The class of multiplicative error models are particularly suited to model nonnegative time series such as financial durations, realized volatility, and squared returns. Threshold models are also known to play an important role in time series analysis. In this talk we shall present a lack-of-fit test for fitting a two-phase threshold model to the conditional mean function in a multiplicative error model. The proposed testing procedure can also be applied to a class of autoregressive conditional heteroscedastic threshold models. A simulation study shows some superiority of the proposed test over some commonly used existing tests. We shall illustrate the testing procedure by some data examples.

We consider the question of variable selection in complex models. This is often a difficult problem due to the inherent nonlinearity of the models and the resulting non-conjugacy in their Bayesian analysis. Bayesian variable selection in time-to-event models often utilize cross-validated predictive model selection criteria which can be relatively easy to estimate for a given model. However, the performances of these criteria are not well-studied in large-scale variable selection problems and, evaluation of these criteria for each model under consideration can be difficult to infeasible. An alternative criterion is based on the highest posterior model but its implementation is difficult in non-conjugate lifetime models. In this presentation, we compare the performances of these different criteria in complex lifetime data models including models with limited failure. We also propose an efficient variable selection method and illustrate its performance in simulation studies and real example.

Two-phase sampling design is a common practice in many medical studies with rare disorders. Generally, the first-phase classification is fallible but relatively cheap, while the accurate second-phase state of-the-art medical diagnosis is complex and rather expensive to perform. When constructed efficiently it offers great potential for higher true case detection as well as for higher precision. In this talk, we consider epidemiological studies with two-phase sampling design. However, instead of a single two-phase study we consider a scenario where a series of two-phase studies are done in longitudinal fashion. Efficient and simultaneous estimation of prevalence as well incidence rate are being considered at multiple time points from a sampling design perspective. Simulation study is presented to measure accuracy of the proposed estimation technique under many different circumstances. Finally, proposed method is applied to a population of elderly adults for the prognosis of major depressive disorder.

Data related to spread of disease bacteria, wind directions, seasonal variations etc. can be represented by directional distributions. Langevin distribution is one of most commonly used directional distributions. We unify the results on admissibility, minimaxity and best equivariance of MLE of direction parameter. Various other estimators of direction parameter are compared with respect to robustness and asymptotic efficiency. Methods of improving estimators for spherical location are developed. Special applications to problems in restricted parameter spaces are given.