A Hausman test for Brownian motion

New tests are proposed for the specification of the intraday price process of a risky asset, based on open, high, low, and close prices. Under the null of a Brownian process we derive two stochastically independent, unbiased volatility estimators. For a Hausman specification test we prove its equivalence with an F-test, consider its robustness against variation in drift and volatility, and analyze the power against an Ornstein–Uhlenbeck process, as well as a random walk with alternative distributions.     

Modelling Variability in the Branching Structure of Strawberry Inflorescences

The branching structure of inflorescences of the cultivated strawberry ( Fragaria × ananassa Duch.) is very variable. This paper demonstrates that some aspects of this variability are well described by a simple stochastic model of branching that has two adjustable parameters. The model is shown to provide a good fit to data from a set of almost 700 inflorescences of the cultivar Elsanta, collected over two successive years. For one parameter the maximum likelihood estimator is a moment estimator which is fully efficient even if the detailed branching structure of the inflorescences is not recorded. This parameter provides a convenient summary of branching vigour. The maximum likelihood estimator of the second parameter must be determined iteratively and can be quite inefficient unless the full branching structure is recorded. The model demonstrates that branching structure is affected by the order in which inflorescences emerge on the plant.     

Improved Monte Carlo inference for models with additive error

Some statistical models defined in terms of a generating stochastic mechanism have intractable distribution theory, which renders parameter estimation difficult. However, a Monte Carlo estimate of the log-likelihood surface for such a model can be obtained via computation of nonparametric density estimates from simulated realizations of the model. Unfortunately, the bias inherent in density estimation can cause bias in the resulting log-likelihood estimate that alters the location of its maximizer. In this paper a methodology for radically reducing this bias is developed for models with an additive error component. An illustrative example involving a stochastic model of molecular fragmentation and measurement is given.     

Alternative Methods for Computing the Sensitivity of Complex Surveillance Systems

Stochastic scenario trees are a new and popular method by which surveillance systems can be analyzed to demonstrate freedom from pests and disease. For multiple component systems—such as a combination of a serological survey and systematically collected observations—it can be difficult to represent the complete system in a tree because many branches are required to represent complex conditional relationships. Here we show that many of the branches of some scenario trees have identical outcomes and are therefore redundant. We demonstrate how to prune branches and derive compact representations of scenario trees using matrix algebra and Bayesian belief networks. The Bayesian network representation is particularly useful for calculation and exposition. It therefore provides a firm basis for arguing disease freedom in international forums.     

A hybrid genetic algorithm/mathematical programming approach to the multi-family flowshop scheduling problem with lot streaming

This paper presents a hybrid genetic algorithm/mathematical programming heuristic for the n-job, m-machine flowshop problems with lot streaming. The number of sublots for each job and the size of sublots are directly addressed by the heuristic and setups may be sequence-dependent. A new aspect of the problem, the interleaving of sublots from different jobs in the processing sequence, is developed and addressed. Computational results from 12 randomly generated test sets of 24 problems each are presented.     

EFFECTS OF EXPOSURE ON PREVALENCE AND CUMULATIVE RELATIVE RISK: DIRECT AND INDIRECT EFFECTS IN A RECURSIVE HAZARD MODEL

This paper outlines decomposition methods for assessing how exposure affects prevalence and cumulative relative risk. Let     x     denote a vector of exogenous covariates and suppose that a single dimension of time   t   governs two event processes     T ₁  and   T ₂.    If the occurrence of the event     T ₁    determines entry into the risk of the event     T ₂,    then subgroup variation in     T ₁    will affect the prevalence     T ₂,    even if subgroups in the population are otherwise identical. Although researchers often acknowledge this phenomenon, the literature has not provided procedures to assess the magnitude of an exposure effect of     T ₁    on the prevalence of     T ₂.    We derive decompositions that assess how variation in exposure generated by direct and indirect effects of the covariates     x     affect measures of absolute and relative prevalence of     T ₂.    We employ a parametric but highly flexible specification for baseline hazard for the     T ₁  and   T ₂    processes and use the resulting parametric proportional hazard model to illustrate the direct and indirect effects of family structure when     T ₁    is age at first sexual intercourse and     T ₂    is age at a premarital first birth for data on a cohort of non-hispanic white U.S. women.     

A Note on the Large Sample Properties of Estimators Based on Generalized Linear Models for Correlated Pseudo‐observations

Pseudo‐values have proven very useful in censored data analysis in complex settings such as multi‐state models. It was originally suggested by Andersen et al., Biometrika, 90, 2003, 335 who also suggested to estimate standard errors using classical generalized estimating equation results. These results were studied more formally in Graw et al., Lifetime Data Anal., 15, 2009, 241 that derived some key results based on a second‐order von Mises expansion. However, results concerning large sample properties of estimates based on regression models for pseudo‐values still seem unclear. In this paper, we study these large sample properties in the simple setting of survival probabilities and show that the estimating function can be written as a U‐statistic of second order giving rise to an additional term that does not vanish asymptotically. We further show that previously advocated standard error estimates will typically be too large, although in many practical applications the difference will be of minor importance. We show how to estimate correctly the variability of the estimator. This is further studied in some simulation studies.