Measuring the complexity of generalized linear hierarchical models

Measuring a statistical model's complexity is important for model criticism and comparison. However, it is unclear how to do this for hierarchical models due to uncertainty about how to count the random effects. The authors develop a complexity measure for generalized linear hierarchical models based on linear model theory. They demonstrate the new measure for binomial and Poisson observables modeled using various hierarchical structures, including a longitudinal model and an areal‐data model having both spatial clustering and pure heterogeneity random effects. They compare their new measure to a Bayesian index of model complexity, the effective number p_D of parameters (Spiegelhalter, Best, Carlin & van der Linde 2002); the comparisons are made in the binomial and Poisson cases via simulation and two real data examples. The two measures are usually close, but differ markedly in some instances where p_D is arguably inappropriate. Finally, the authors show how the new measure can be used to approach the difficult task of specifying prior distributions for variance components, and in the process cast further doubt on the commonly‐used vague inverse gamma prior.     

Testing parameter of the power series distribution of a zero inflated power series model

The Zero Inflated Power Series Distribution (ZIPSD) contains two parameters. The first parameter indicates inflation of zero and the other parameter is that of the Power Series distribution. We provide three asymptotic tests for testing the parameter of Power Series distribution, using an unconditional (standard) likelihood approach, a conditional likelihood approach and a test based on sample mean, respectively. The performance of these three tests has been studied for Zero Inflated Poisson Distribution (ZIPD). Asymptotic Confidence Intervals for the parameter are also provided.     

Exact inference for a simple step-stress model with competing risks for failure from exponential distribution under Type-II censoring

In reliability analysis, accelerated life-testing allows for gradual increment of stress levels on test units during an experiment. In a special class of accelerated life tests known as step-stress tests, the stress levels increase discretely at pre-fixed time points, and this allows the experimenter to obtain information on the parameters of the lifetime distributions more quickly than under normal operating conditions. Moreover, when a test unit fails, there are often more than one fatal cause for the failure, such as mechanical or electrical. In this article, we consider the simple step-stress model under Type-II censoring when the lifetime distributions of the different risk factors are independently exponentially distributed. Under this setup, we derive the maximum likelihood estimators (MLEs) of the unknown mean parameters of the different causes under the assumption of a cumulative exposure model. The exact distributions of the MLEs of the parameters are then derived through the use of conditional moment generating functions. Using these exact distributions as well as the asymptotic distributions and the parametric bootstrap method, we discuss the construction of confidence intervals for the parameters and assess their performance through Monte Carlo simulations. Finally, we illustrate the methods of inference discussed here with an example.     

Asymptotic Inference on Cointegrating Rank in Partial Systems

The likelihood ratio test for cointegrating rank is analyzed for partial (or conditional) systems in the vector autoregressive error-correction model. Under the assumption of weak exogeneity for the cointegrating parameters, the asymptotic distributions are given and tables of critical values are provided. A discussion is given of some of the assumptions of the model, why they are needed, and how they are tested.     

Heteroskedasticity-consistent interval estimators

The linear regression model is commonly used in applications. One of the assumptions made is that the error variances are constant across all observations. This assumption, known as homoskedasticity, is frequently violated in practice. A commonly used strategy is to estimate the regression parameters by ordinary least squares and to compute standard errors that deliver asymptotically valid inference under both homoskedasticity and heteroskedasticity of an unknown form. Several consistent standard errors have been proposed in the literature, and evaluated in numerical experiments based on their point estimation performance and on the finite sample behaviour of associated hypothesis tests. We build upon the existing literature by constructing heteroskedasticity-consistent interval estimators and numerically evaluating their finite sample performance. Different bootstrap interval estimators are also considered. The numerical results favour the HC4 interval estimator.     

Splines for financial volatility

Summary.  We propose a flexible generalized auto-regressive conditional heteroscedasticity type of model for the prediction of volatility in financial time series. The approach relies on the idea of using multivariate B -splines of lagged observations and volatilities. Estimation of such a B -spline basis expansion is constructed within the likelihood framework for non-Gaussian observations. As the dimension of the B -spline basis is large, i.e. many parameters, we use regularized and sparse model fitting with a boosting algorithm. Our method is computationally attractive and feasible for large dimensions. We demonstrate its strong predictive potential for financial volatility on simulated and real data, and also in comparison with other approaches, and we present some supporting asymptotic arguments.     

Bad Probability,Good Statistics,and Group Testing for Binomial Estimation

This article examines some improperly stated but often used textbook probability problems. Moving from a probabilistic to a statistical setting provides insight into group testing (i.e., observing only whether one or more of a group responds and not the response of each individual). Exact methods are used to construct tables showing (i) that group testing n times to estimate p can be more efficient than n individual tests even for small n and large p, (ii) optimal grouping strategies for various (n, p) combinations, and (iii) the efficiencies and biases achieved.     

深沪股指收益率波动研究

文章选取沪、深两市1991年1月1日至2005年2月18日的股票指数作为样本,运用EGARCH(1,1)模型,研究指数日收益率波动的性质特征,并探讨了不同阶段股市对利好消息和利空消息的反映。结果表明:不同阶段的指数收益率序列具有结构特征,各阶段沪、深两市指数收益率均与滞后一阶高度相关,且两市指数收益率均具有信息不对称效果。     

Algebraic exact inference for rater agreement models

In recent years, a method for sampling from conditional distributions for categorical data has been presented by Diaconis and Sturmfels. Their algorithm is based on the algebraic theory of toric ideals which are used to create so called “Markov Bases”. The Diaconis-Sturmfels algorithm leads to a non-asymptotic Monte Carlo Markov Chain algorithm for exact inference on some classes of models, such as log-linear models. In this paper we apply the Diaconis-Sturmfels algorithm to a set of models arising from the rater agreement problem with special attention to the multi-rater case. The relevant Markov bases are explicitly computed and some results for simplify the computation are presented. An extended example on a real data set shows the wide applicability of this methodology. Partially supported by MIUR Cofin03 (G. Consonni) and by INdAM projectAlgebraic Statistics.     

A structured variational learning approach for switching latent factor models

A data-driven approach for modeling volatility dynamics and co-movements in financial markets is introduced. Special emphasis is given to multivariate conditionally heteroscedastic factor models in which the volatilities of the latent factors depend on their past values, and the parameters are driven by regime switching in a latent state variable. We propose an innovative indirect estimation method based on the generalized EM algorithm principle combined with a structured variational approach that can handle models with large cross-sectional dimensions. Extensive Monte Carlo simulations and preliminary experiments with financial data show promising results.