Invariance In the linear model – an argument for χ2 and F in nonnormal situations

For a suitable norm, conservation of the distance between expectation and hypothesis may furnish a basis for data reduction by invariance in the linear, not neces-sarily normal, model. If the norm is Euclidean (i.e. based on some inner product), the maximal invariant is a pair of sums of squares. This provides support for traditional χ² (or F) - methods also in nonnormal cases. If the norm is l^p p≠2, or the supnorm, the maximal invariant is, at the best a air of order statistics.     

One–sided simulataneous prediction intervals for the order statistics of a future samples from an exponential distribution

Assume that a sample is available from a population having an exponential distribution, and that l Future sample are to be taken from the same population. This paper provides a formula for the same population. This paper provides a formula for computing a one–sided lower simulataneous prediction limit which is to be below the (k_i ? m_i + 1) –st order statistics of a future sample of size k_i for the i = 1,…,2, hased on the sample mean of a past sample. Tables for factors for one–sided lower simultaneous predicition limits are provided. Such limits are of practical importance in determining acceptance criteria and predicting system survival times.     

Percentiles from a set of classes or from the raw data? an argument based on the trinomial distribution

In a former study (Chatillon, Gelinas, Martin and Laurencelle, 1987), the authors arrived at the conclusion that for small to moderate sample sizes (n≦90), and for population distributions that are not too skewed nor heavy tailed, the percentiles computed from a set of 9 classes are at least as precise as the corresponding percentiles computed with raw data. Their proof was based essentially on Monte Carlo simulations. The present paper gives a different and complementary proof, based on an exact evaluation of the mean squared error. The method of proof uses the trinomial distribution in an interesting way.     

Proportional odds model – a quantile approach

The paper discusses a quantile-based definition for the well-known proportional odds model. We present various reliability properties of the model using quantile functions. Different ageing properties are derived. A generalization for the class of distributions with bilinear hazard quantile function is established and the practical application of this model is illustrated with a real-life data set.     

A network algorithm for the exact treatment of the 2×k contingency table

A common statistical problem encountered in biomedical research is to test the hypothesis that the parameters of k binomial populations are all equal. An exact test of significance of this hypothesis is possible in principle, the appropriate null distribution being a normalized product of k binomial coefficients. However, the problem of computing the tail area of this distribution can be formidable since it requires the enumeration of all sets of k binomial coefficients whose product is less than a given constant. Existing algorithms, all of which rely on explicit enumeration to generate feasible binomial coefficients     

Calculating the proportion of triangles in a poisson – voronoi tessellation of the plane

The proportion of triangles in a Poisson – Voronoi tessellation has been recently represented as a five-fold integral. Here we give a simpler representation, reduce it to a fourfold integral and discuss its numerical evaluation.     

Bayesian estimation and stochastic model specification search for dynamic survival models

Dynamic survival models are a useful extension of the popular Cox model as the effects of explanatory variables are allowed to change over time. In this paper a new auxiliary mixture sampler for Bayesian estimation of the model parameters is introduced. This sampler forms the basis of a model space MCMC method for stochastic model specification search in dynamic survival models, which involves selection of covariates to include in the model as well as specification of effects as time-varying or constant. The method is applied to two well-known data sets from the literature.     

The weighted general linear model for longitudinal medical cost data – an application in colorectal cancer

Identifying cost-effective decisions that can take into account of medical cost and health outcome is an important issue under very limited resources. Analyzing medical costs has been challenged owing to skewness of cost distributions, heterogeneity across samples and censoring. When censoring is due to administrative reasons, the total cost might be related to the survival time since longer survivals are likely to be censored and the corresponding total cost will be censored as well. This paper uses the general linear model for the longitudinal data to model the repeated medical cost data and the weighted estimating equation is used to find more accurate estimates for the parameter. Furthermore, the asymptotic properties for the proposed model are discussed. Simulations are used to evaluate the performance of estimators under various scenarios. Finally, the proposed model is implemented on the data extracted from National Health Insurance database for patients with the colorectal cancer.     

Comparison of Confidence Intervals for a Poisson Mean – Further Considerations

I make recommendations in choosing a confidence interval for the Poisson mean, from twelve different methods, that are based on four general principles: actual coverage should closely match the nominal coverage; narrower expected widths of confidence intervals are better; the right and left non-coverage should be fairly balanced; and some investigators may prefer closed-form intervals. The interval chosen depends on the relative importance the investigator places on each of these principles. The confidence intervals are examined through graphs of their coverage probability, interval widths and shapes.     

Pseudo-perfect and adaptive variants of the Metropolis–Hastings algorithm with an independent candidate density

We describe and examine an imperfect variant of a perfect sampling algorithm based on the Metropolis–Hastings algorithm that appears to perform better than a more traditional approach in terms of speed and accuracy. We then describe and examine an ‘adaptive’ Metropolis–Hastings algorithm which generates and updates a self-target candidate density in such a way that there is no ‘wrong choice’ for an initial candidate density. Simulation examples are provided.     

Statistical analysis of an endemic disease from a capture–recapture experiment

There are a number of statistical techniques for analysing epidemic outbreaks. However, many diseases are endemic within populations and the analysis of such diseases is complicated by changing population demography. Motivated by the spread of cowpox amongst rodent populations, a combined mathematical model for population and disease dynamics is introduced. A Markov chain Monte Carlo algorithm is then constructed to make statistical inference for the model based on data being obtained from a capture–recapture experiment. The statistical analysis is used to identify the key elements in the spread of the cowpox virus.     

Optimality of quasi-score in the multivariate mean–variance model with an application to the zero-inflated Poisson model with measurement errors

In a multivariate mean–variance model, the class of linear score (LS) estimators based on an unbiased linear estimating function is introduced. A special member of this class is the (extended) quasi-score (QS) estimator. It is ‘extended’ in the sense that it comprises the parameters describing the distribution of the regressor variables. It is shown that QS is (asymptotically) most efficient within the class of LS estimators. An application is the multivariate measurement error model, where the parameters describing the regressor distribution are nuisance parameters. A special case is the zero-inflated Poisson model with measurement errors, which can be treated within this framework.     

A Bayesian benchmarking of the Scott–Smith model for small areas

When the finite population ‘totals’ are estimated for individual areas, they do not necessarily add up to the known ‘total’ for all areas. Benchmarking (BM) is a technique used to ensure that the totals for all areas match the grand total, which can be obtained from an independent source. BM is desirable to practitioners of survey sampling. BM shifts the small-area estimators to accommodate the constraint. In doing so, it can provide increased precision to the small-area estimators of the finite population means or totals. The Scott–Smith model is used to benchmark the finite population means of small areas. This is a one-way random effects model for a superpopulation, and it is computationally convenient to use a Bayesian approach. We illustrate our method by estimating body mass index using data in the third National Health and Nutrition Examination Survey. Several properties of the benchmarked small-area estimators are obtained using a simulation study.     

Not every Gibbs sampler is a special case of the Metropolis–Hastings algorithm

It is commonly asserted that the Gibbs sampler is a special case of the Metropolis–Hastings (MH) algorithm. While this statement is true for certain Gibbs samplers, it is not true in general for the version that is taught and used most often, namely, the deterministic scan Gibbs sampler. In this note, I prove that that there exist deterministic scan Gibbs samplers that do not exhibit detailed balance and hence cannot be considered MH samplers. The nuances of various Gibbs sampling schemes are discussed.     

Second-order stochastic differential equation model as an alternative for the ALT and CALT models

The paper first discusses the autoregressive latent trajectory (ALT) model and presents in detail its improved version, the continuous-time autoregressive latent trajectory (CALT) model. Next, serious problems related to the linear components in the ALT and CALT models are dealt with. As an alternative for the linear component, the first-order derivative in a second-order stochastic differential equation model is proposed. This is applied to Marital Satisfaction data, collected in four consecutive years (2002–2005). It is pointed out that the first-order derivative as explanatory variable has none of the problems associated with the linear component.     

Assessing the market values of soccer players – a robust analysis of data from German 1. and 2. Bundesliga

The paper examines to what extent a player's market value depends on his skills. Therefore, a data set covering 28 performance measures and the market values of about 493 players from 1. and 2. German Bundesliga is analysed. Applying robust analysis techniques, we are able to robustly estimate market values of soccer players. The results show (1) that there are significantly underrated and overrated players and (2) that a player's affiliation to a certain team may contribute to his market value. We conclude that a club's reputation affects the market values of its players and that star players are in tendency overrated.     

A Bayesian hierarchical model for estimating the cost of postponing the cyclo-cross national championships

In early January 2015, the multi-event national cyclo-cross bicycle races were set to take place in Austin, Texas. Cyclo-cross has a rich history in this country, and throughout the world, attracting huge crowds and competitors. Being primarily a winter sport, these athletes often compete in harsh conditions, which include rain, snow, mud, and revel in the excitement that comes with such elements. Unfortunately, the competition was postponed mid-event when a local arborist group protested to the parks department. The issue: there was too much mud, in an event where many spectators and racers alike hope for such conditions. For many competitors, the postponement generated additional expenses, such as flights, hotels, and car rentals. Although people on opposite sides of the debate may greatly disagree, we instead focus on the competitors themselves. We analyze the financial impact of the disagreement using a hierarchical Bayesian mixed model which accounts for heterogeneity within the costs endured by the event's participants.     

Estimation of parameters for a Birnbaum–Saunders regression model with censored data

Little work has been published on the analysis of censored data for the Birnbaum–Saunders distribution (BISA). In this article, we implement the EM algorithm to fit a regression model with censored data when the failure times follow the BISA. Three approaches to implement the E-Step of the EM algorithm are considered. In two of these implementations, the M-Step is attained by an iterative least-squares procedure. The algorithm is exemplified with a single explanatory variable in the model.