Characterizations,length-biasing,and infinite divisibility

SupposeL(X) is the law of a positive random variableX, andZ is positive and independent ofX. Admissible solution pairs (L(X),L(Z)) are sought for the in-law equation $\hat X \cong X o Z$ °Z, where $L\left( {\hat X} \right)$ is a weighted law constructed fromL(X), and ° is a binary operation which in some sense is increasing. The class of weights includes length biasing of arbitrary order. When ° is addition and the weighting is ordinary length biasing, the class of admissibleL(X) comprises the positive infinitely divisible laws. Examples are given subsuming all known specific cases. Some extensions for general order of length-biasing are discussed.     

ON THE GENERALIZED RAO-RUBIN CONDITION and SOME VARIANTS

This paper gives a characterization of some members of the compound Poisson family of distributions based on the generalized Rao-Rubin condition. By considering some variants of this condition and using power series arguments, characterizations of the Poisson distribution are also obtained.     

RANKINGS OF ACADEMIC JOURNALS AND INSTITUTIONS IN ECONOMICS

We conducted a worldwide ranking of academic institutions that produce research in a list of thirty top research journals in economics. We also computed journal rankings for the same period and hence we do not rely on weights that were computed for research carried out in earlier periods. The United States is clearly the dominant force in the top‐fifty group, but European academic institutions are well represented in the group of the top 200 universities worldwide as are universities from Asia and the Far East in particular. (JEL: A14, A10)     

Wavelet thresholding via a Bayesian approach

We discuss a Bayesian formalism which gives rise to a type of wavelet threshold estimation in nonparametric regression. A prior distribution is imposed on the wavelet coefficients of the unknown response function, designed to capture the sparseness of wavelet expansion that is common to most applications. For the prior specified, the posterior median yields a thresholding procedure. Our prior model for the underlying function can be adjusted to give functions falling in any specific Besov space. We establish a relationship between the hyperparameters of the prior model and the parameters of those Besov spaces within which realizations from the prior will fall. Such a relationship gives insight into the meaning of the Besov space parameters. Moreover, the relationship established makes it possible in principle to incorporate prior knowledge about the function's regularity properties into the prior model for its wavelet coefficients. However, prior knowledge about a function's regularity properties might be difficult to elicit; with this in mind, we propose a standard choice of prior hyperparameters that works well in our examples. Several simulated examples are used to illustrate our method, and comparisons are made with other thresholding methods. We also present an application to a data set that was collected in an anaesthesiological study.     

Testing for additivity and joint effects in multivariate nonparametric regression using Fourier and wavelet methods

We consider the problem of testing for additivity and joint effects in multivariate nonparametric regression when the data are modelled as observations of an unknown response function observed on a d-dimensional (d 2) lattice and contaminated with additive Gaussian noise. We propose tests for additivity and joint effects, appropriate for both homogeneous and inhomogeneous response functions, using the particular structure of the data expanded in tensor product Fourier or wavelet bases studied recently by Amato and Antoniadis (2001) and Amato, Antoniadis and De Feis (2002). The corresponding tests are constructed by applying the adaptive Neyman truncation and wavelet thresholding procedures of Fan (1996), for testing a high-dimensional Gaussian mean, to the resulting empirical Fourier and wavelet coefficients. As a consequence, asymptotic normality of the proposed test statistics under the null hypothesis and lower bounds of the corresponding powers under a specific alternative are derived. We use several simulated examples to illustrate the performance of the proposed tests, and we make comparisons with other tests available in the literature.     

A PRIMER ON CARDINAL VERSUS ORDINAL TOURNAMENTS

This paper fills in a gap in the tournament literature by developing a framework that can be used to analyze both cardinal and ordinal tournaments, as well as piece rates. The analysis aims to obtain a Pareto ranking of cardinal versus ordinal tournaments, which is an open question in the literature. The analysis shows that, surprisingly, cardinal tournaments are superior to ordinal tournaments. The rationale is that, by utilizing all the available information more efficiently, cardinal tournaments allow the principal to implement higher power incentives, which makes them superior even though they restrict the form of the contract more than ordinal tournaments. (JEL D82, D21)