A new approach to inter-rater agreement through stochastic orderings: the discrete case

We wish to study inter-rater agreement comparing groups of observers who express their ratings on a discrete or ordinal scale. The starting point is that of defining what we mean by “agreement”. Given d observers, let the scores they assign to a given statistical unit be expressed as a d-vector in the real space. We define a deterministic ordering among these vectors, which expresses the degree of the raters’ agreement. The overall scoring of the raters on the sample space will be a d-dimensional random vector. We then define an associated partial ordering among the random vectors of the ratings, illustrate a number of its properties, and look at order-preserving functions (agreement measures). In this paper we also show how to test the hypothesis of greater agreement against the unrestricted hypothesis, and the hypothesis of equal agreement against the hypothesis that an agreement ordering holds. The test is applied to real data on two medical observers rating clinical guidelines.     

A facility location problem with clients' preference orderings

The Simple Plant Location Problem (SPLP) consists in identifying a pattern of facilities among a set of potential sites so that the sum of the costs for opening the facilities and for supplying a group of geographically dispersed clients therefrom is minimized. It is posited in this framework that the locator rules on the allocation of the clients to the facilities. When the clients are free to decide upon which facility they will attend, their choices do not necessarily match the most economical supply pattern from the point of view of the locator. We suppose here that each client has a preference ordering on the list of potential sites whereby he determines his allocation out of any set of open facilities. This preference ordering depends on characteristics of the client, of the sites, and of the trip between the client's location and the sites. Mathematically, we translate the orderings into a set of constraints to be appended to the SPLP. This new problem, termed SPLPO, has a wide range of applications as shown by a series of examples. We present an algorithm for solving the SPLPO and extensive computational experiments are reported.     

A new family of bivariate max-infinitely divisible distributions

In this article we discuss the asymptotic behaviour of the componentwise maxima for a specific bivariate triangular array. Its components are given in terms of linear transformations of bivariate generalised symmetrised Dirichlet random vectors introduced in Fang and Fang (Statistical inference in elliptically contoured and related distributions. Allerton Press, New York, 1990). We show that the componentwise maxima of such triangular arrays is attracted by a bivariate max-infinitely divisible distribution function, provided that the associated random radius is in the Weibull max-domain of attraction.     

Stochastic orderings of convolution residuals

In this paper we study convolution residuals, that is, if $X_1,X_2,\ldots ,X_n$ are independent random variables, we study the distributions, and the properties, of the sums $\sum _{i=1}^lX_i-t$ given that $\sum _{i=1}^kX_i>t$ , where $t\in \mathbb R $ , and $1\le k\le l\le n$ . Various stochastic orders, among convolution residuals based on observations from either one or two samples, are derived. As a consequence computable bounds on the survival functions and on the expected values of convolution residuals are obtained. Some applications in reliability theory and queueing theory are described.     

A new bivariate distribution in natural exponential family

We propose a new bivariate distribution following a GLM form i.e., natural exponential family given the constantly correlated covariance matrix. The proposed distribution can represent an independent bivariate gamma distribution as a special case. In order to derive the distribution we utilize an integrating factor method to satisfy the integrability condition of the quasi-score function. The derived distribution becomes a mixture of discrete and absolute continuous distributions. The proposal of our new bivariate distribution will make it possible to develop some bivariate generalized linear models. Further the discrete correlated bivariate distribution will also arise from an independent bivariate Poisson mass function by compounding our proposed distribution (Iwasaki and Tsubaki, 2002).Received March 2003     

Ethnic polarization orderings and indices

An ethnic polarization index is a summary statistic of ethnic diversity in a population. Reynal-Querol (J Confl Resolut 46:29–54, 2002) suggested an index of ethnic polarization, the RQ index, and discussed its properties. In this paper we develop two ethnic polarization orderings that can rank ethnic distributions in terms of all ethnic polarization indices satisfying certain intuitively reasonable postulates. Some of these postulates and some additional ones taken from the earlier literature are employed to develop some axiomatic characterizations of the RQ index. In the process, a generalized form of the RQ index is also characterized.     

Implementation and orderings of public information

We explore the relationship between public information and implementable outcomes in an environment characterized by random endowments and private information. We show that if public signals carry no information about private types, then an exact relationship holds: a more informative public signal structure, in the sense of Blackwell, induces a smaller set of ex-ante implementable social choice functions. This holds for a large set of implementation standards, including Nash implementation, and Bayesian incentive compatibility. The result extends the notion, dating to Hirshleifer (1971), that public information can have negative value to an endowment economy under uncertainty.Received: 23 September 2003, Accepted: 30 July 2004, JEL Classification: D80Colin M. Campbell: I thank two referees and seminar participants at the 2002 meetings of the Society for Economic Design, at the 2003 Winter Meetings of the Econometric Society, and at Yale University for helpful input.     

Walrasian social orderings in exchange economies

We study social ordering functions in exchange economies. We show that if a social ordering function satisfies certain Pareto, individual rationality, and local independence conditions, then (i) the set of top allocations of the chosen social ordering is contained in the set of Walrasian allocations and is typically non-empty, and (ii) all individually rational but non-Walrasian allocations are typically ranked indifferently. Thus, such a social ordering function is quite similar to the Walrasian correspondence, which can be regarded as the social ordering function whose associated indifference classes are the set of Walrasian allocations and the set of other allocations.     

Structural information in recursive VAR orderings

This paper investigates structural models that will permit a Cholesky decomposition of the covariance matrix of VAR residuals to identify some structural impulse response functions. Cholesky decompositions are found to be useful identification tools for the set of partially recursive structural models. A partially recursive structure is defined as any block recursive system where the equations in one block can be recursively ordered and where the structural shocks are uncorrelated. Using this class of models, we derive necessary and sufficient conditions for the moving average representation from a Cholesky decomposition to identify structure. The paper concludes by discussing implications of these results for empirical research.     

The field of family planning: A review and new conceptual framework

In that work in family planning has been fragmented by a great diversity of researchers and administrators, this paper suggests a conceptualization to integrate the subject matter of the field. As background, the historical efforts and conceptual underpinnings of family planning programs and research in the Third World over the last three decades are reviewed noting the changes from a clinic orientation to outreach stratgies to the present diversity of approaches. Next, the two parts of the conceptualization are discussed. The first part, a macro-model, envisions family planning as a general diffusion process with six major components: the innovation, the setting, the diffusion agency, its strategy, the adoption process, and systematic feedback. The second part views family planning on the micro-level as a transaction with four major elements: The potential user and provider, the “gap” between them, and the setting. Finally, several policy implications of this new conceptualization are mentioned, most importantly the possibility of systematically organizing the field and the Value of the framework for empirically testing the relative importance of each major aspect of family planning.     

A new family of copulas,with application to estimation of a production frontier system

Journal of Productivity Analysis - In the empirical literature, the analysis of aggregate productivity dynamics using firm-level productivity has mostly been based on changes in the mean of...     

Multivariate likelihood ratio orderings between spacings of heterogeneous exponential random variables

Let X ₁, X ₂, ..., X _n be independent exponential random variables such that X _i has failure rate λ for i = 1, ..., p and X _j has failure rate λ^* for j = p + 1, ..., n, where p ≥ 1 and q = n − p ≥ 1. Denote by D _i:n (p,q) = X _i:n −X _i-1:n the ith spacing of the order statistics X _1:n ≤ X _2:n ≤ ... ≤ X _n:n , i = 1, ..., n, where X _0:n ≡ 0. The purpose of this paper is to investigate multivariate likelihood ratio orderings between spacings D _i:n (p,q), generalizing univariate comparison results in Wen et al.(J Multivariate Anal 98:743–756, 2007). We also point out that such multivariate likelihood ratio orderings do not hold for order statistics instead of spacings. Supported by National Natural Science Foundation of China, the Program for New Century Excellent Talents in University (No.: NCET-04-0569), and by the Knowledge Innovation Program of the Chinese Academy of Sciences (No.: KJCX3-SYW-S02).     

Self-employment: the new solution for balancing family and career?

We examine the hypothesis that white married women, particularly more educated women, are increasingly choosing self-employment as a strategy to balance family and career. We test two models using data from the CPS, NLS and NLSY, to examine the determinants of self-employment for women in the late 1970s, 1980s and 1990s. Our findings suggest that married women with greater family responsibilities are more likely to be self-employed, and these impacts are stronger for more educated women. However, we find little support for the hypothesis that women are more likely in recent years to choose self-employment in response to family demands.     

A search interpretation of the family gap

This paper proposes a general equilibrium search model to investigate what is known as the family gap: wage differentials between mothers and non-mothers. In the human capital literature a substantial amount of the family gap is left unexplained after controlling for schooling and experience. This paper suggests that differences in labor market behavior between mothers and non-mothers are an important factor in explaining the family gap. For college graduates, estimation results show that employed mothers search 70% less than non-mothers and more than 50% of the family gap can be explained by the labor market behavior differences between mothers and non-mothers. Such differences, however, can not explain the family gap for high school graduates.     

A family production overlapping generations economy

This paper provides a theoretical analysis of an overlapping generations economy in which production decisions and input–output allocations are all carried out at the family level. I consider a single class of output allocation schemes and various degrees of knowledge about the production technology. Under complete knowledge, I show that a family organizational structure in which everyone receives his marginal contribution to output, invests less in physical capital than under a perfectly competitive equilibrium environment. Under incomplete knowledge, I analyze and compare how beliefs about the input–output relationship affect the physical capital accumulation dynamics and the long-run standards of living.     

A family of Markovian models of recurrent choice

This paper presents a Markovian binary choice model for a heterogeneous population using a bivariate S_BB mixing distribution. Special forms of this model include Markov models with independent parameters, Last Place Loyal, Place Loyal and Bernoulli models. The modelling framework adopted allows these special forms to be both identified and tested. Analysis of recurrent shopping trips from travel diary data from Uppsala, Sweden [Burnett (1977)] finds no Markovian adaptive behaviour.