Testing lack of symmetry in spatial–temporal processes

Symmetry and separability of a covariance function are common assumptions to simplify the modeling effort of spatial–temporal processes. However, many studies in environmental sciences show that real data have complex spatial–temporal dependency structures resulting from lack of symmetry or violation of other standard assumptions of the covariance function. In this study, we propose new formal tests for lack of symmetry by using spectral representations of the spatial–temporal covariance functions of regularly spaced spatial–temporal data. The advantage of the proposed tests is that classical analysis of variance (ANOVA) models can be used for detecting lack of symmetry inherent in spatial–temporal processes. We evaluate the performance of the tests with simulation studies and we apply them to air pollution data.     

Orthogonal decomposition of point-symmetry for multiway tables

For multiway contingency tables, Wall and Lienert (Biom. J. 18:259–264, 1976) considered the point-symmetry model. For square contingency tables, Tomizawa (Biom. J. 27:895–905, 1985) gave a theorem that the point-symmetry model holds if and only if both the quasi point-symmetry and the marginal point-symmetry models hold. This paper proposes some quasi point-symmetry models and marginal point-symmetry models for multiway tables, and extends Tomizawa’s (Biom. J. 27:895–905, 1985) theorem into multiway tables. We also show that for multiway tables the likelihood ratio statistic for testing goodness of fit of the point-symmetry model is asymptotically equivalent to the sum of those for testing the quasi point-symmetry model with some order and the marginal point-symmetry model with the corresponding order. An example is given.     

Exact Estimation of Demand Functions under Block-Rate Pricing

This article proposes an exact estimation of demand functions under block-rate pricing by focusing on increasing block-rate pricing. This is the first study that explicitly considers the separability condition which has been ignored in previous literature. Under this pricing structure, the price changes when consumption exceeds a certain threshold and the consumer faces a utility maximization problem subject to a piecewise-linear budget constraint. Solving this maximization problem leads to a statistical model in which model parameters are strongly restricted by the separability condition. In this article, by taking a hierarchical Bayesian approach, we implement a Markov chain Monte Carlo simulation to properly estimate the demand function. We find, however, that the convergence of the distribution of simulated samples to the posterior distribution is slow, requiring an additional scale transformation step for parameters to the Gibbs sampler. These proposed methods are then applied to estimate the Japanese residential water demand function.     

On strict positive definiteness of product and product-sum covariance models

Although positive definiteness is a sufficient condition for a function to be a covariance, the stronger strict positive definiteness is important for many applications, especially in spatial statistics, since it ensures that the kriging equations have a unique solution. In particular, spatial-temporal prediction has received a lot of attention, hence strictly positive definite spatial-temporal covariance models (or equivalently strictly conditionally negative definite variogram models) are needed.In this paper the necessary and sufficient condition for the product and the product-sum space-time covariance models to be strictly positive definite (or the variogram function to be strictly conditionally negative definite) is given. In addition it is shown that an example appeared in the recent literature which purports to show that product-sum covariance functions may be only semi-definite is itself invalid. Strict positive definiteness of the sum of products model is also discussed.     

A Monte Carlo Study of Tests of Blockwise Weak Separability

Separability assumptions on functional structure have received a great deal of attention from econometricians and economic theorists because (a) separability provides the fundamental linkage between aggregation over goods and the maximization principles in economic theory, (b) separability provides the theoretical basis for partitioning the economy's structure into sectors, and (c) separability provides a theoretical hypothesis, which can produce parameter restrictions, permitting great simplification in estimation of large demand systems. The power of the various available tests for separability has never been determined, however. We conduct Monte Carlo studies to examine the capability of currently available methods to provide correct inferences about separability.     

Strict Positive Definiteness of a Product of Covariance Functions

Positive definiteness represents an admissibility condition for a function to be a covariance. Nevertheless, the more restricted condition of strict positive definiteness has received attention in literature, especially in spatial statistics, since it ensures that the kriging system has a unique solution. Most known covariance functions are isotropic but there are applications where isotropy is not appropriate, e.g., space-time covariance functions. One way to construct non-isotropic covariance functions is to use a product or a product-sum. In this article, it is given a necessary as well as a sufficient condition for a product of two covariance functions to be strictly positive definite. This result is extended to the well-known product-sum covariance model.     

From separability to unweighted sum: A case for utilitarianism

After reviewing the compelling case for separability (`social welfare is a separable function of individual utilities'), an argument is advanced for utilitarianism (defined as `social welfare is the unweighted sum of individual utilities'). Basically, a compelling individualism-type axiom leads us to (social welfare as an) unweighted sum (of individual utilities), given separability.     

仲裁条款独立性理论及其在我国的应用

仲裁条款独立性理论认为,仲裁条款是从属于商事合同(主合同)的一项争议解决条款,具有相对独立性,其有效性不受主合同有效性的影响。它虽是在仲裁实践中产生的,却蕴含着对当事人意愿的尊重、对仲裁协议法律属性的清醒认识。      

Testing the Validity of Aggregates

This article develops a new approach for testing aggregation restrictions in estimated production-function and cost-function models. Rather than using the well-known separability conditions for the existence of an aggregate, this approach focuses on testing whether a particular aggregate is valid and develops empirically testable necessary and sufficient conditions for the validity of some known aggregation scheme. An empirical section examines the power of this test in the context of a simple production-function model.     

A tuning parameter free test for properties of space–time covariance functions

We propose a new nonparametric test to test for symmetry and separability of space–time covariance functions. Unlike the existing nonparametric tests, our test has the attractive convenience of being free of choosing any user-chosen number or smoothing parameter. The asymptotic null distributions of the test statistics are free of nuisance parameters and the critical values have been tabulated in the literature. From a practical point of view, our test is easy to implement and can be readily used by the practitioner. A Monte-Carlo experiment and real data analysis illustrate the finite sample performance of the new test.