A Pairwise Likelihood Procedure for Analyzing Exchangeable Binary Data with Random Cluster Sizes

For the exchangeable binary data with random cluster sizes, we use a pairwise likelihood procedure to give a set of approximately optimal unbiased estimating equations for estimating the mean and variance parameters. Theoretical results are obtained establishing the large sample properties of the solutions to the estimating equations. An application to a developmental toxicity study is given. Simulation results show that the pairwise likelihood procedure is valid and performs better than the GEE procedure for the exchangeable binary data.     

GSH Dependence Modeling with an Application to Risk Management

The generalized secant hyperbolic distribution (GSH) can be used to represent financial data with heavy tails as an alternative to the Student-t, because it guarantees the existence of all moments, also with a high kurtosis value. In order to obtain a multivariate extension of the GSH distribution, in this article we present two approaches to model the dependence, the copula approach and independent component analysis. Since the methodologies considered allow to simulate the GSH dependence, we show also the empirical results obtained in the estimation of risk of a financial portfolio by the Monte Carlo method.     

Robust Tests Against Smooth Transition Autoregressive Models

In this paper, we consider testing for linearity against a well-known class of regime switching models known as the smooth transition autoregressive (STAR) models. Apart from the model selection issues, one reason for interest in testing for linearity in time-series models is that non-linear models such as the STAR are considerably more difficult to use. This testing problem is non-standard because a nuisance parameter becomes unidentified under the null hypothesis. In this paper, we further explore the class of tests proposed by Luukkonen, Saikonnen and Terasvirta (1988). Luukkonen et al . (1988) proposed LM tests for linearity against STAR models. A potential difficulty here is that the linear approximation introduces high leverage points, and hence outliers are likely to be quite influential. To overcome this difficulty, we use the same approximating linear model of Luukkonen et al . (1988), but we apply Wald and F -tests based on l 1 - and bounded influence estimates. The efficiency gains of this procedure cannot be easily deduced from the existing theoretical results because the test is based on a misspecified model under H 1 . Therefore, we carried out a simulation study, in which we observed that the robust tests have desirable properties compared to the test of Luukkonen et al . (1988) for a range of error distributions in the STAR model, in particular the robust tests have power advantages over the LM test.     

Estimating the variance of a normal population by utilizing the information in a sample from a second related normal population

A class of estimators of the variance σ₁ ² of a normal population is introduced, by utilization the information in a sample from a second normal population with different mean and variance σ₂ ², under the restriction that σ₁ ²?≤?σ₂ ². Simulation results indicate that some members of this class are more efficient than the usual minimum variance unbiased estimator (MVUE) of σ₁ ², Stein estimator and Mehta and Gurland estimator. The case of known and unknown means are considered.     

An automated (Markov chain) Monte Carlo EM algorithm

We present an automated Monte Carlo EM (MCEM) algorithm which efficiently assesses Monte Carlo error in the presence of dependent Monte Carlo, particularly Markov chain Monte Carlo, E-step samples and chooses an appropriate Monte Carlo sample size to minimize this Monte Carlo error with respect to progressive EM step estimates. Monte Carlo error is gauged though an application of the central limit theorem during renewal periods of the MCMC sampler used in the E-step. The resulting normal approximation allows us to construct a rigorous and adaptive rule for updating the Monte Carlo sample size each iteration of the MCEM algorithm. We illustrate our automated routine and compare the performance with competing MCEM algorithms in an analysis of a data set fit by a generalized linear mixed model.     

Exact likelihood inference based on an unified hybrid censored sample from the exponential distribution

Recently, exact confidence bounds and exact likelihood inference have been developed based on hybrid censored samples by Chen and Bhattacharyya [Chen, S. and Bhattacharyya, G.K. (1998). Exact confidence bounds for an exponential parameter under hybrid censoring. Communications in Statistics—Theory and Methods, 17, 1857–1870.], Childs et al. [Childs, A., Chandrasekar, B., Balakrishnan, N. and Kundu, D. (2003). Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution. Annals of the Institute of Statistical Mathematics, 55, 319–330.], and Chandrasekar et al. [Chandrasekar, B., Childs, A. and Balakrishnan, N. (2004). Exact likelihood inference for the exponential distribution under generalized Type-I and Type-II hybrid censoring. Naval Research Logistics, 51, 994–1004.] for the case of the exponential distribution. In this article, we propose an unified hybrid censoring scheme (HCS) which includes many cases considered earlier as special cases. We then derive the exact distribution of the maximum likelihood estimator as well as exact confidence intervals for the mean of the exponential distribution under this general unified HCS. Finally, we present some examples to illustrate all the methods of inference developed here.     

Efficient Regularization Parameter Selection Via Information Criteria

In a nonlinear regression model based on a regularization method, selection of appropriate regularization parameters is crucial. Information criteria such as generalized information criterion (GIC) and generalized Bayesian information criterion (GBIC) are useful for selecting the optimal regularization parameters. However, the optimal parameter is often determined by calculating information criterion for all candidate regularization parameters, and so the computational cost is high. One simple method by which to accomplish this is to regard GIC or GBIC as a function of the regularization parameters and to find a value minimizing GIC or GBIC. However, it is unclear how to solve the optimization problem. In the present article, we propose an efficient Newton–Raphson type iterative method for selecting optimal regularization parameters with respect to GIC or GBIC in a nonlinear regression model based on basis expansions. This method reduces the computational time remarkably compared to the grid search and can select more suitable regularization parameters. The effectiveness of the method is illustrated through real data examples.     

Testing and Valuing Dynamic Correlations for Asset Allocation

We evaluate alternative models of variances and correlations with an economic loss function. We construct portfolios to minimize predicted variance subject to a required return. It is shown that the realized volatility is smallest for the correctly specified covariance matrix for any vector of expected returns. A test of relative performance of two covariance matrices is based on work of Diebold and Mariano. The method is applied to stocks and bonds and then to highly correlated assets. On average, dynamically correct correlations are worth around 60 basis points in annualized terms, but on some days they may be worth hundreds.