symmetric and unimodal densities. By the Khintchine and Shepp theorem, the density of response variable can be written as a scale mixture of uniform densities. The mixing distribution is assumed to have a Dirichlet process prior. We further consider appropriate prior distributions for other parameters as the components of the predictive device. Among the possible submodels, we select the one which has the highest posterior probability. An example is given to illustrate the approach.     

SKEWNESS FOR THE WEIBULL FAMILY

Abstract. The skewness of the Weibull family of distributions is discussed for all values of the shape parameter. This class includes unimodal probability densities for which the coefficient of skewness μ₃/o³ is positive, but the order of the mean, median and mode is μ < m < M. For values of the shape parameter used in practice the distributions are skewed to the right by a well accepted definition of skewness.     

An efficient nonparametric estimator for models with nonlinear dependence

We provide a convenient econometric framework for the analysis of nonlinear dependence in financial applications. We introduce models with constrained nonparametric dependence, which specify the conditional distribution or the copula in terms of a one-dimensional functional parameter. Our approach is intermediate between standard parametric specifications (which are in general too restrictive) and the fully unrestricted approach (which suffers from the curse of dimensionality). We introduce a nonparametric estimator defined by minimizing a chi-square distance between the constrained densities in the family and an unconstrained kernel estimator of the density. We derive the nonparametric efficiency bound for linear forms and show that the minimum chi-square estimator is nonparametrically efficient for linear forms.     

Minimum kolmogorov distance estimates of parameters and parametrized distributions

Minimum Kolmogorov distance estimates of arbitrary parameters are considered. They are shown to be strongly consistent if the parameter space metric is topologically weaker than the metric induced by the Kolmogorov distance of distributions from the statistical model. If the parameter space metric can be locally uniformly upper-bounded by the induced metric then these estimates are shown to be consistent of ordern ^−1/2. Similar results are proved for minimum Kolmogorov distance estimates of densities from parametrized families where the consistency is considered in theL ₁-norm. The presented conditions for the existence, consistency, and consistency of ordern ^−1/2 are much weaker than those established in the literature for estimates with similar properties. It is shown that these assumptions are satisfied e.g. by all location and scale models with parent distributions different from Dirac, and by all standard exponential models. Supported by the scientific exchange program between the Hungarian Academy of Sciences and the Royal Belgian Academy of Sciences, and by GACR grant 201/93/0232.     

Asymptotic behavior of the estimated weights and of the estimated performance measures of the minimum VaR and the minimum CVaR optimal portfolios for dependent data

In this paper we derive the asymptotic distributions of the estimated weights and of estimated performance measures of the minimum value-at-risk portfolio and of the minimum conditional value-at-risk portfolio assuming that the asset returns follow a strictly stationary process. It is proved that the estimated weights as well as the estimated performance measures are asymptotically multivariate normally distributed. We also present an asymptotic test for the weights and a joint test for the characteristics of both portfolios. Moreover, the asymptotic densities of the estimated performance measures are compared with the corresponding exact densities. It is shown that the asymptotic approximation performs well even for the moderate sample size.     

Congestion in a city with a central bottleneck

We consider dynamic congestion in an urban setting where trip origins are spatially distributed. All travelers must pass through a downtown bottleneck in order to reach their destination in the CBD. Each traveler chooses departure time to maximize general concave scheduling utility. We find that, at equilibrium, travelers sort according to their distance to the destination; the queue is always unimodal regardless of the spatial distribution of trip origins. We construct a welfare maximizing tolling regime, which eliminates congestion. All travelers located beyond a critical distance from the CBD gain from tolling, even when toll revenues are not redistributed, while nearby travelers lose. We discuss our results in the context of acceptability of tolling policies.     

Estimators of distance distributions for spatial patterns

Baddeley and Gill (1994, 1996) have introduced an edge-corrected Kaplan–Meier type estimator of the empty space function, which is very important in point process statistics. The present paper suggests a further estimator of this function, which is based on a method used by Hanisch (1984) for unbiased edge-corrected estimation of the nearest neighbour distance distribution function. Moreover, it turns out that the Kaplan–Meier and the new estimator are closely related, since their densities are border method or minus-sampling type estimators.     

Nonparametric density estimates consistent of the order of <Emphasis Type="Italic">n</Emphasis><Superscript>−1/2</Superscript> in the <Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript>–norm

We introduce an approximate minimum Kolmogorov distance density estimate of a probability density f₀ on the real line and study its rate of consistency for n. We define a degree of variations of a nonparametric family of densities containing the unknown f₀. If this degree is finite then the approximate minimum Kolmogorov distance estimate is consistent of the order of n^–1/2 in the L₁-norm and also in the expected L₁-norm. Comparisons with two other criteria leading to the same order of consistency are given.Received June 2002     

基于高效性与平衡性双重因素的出口集装箱堆场动态空间配置

从效率和成本两方面优化出口集装箱堆场空间资源,运用数学规划方法,从最小化箱区Bay位箱量的不平衡性和最小化总路径距离入手,建立了出口集装箱堆场空间资源动态配置模型。与出口集装箱随机配置模型相比,发现出口集装箱在动态模型配置下,平衡了各箱区间的箱量,提高了出口集装箱装船效率,降低了集装箱作业成本。     

Semi-parametric estimation of simultaneous equations with limited dependent variables: A case study of female labour supply

We propose a general strategy to estimate semi-parametrically simultaneous equations with limited dependent variables. First, each reduced form (RF) is estimated with various semi-parametric methods. Second, the specification of each RF is tested to select an appropriate method. Third, the structural form (SF) equations are estimated using minimum distance methods and the restrictions among the SF and RF parameters. A case study of female labour supply is presented.     

Frequency based analysis of collective aggregation rules

A new property for collective aggregation rules called positive discrimination is introduced. This property is satisfied by many anonymous and neutral collective aggregation rules. We discuss unimodal profiles (or distributions) for which this property on its own determines the outcome as the mode of a unimodal distribution. We investigate relaxations of this unimodal distribution condition and show that the Condorcet consistent rules as well as the Borda rule and the plurality rule have the mode as the outcome at such profiles. Further, we show, by an example, how the addition of unimodal profiles and the property of positive discrimination can help to determine an outcome in the case of a large number of voters.     

On the measurability and consistency of minimum contrast estimates

Summary The concept of minimum contrast (m.c.) estimates used in this paper covers maximum likelihood (m.l.) estimates as a special case. Section 1 contains sufficient conditions for the existence of measurable m.c. estimates and for their consistency. The application of these results to m.l. estimates (section 2) yields the existence of m.l. estimates for families ofp-measures (probability measures) which are compact metric or locally compact with countable base, admitting upper semicontinuous densities, whereas the classical results refer to continuous densities. This generalization is insofar of interest as upper semicontinuous versions of the densities exist whenever the densities areμ-upper semicontinuous (whereasμ-continuity does not, in general, entail the existence of continuous versions). Under appropriate regularity conditions, consistency of asymptotic maximum likelihood estimates is proven for compact (and also locally compact) separable metric families ofp-measures with upper semicontinuous densities and for arbitrary families having uniformly continuous densities with respect to the uniformity of vague convergence. The conditions sufficient for consistency are shown “indispensable” by counterexamples. Section 3 contains auxiliary results. Besides their relevance for sections 1 and 2, some of them may also be of interest in themselves, e.g. Theorem (3.4) on the selection of semicontinuous functions from semicontinuous equivalence classes.     

TheN-armed bandit with unimodal structure

In this paper we study a special class of bandit problems, which are characterized by a unimodal structure of the expected rewards of the arms. In Section 1, the motivation for studying this problem is explained. In the next two sections, two different decision procedures are analyzed, which are based on a stochastic approximation of the best arm of the bandit. Finally, in Section 4, a special procedure is discussed and some numerical data are presented, which were obtained by applying it to a concreteN-armed bandit with unimodal structure.     

Minimum Distance Estimation and Testing of DSGE Models from Structural VARs*

The aim of this paper is to complement the minimum distance estimation–structural vector autoregression approach when the weighting matrix is not optimal. In empirical studies, this choice is motivated by stochastic singularity or collinearity problems associated with the covariance matrix of impulse response functions. Consequently, the asymptotic distribution cannot be used to test the economic model's fit. To circumvent this difficulty, we propose a simple simulation method to construct critical values for the test statistics. An empirical application with US data illustrates the proposed method.     

Dynamics of urban residential growth

This paper develops a dynamic model of the urban residential market. Under specific assumptions about market behavior on both the supply and the demand sides it is shown that cities grow by attaining a sequence of short run equilibria. A set of recursive equations is derived and through these the impact of growth on the structure of rents, densities, and consumer welfare is analyzed. The dynamic model explains the decay of the central locations in large old American cities. Housing obsolescence and abandonment arises under special conditions and is reflected in positively sloped rent gradients in central locations. The well-known static result of declining densities with distance from the center is shown to occur only under special conditions such as rising income levels. Directions for further analyzing urban growth, by expanding this dynamic approach, are pointed out.     

上海公园空间可达性与公平性分析

公园是城市绿色基础设施的重要组成部分,是城市居民游憩活动的重要场所,具有重要的生态、娱乐、休憩和社会文化等功能.在遥感和地理信息系统技术的支持下,以上海市为例,运用最小邻近距离分析方法时研究区公园的空间可达性进行了定量评价,并结合上海市第五次人口普查数据资料,采用需求指数,分析了研究区各街道居民对城市公园的需求情况,在此基础上,采用定序变量相关分析和因子空间叠置分析两种方法定量测度了研究区公园布局的空间公平性程度.研究结果表明:(1)研究区可达性水平总体上较高,超过半数的居住区出行不足1000 m即可到达一个公园,超过70%的街道可达性水平较好;(2)在街道水平上研究区公园空间布局总体上比较公平、较为合理,可这性水平与需求指数呈显著相关,很高或高需求的街道70%左右均具有很好或好的可达性.     

Occupation and the journey-to-work: Some further analysis

This paper examines the impact of occupation upon commuting distances in the Toronto Census Metropolitan Area (CMA). Specifically, from the residential and job location patterns of each occupational group a “minimum distance” indicator of the degree of job-residence access of each occupational group is developed with the aid of a linear programming transportation model. The differences in “minimum distance” that must be travelled by the members of each occupational group are explained. The actual distances travelled to work by the members of each occupational group are then investigated and attempts are made to separate the determinants of each occupational group's average journey-to-work distance into two main factors—job residence access and propensity to commute. On the basis of the locational patterns, the analysis suggests that job residence access was generally greater for blue-collar workers than for white-collar workers. Although occupation did have an impact, then, on journey-to-work distance through its influence upon locational patterns of job and residence, little evidence of its effect on the propensity to commute was found. Rather, the results suggest that the main determinant of this factor was sex since female workers exhibited a far lower disposition to commute than did their male counterparts.     

Convergence in distribution of minimum-distance estimators

It is shown that (under some regularity conditions) minimum distance estimators for a (possibly multidimensional) real parameter of a family of univariate continuous distribution functions have an asymptotic distribution. If the distance is derived from the mean-square norm it is proved that the asymptotic distribution is normal. Weak convergence of empirical distribution to the Brownian bridge is the essential tool for the proof.     

On Quantile‐based Asymmetric Family of Distributions: Properties and Inference

In this paper, we provide a detailed study of a general family of asymmetric densities. In the general framework, we establish expressions for important characteristics of the distributions and discuss estimation of the parameters via method‐of‐moments as well as maximum likelihood estimation. Asymptotic normality results for the estimators are provided. The results under the general framework are then applied to some specific examples of asymmetric densities. The use of the asymmetric densities is illustrated in a real‐data analysis.     

An extension of the monocentric urban spatial equilibrium model to a multicenter setting: The case of the two-center city

Firms in a monocentric city conforming in substance to the “new urban economics” produce an export commodity under agglomeration economies and employ homogeneous labor and capital. Workers reside about the CBD in decreasing densities with distance. A developer establishes a second export production center within the city's residential area. Conditions for economic viability and growth of the subcenter are examined, and its impacts on short-run and long-run city location patterns are discussed. A limiting condition on subcenter employment size is provided.