Geometric Anisotropic Spatial Point Pattern Analysis and Cox Processes

We consider spatial point processes with a pair correlation function, which depends only on the lag vector between a pair of points. Our interest is in statistical models with a special kind of ‘structured’ anisotropy: the pair correlation function is geometric anisotropic if it is elliptical but not spherical. In particular, we study Cox process models with an elliptical pair correlation function, including shot noise Cox processes and log Gaussian Cox processes, and we develop estimation procedures using summary statistics and Bayesian methods. Our methodology is illustrated on real and synthetic datasets of spatial point patterns.     

Testing Treatment-Covariate Interaction in a Nonparametric Analysis of Covariance Model

We consider a recently introduced nonparametric model for Analysis of Covariance and derive an asymptotic test for interaction between covariate and treatment. Furthermore, we suggest data depth techniques to obtain joint confidence regions for the covariate effects in this model.

The finite sample behavior of the asymptotic method is evaluated in simulations. Application of the procedures is illustrated using an epileptic seizures and chemotherapy data set.     

Estimation of odds ratios under order restrictions

A new method for estimating a set of odds ratios under an order restriction based on estimating equations is proposed. The method is applied to those of the conditional maximum likelihood estimators and the Mantel-Haenszel estimators. The estimators derived from the conditional likelihood estimating equations are shown to maximize the conditional likelihoods. It is also seen that the restricted estimators converge almost surely to the respective odds ratios when the respective sample sizes become large regularly. The restricted estimators are compared with the unrestricted maximum likelihood estimators by a Monte Carlo simulation. The simulation studies show that the restricted estimates improve the mean squared errors remarkably, while the Mantel-Haenszel type estimates are competitive with the conditional maximum likelihood estimates, being slightly worse.     

Performance of traditional f tests in repeated measures designs under covariance heterogeneity

This study investigates the performance of two traditional F tests, one for main effects and the other for interaction in repeated measures designs under several conditions of covariance heterogeneity. Overall, the test for interaction is more vulnerable than the one for main effects. Distortion in the level of significance is less serious for the case of equal group size.     

Influence in covariance structure analysis: with an application to confirmatory factor analysis

Influence functions are derived for the parameters in covariance structure analysis, where the parameters are estimated by minimizing a discrepancy function between the assumed covariance matrix and the sample covariance matrix. The case of confirmatory factor analysis is studied precisely with a numerical example. Comparing with a general procedure called one-step estimation, the proposed procedure has two advantages:1) computing cost is cheaper, 2) the property that arbitrary influence can be decomposed into a fi-nite number of components discussed by Tanaka and Castano-Tostado(1990) can be used for efficient computing and the characterization of a covariance structure model from the sensitivity perspective. A numerical comparison is made among the confirmatory factor analysis and some procedures of ex-ploratory factor analysis by using the decomposition mentioned above.     

Updating finite markov chains by using techniques of group matrix inversion

Several jackknife methods for the proportional hazards model are proposed. Instead of deleting observations in the calculation of the pseudovalues, we delete the conditional probabilities from the partial likelihood function. The parameter estimators and variance estimators for both the linear and weighted linear jackknife methods are strongly consistent. A limitted simulation study is conducted.     

On the simple step-stress model for two-parameter exponential distribution

In this paper, we consider the simple step-stress model for a two-parameter exponential distribution, when both the parameters are unknown and the data are Type-II censored. It is assumed that under two different stress levels, the scale parameter only changes but the location parameter remains unchanged. It is observed that the maximum likelihood estimators do not always exist. We obtain the maximum likelihood estimates of the unknown parameters whenever they exist. We provide the exact conditional distributions of the maximum likelihood estimators of the scale parameters. Since the construction of the exact confidence intervals is very difficult from the conditional distributions, we propose to use the observed Fisher Information matrix for this purpose. We have suggested to use the bootstrap method for constructing confidence intervals. Bayes estimates and associated credible intervals are obtained using the importance sampling technique. Extensive simulations are performed to compare the performances of the different confidence and credible intervals in terms of their coverage percentages and average lengths. The performances of the bootstrap confidence intervals are quite satisfactory even for small sample sizes.     

Specification and testing of multiplicative time-varying GARCH models with applications

In this article, we develop a specification technique for building multiplicative time-varying GARCH models of Amado and Teräsvirta (2008, 2013). The variance is decomposed into an unconditional and a conditional component such that the unconditional variance component is allowed to evolve smoothly over time. This nonstationary component is defined as a linear combination of logistic transition functions with time as the transition variable. The appropriate number of transition functions is determined by a sequence of specification tests. For that purpose, a coherent modelling strategy based on statistical inference is presented. It is heavily dependent on Lagrange multiplier type misspecification tests. The tests are easily implemented as they are entirely based on auxiliary regressions. Finite-sample properties of the strategy and tests are examined by simulation. The modelling strategy is illustrated in practice with two real examples: an empirical application to daily exchange rate returns and another one to daily coffee futures returns.     

A Conditional Approach for Regression Analysis of Longitudinal Data with Informative Observation Time and Non-negligible Observation Duration

Recently, there has been a great interest in the analysis of longitudinal data in which the observation process is related to the longitudinal process. In literature, the observation process was commonly regarded as a recurrent event process. Sometimes some observation duration may occur and this process is referred to as a recurrent episode process. The medical cost related to hospitalization is an example. We propose a conditional modeling approach that takes into account both informative observation process and observation duration. We conducted simulation studies to assess the performance of the method and applied it to a dataset of medical costs.