Approximate maximum likelihood estimation in the presence of extra-poisson variation

A two-stage hierarchical model for analysis of discrete data with extra-Poisson variation is examined. The model consists of a Poisson distribution with a mixing lognormal distribution for the mean. A method of approximate maximum likelihood estimation of the parameters is proposed. The method uses the EM algorithm and approximations to facilitate its implementation are derived. Approximate standard errors of the estimates are provided and a numerical example is used to illustrate the method.     

Sampling nested Archimedean copulas

We give algorithms for sampling from non-exchangeable Archimedean copulas created by the nesting of Archimedean copula generators, where in the most general algorithm the generators may be nested to an arbitrary depth. These algorithms are based on mixture representations of these copulas using Laplace transforms. While in principle the approach applies to all nested Archimedean copulas, in practice the approach is restricted to certain cases where we are able to sample distributions with given Laplace transforms. Precise instructions are given for the case when all generators are taken from the Gumbel parametric family or the Clayton family; the Gumbel case in particular proves very easy to simulate.     

A Class of Convolution‐Based Models for Spatio‐Temporal Processes with Non‐Separable Covariance Structure

Abstract. In this article, we propose a new parametric family of models for real‐valued spatio‐temporal stochastic processes S ( x , t ) and show how low‐rank approximations can be used to overcome the computational problems that arise in fitting the proposed class of models to large datasets. Separable covariance models, in which the spatio‐temporal covariance function of S ( x , t ) factorizes into a product of purely spatial and purely temporal functions, are often used as a convenient working assumption but are too inflexible to cover the range of covariance structures encountered in applications. We define positive and negative non‐separability and show that in our proposed family we can capture positive, zero and negative non‐separability by varying the value of a single parameter.     

1973 Section Officers,Committees and Association Representatives

The occurrence of missing data cells precludes a universally correct procedure for performing an analysis of variance. This is illustrated by the use of two computer routines to analyze a 2 × 3 factorial experiment with one missing cell. One of these routines does, however, provide information that may enhance the usefulness of the associated results.     

Poliovirus Surveillance by Examining Sewage Water Specimens: Studies on Detection Probability Using Simulation Models

Efficiency of environmental surveillance of poliovirus circulation was studied using simulation models. First, three transmission models were defined for describing different scenarios of poliovirus infections in a large unstructured population. Second, environmental factors, such as the total volume of the sewage network and losses of viruses, were modeled for computing the virus output at the sewage sampling site. Third, the effect of sampling and laboratory procedures was accounted for in the probability of detection, given the amount of polioviruses in a specimen. The simulation model can be used for theoretical assessments of the likely efficiency of environmental surveillance, compared with acute flaccid paralysis (AFP) surveillance. Under reasonable assumptions in a vaccinated population, the AFP surveillance can be outperformed if the poliovirus outbreak is not large. However, this depends on the assumed case-to-infection ratio and on the sampling frequency of the sewage water specimens. Increasing the latter will lead to a higher detection probability, which will further enhance the method based on environmental surveillance.     

Partial least squares estimator for single-index models

The partial least squares (PLS) approach first constructs new explanatory variables, known as factors (or components), which are linear combinations of available predictor variables. A small subset of these factors is then chosen and retained for prediction. We study the performance of PLS in estimating single-index models, especially when the predictor variables exhibit high collinearity. We show that PLS estimates are consistent up to a constant of proportionality. We present three simulation studies that compare the performance of PLS in estimating single-index models with that of sliced inverse regression (SIR). In the first two studies, we find that PLS performs better than SIR when collinearity exists. In the third study, we learn that PLS performs well even when there are multiple dependent variables, the link function is non-linear and the shape of the functional form is not known.     

Modified weighted squared error estimation procedures with special emphasis on the stable laws

Two families of parameter estimation procedures for the stable laws based on a variant of the characteristic function are provided. The methodology which produces viable computational procedures for the stable laws is generally applicable to other families of distributions across a variety of settings. Both families of procedures may be described as a modified weighted chi-squared minimization procedure, and both explicitly take account of constraints on the parameter space. Influence func-tions for and efficiencies of the estimators are given. If x₁, x₂, …x_n random sample from an unknown distribution F , a method for determining the stable law to which F is attracted is developed. Procedures for regression and autoregres-sion with stable error structure are provided. A number of examples are given.     

Unbiased estimation of a nonlinear function a normal mean with application to measurement err oorf models

Let W be a normal random variable with mean μand known variance σ². Conditions on the function f(·) are given under which there exists an unbiased estimator, f(W), of f(μ) for all real μ. In particular it is shown that f(·) must be an entire function over the complex plane. Infinite series solutions for F(·) are obtained which are shown to be valid under growth conditions of the derivatives, f^k( ·), of f(·). Approximate solutions are given for the cases in which no exact solution exists. The theory is applied to nonlinear measurement-error models as a means of finding unbiased score functions when measurement error is normally distributed. Relative efficiencies comparing the proposed method to the use of conditional scores (Stefanski and Carroll, 1987) are given for the Poisson regression model with canonical link.     

Identification of composite (∑+II) arma models by relatively simpler models

In the real world situations, many time series are aggregates of two or more time series. An aggregation may take place due to an addition or the product or both of two or more time series. We are often interested in the study of the properties of aggregates which are, in turn, dependent on the properties of the constituent series. Motivated by this problem, the authors study in this paper the properties of models generated by the operator (Σ+II) on autoregressive-moving-average (ARMA) processes of orders (p_i,q_i), i = l→n . A few practical examples where such models have been used are given in the introduction and an illustrative numerical example is discussed at the end of the paper.     

Calculating the power or sample size for the logistic and proportional hazards models

An algorithm is presented for calculating the power for the logistic and proportional hazards models in which some of the covariates are discrete and the remainders are multivariate normal. The mean and covariance matrix of the multivariate normal covariates may depend on the discrete covariates.

The algorithm, which finds the power of the Wald test, uses the result that the information matrix can be calculated using univariate numerical integration even when there are several continuous covariates. The algorithm is checked using simulation and in certain situations gives more accurate results than current methods which are based on simple formulae. The algorithm is used to explore properties of these models, in particular, the power gain from a prognostic covariate in the analysis of a clinical trial or observational study. The methods can be extended to determine power for other generalized linear models.