Characterizations based on Rényi entropy of order statistics and record values

Two different distributions may have equal Rényi entropy; thus a distribution cannot be identified by its Rényi entropy. In this paper, we explore properties of the Rényi entropy of order statistics. Several characterizations are established based on the Rényi entropy of order statistics and record values. These include characterizations of a distribution on the basis of the differences between Rényi entropies of sequences of order statistics and the parent distribution.     

A mixture model for random graphs

The Erdös–Rényi model of a network is simple and possesses many explicit expressions for average and asymptotic properties, but it does not fit well to real-world networks. The vertices of those networks are often structured in unknown classes (functionally related proteins or social communities) with different connectivity properties. The stochastic block structures model was proposed for this purpose in the context of social sciences, using a Bayesian approach. We consider the same model in a frequentest statistical framework. We give the degree distribution and the clustering coefficient associated with this model, a variational method to estimate its parameters and a model selection criterion to select the number of classes. This estimation procedure allows us to deal with large networks containing thousands of vertices. The method is used to uncover the modular structure of a network of enzymatic reactions.     

Bayesian inference and model comparison for asymmetric smooth transition heteroskedastic models

Inference, quantile forecasting and model comparison for an asymmetric double smooth transition heteroskedastic model is investigated. A Bayesian framework in employed and an adaptive Markov chain Monte Carlo scheme is designed. A mixture prior is proposed that alleviates the usual identifiability problem as the speed of transition parameter tends to zero, and an informative prior for this parameter is suggested, that allows for reliable inference and a proper posterior, despite the non-integrability of the likelihood function. A formal Bayesian posterior model comparison procedure is employed to compare the proposed model with its two limiting cases: the double threshold GARCH and symmetric ARX GARCH models. The proposed methods are illustrated using both simulated and international stock market return series. Some illustrations of the advantages of an adaptive sampling scheme for these models are also provided. Finally, Bayesian forecasting methods are employed in a Value-at-Risk study of the international return series. The results generally favour the proposed smooth transition model and highlight explosive and smooth nonlinear behaviour in financial markets.     

Local polynomial estimation of Poisson intensities in the presence of reporting delays

Summary.  The system for monitoring suicides in Hong Kong has considerable delays in reporting as the cause of death needs to be determined by a coroner's investigation. However, timely estimates of suicide rates are desirable to assist in the formulation of public health policies. This motivated us to develop a non-parametric procedure to estimate the intensity function of a Poisson process in the presence of reporting delays. We give closed form estimators of the Poisson intensity and the delay distribution, conduct simulation studies to evaluate the method proposed and derive their asymptotic properties. The method proposed is applied to estimate the intensity of suicide in Hong Kong.     

A new mixture model for capture heterogeneity

Summary.  We propose a mixture of binomial and beta–binomial distributions for estimating the size of closed populations. The new mixture model is applied to several real capture–recapture data sets and is shown to provide a convenient, objective framework for model selection. The new model is compared with three alternative models in a simulation study, and the results shed light on the general performance of models in this area. The new model provides a robust flexible analysis, which automatically deals with small capture probabilities.     

Spatially varying dynamic coefficient models

In this work we present a flexible class of linear models to treat observations made in discrete time and continuous space, where the regression coefficients vary smoothly in time and space. This kind of model is particularly appealing in situations where the effect of one or more explanatory processes on the response present substantial heterogeneity in both dimensions. We describe how to perform inference for this class of models and also how to perform forecasting in time and interpolation in space, using simulation techniques. The performance of the algorithm to estimate the parameters of the model and to perform prediction in time is investigated with simulated data sets. The proposed methodology is used to model pollution levels in the Northeast of the United States.     

A class of count models and a new consistent test for the Poisson distribution

We define a class of count distributions which includes the Poisson as well as many alternative count models. Then the empirical probability generating function is utilized to construct a test for the Poisson distribution, which is consistent against this class of alternatives. The limit distribution of the test statistic is derived in case of a general underlying distribution, and efficiency considerations are addressed. A simulation study indicates that the new test is comparable in performance to more complicated omnibus tests.     

Canonical correlation analysis for the vector AR(1) model with ARCH innovations

This paper extends the results of canonical correlation analysis of Anderson [2002. Canonical correlation analysis and reduced-rank regression in autoregressive models. Ann. Statist. 30, 1134–1154] to a vector AR(1) process with a vector ARCH(1) innovations. We obtain the limiting distributions of the sample matrices, the canonical correlations and the canonical vectors of the process. The extension is important because many time series in economics and finance exhibit conditional heteroscedasticity. We also use simulation to demonstrate the effects of ARCH innovations on the canonical correlation analysis in finite sample. Both the limiting distributions and simulation results show that overlooking the ARCH effects in canonical correlation analysis can easily lead to erroneous inference.