Estimation of the Predictive Ability of Ecological Models

The conventional criteria for predictive model selection do not indicate the absolute goodness of models. For example, the quantity of Akaike Information Criterion (AIC) has meanings only when we compare AIC of different models for a given amount of data. Thus, the existing criteria do not tell us whether the quantity and quality of data is satisfactory, and hence we cannot judge whether we should collect more data to further improve the model or not. To solve such a practical problem, we propose a criterion R_D that lies between 0 and 1. R_D is an asymptotic estimate of the proportion of improvement in the predictive ability under a given error structure, where the predictive ability is defined by the expected logarithmic probability by which the next dataset (2nd dataset) occurs under a model constructed from the current dataset (1st dataset). That is, the predictive ability is defined by the expected logarithmic probability of the 2nd dataset evaluated at the model constructed from the 1st dataset. Appropriate choice of error structures is important in the calculation of R_D. We illustrate examples of calculations of R_D by using a small dataset about the moth abundance.     

On the Correlation Structure of Gaussian Copula Models for Geostatistical Count Data

We describe a class of random field models for geostatistical count data based on Gaussian copulas. Unlike hierarchical Poisson models often used to describe this type of data, Gaussian copula models allow a more direct modelling of the marginal distributions and association structure of the count data. We study in detail the correlation structure of these random fields when the family of marginal distributions is either negative binomial or zero‐inflated Poisson; these represent two types of overdispersion often encountered in geostatistical count data. We also contrast the correlation structure of one of these Gaussian copula models with that of a hierarchical Poisson model having the same family of marginal distributions, and show that the former is more flexible than the latter in terms of range of feasible correlation, sensitivity to the mean function and modelling of isotropy. An exploratory analysis of a dataset of Japanese beetle larvae counts illustrate some of the findings. All of these investigations show that Gaussian copula models are useful alternatives to hierarchical Poisson models, specially for geostatistical count data that display substantial correlation and small overdispersion.     

Goodness-of-fit for regime-switching copula models with application to option pricing

We consider several time series, and for each of them, we fit an appropriate dynamic parametric model. This produces serially independent error terms for each time series. The dependence between these error terms is then modelled by a regime-switching copula. The EM algorithm is used for estimating the parameters and a sequential goodness-of-fit procedure based on Cramér–von Mises statistics is proposed to select the appropriate number of regimes. Numerical experiments are performed to assess the validity of the proposed methodology. As an example of application, we evaluate a European put-on-max option on the returns of two assets. To facilitate the use of our methodology, we have built a R package HMMcopula available on CRAN. The Canadian Journal of Statistics 48: 79–96; 2020 © 2020 Statistical Society of Canada     

Empirical likelihood for nonlinear regression models with nonignorable missing responses

This article develops three empirical likelihood (EL) approaches to estimate parameters in nonlinear regression models in the presence of nonignorable missing responses. These are based on the inverse probability weighted (IPW) method, the augmented IPW (AIPW) method and the imputation technique. A logistic regression model is adopted to specify the propensity score. Maximum likelihood estimation is used to estimate parameters in the propensity score by combining the idea of importance sampling and imputing estimating equations. Under some regularity conditions, we obtain the asymptotic properties of the maximum EL estimators of these unknown parameters. Simulation studies are conducted to investigate the finite sample performance of our proposed estimation procedures. Empirical results provide evidence that the AIPW procedure exhibits better performance than the other two procedures. Data from a survey conducted in 2002 are used to illustrate the proposed estimation procedure. The Canadian Journal of Statistics 48: 386–416; 2020 © 2020 Statistical Society of Canada     

Extended binomial AR(1) processes with generalized binomial thinning operator

Abstract

In this article, we introduce an extended binomial AR(1) model based on the generalized binomial thinning operator. This operator relaxes the independence assumption of the binomial thinning operator and contains dependent Bernoulli counting series. The new model contains the binomial AR(1) model as a particular case. Some probabilistic and statistical properties are explored. Estimators of the model parameters are derived by conditional maximum likelihood (CML), conditional least squares (CLS) and weighted conditional least squares (WCLS) methods. Some asymptotic properties and numerical results of the estimators are studied. The good performance of the new model is illustrated, among other competitive models in the literature, by an application to the monthly drunken driving counts.     

A bivariate mixture of negative binomial distributions and its applications

Abstract

We construct a new bivariate mixture of negative binomial distributions which represents over-dispersed data more efficiently. This is an extension of a univariate mixture of beta and negative binomial distributions. Characteristics of this joint distribution are studied including conditional distributions. Some properties of the correlation coefficient are explored. We demonstrate the applicability of our proposed model by fitting to three real data sets with correlated count data. A comparison is made with some previously used models to show the effectiveness of the new model.     

An asymmetric multivariate weibull distribution

Abstract

A class of multivariate laws as an extension of univariate Weibull distribution is presented. A well known representation of the asymmetric univariate Laplace distribution is used as the starting point. This new family of distributions exhibits some similarities to the multivariate normal distribution. Properties of this class of distributions are explored including moments, correlations, densities and simulation algorithms. The distribution is applied to model bivariate exchange rate data. The fit of the proposed model seems remarkably good. Parameters are estimated and a bootstrap study performed to assess the accuracy of the estimators.     

Upper non positive bounds on expectations of generalized order statistics from DD and DDA populations

We present the upper non positive bounds on the expectations of gOSs centered about the sample mean, which are based on the parent distributions with decreasing density and decreasing density on average distributions. Such bounds can be obtained only for particular cases of gOSs and they are expressed in units generated by the central absolute moments of a fixed order. The attainability conditions are also described. The method of deriving presented bounds is based on the maximization of appropriate norms over properly chosen convex sets. The paper complements the results of Bieniek [J. Statist. Plann. Inference, 2008; 138:971–981].     

An R package for the simulation of correlated discrete variables

A package for the stochastic simulation of discrete variables with assigned marginal distributions and correlation matrix is presented and discussed. The simulating mechanism relies upon the Gaussian copula, linking the discrete distributions together, and an iterative scheme recovering the correlation matrix for the copula that ensures the desired correlations among the discrete variables. Examples of its use are provided as well as three possible applications (related to probability, sampling, and inference), which illustrate the utility of the package as an efficient and easy-to-use tool both in statistical research and for didactic purposes.     

Poisson-mixed Inverse Gaussian Regression Model and Its Application

In this article, we have developed a Poisson-mixed inverse Gaussian (PMIG) distribution. The mixed inverse Gaussian distribution is a mixture of the inverse Gaussian distribution and its length-biased counterpart. A PMIG regression model is developed and the maximum likelihood estimation of the parameters is studied. A dataset dealing with the number of hospital stays among the elderly population is analyzed by using the PMIG and the PIG (Poisson-inverse Gaussian) regression models and it has been shown that the PMIG model fits the data better than the PIG model.