A Monte Carlo approach to quantifying discrepancies between intractable posterior distributions

The computational demand required to perform inference using Markov chain Monte Carlo methods often obstructs a Bayesian analysis. This may be a result of large datasets, complex dependence structures, or expensive computer models. In these instances, the posterior distribution is replaced by a computationally tractable approximation, and inference is based on this working model. However, the error that is introduced by this practice is not well studied. In this paper, we propose a methodology that allows one to examine the impact on statistical inference by quantifying the discrepancy between the intractable and working posterior distributions. This work provides a structure to analyse model approximations with regard to the reliability of inference and computational efficiency. We illustrate our approach through a spatial analysis of yearly total precipitation anomalies where covariance tapering approximations are used to alleviate the computational demand associated with inverting a large, dense covariance matrix.     

Estimation and prediction of time-varying GARCH models through a state-space representation: a computational approach

We propose a state-space approach for GARCH models with time-varying parameters able to deal with non-stationarity that is usually observed in a wide variety of time series. The parameters of the non-stationary model are allowed to vary smoothly over time through non-negative deterministic functions. We implement the estimation of the time-varying parameters in the time domain through Kalman filter recursive equations, finding a state-space representation of a class of time-varying GARCH models. We provide prediction intervals for time-varying GARCH models and, additionally, we propose a simple methodology for handling missing values. Finally, the proposed methodology is applied to the Chilean Stock Market (IPSA) and to the American Standard&Poor's 500 index (S&P500).     

A Generalized Estimating Equations Approach for Analysis of the Impact of New Technology on a Trawl Fishery

The article describes a generalized estimating equations approach that was used to investigate the impact of technology on vessel performance in a trawl fishery during 1988–96, while accounting for spatial and temporal correlations in the catch-effort data. Robust estimation of parameters in the presence of several levels of clustering depended more on the choice of cluster definition than on the choice of correlation structure within the cluster. Models with smaller cluster sizes produced stable results, while models with larger cluster sizes, that may have had complex within-cluster correlation structures and that had within-cluster covariates, produced estimates sensitive to the correlation structure. The preferred model arising from this dataset assumed that catches from a vessel were correlated in the same years and the same areas, but independent in different years and areas. The model that assumed catches from a vessel were correlated in all years and areas, equivalent to a random effects term for vessel, produced spurious results. This was an unexpected finding that highlighted the need to adopt a systematic strategy for modelling. The article proposes a modelling strategy of selecting the best cluster definition first, and the working correlation structure (within clusters) second. The article discusses the selection and interpretation of the model in the light of background knowledge of the data and utility of the model, and the potential for this modelling approach to apply in similar statistical situations.     

考虑组合动态调整效率的相关性估计模型比较

准确估计组合内资产收益相关性是构建投资组合、定价衍生品以及风险管理的关键.引入波动择时策略从组合动态调整效率角度比较两类组合相关性估计模型的应用价值,并且利用不重叠的Block Bootstrap抽样对原始数据进行模拟,以期获得更可信的实证结论.结果表明根据基于高频数据的"已实现"模型对组合进行动态调整较静态组合会获得更多收益,而根据DCC-GARCH模型调整组合反而会有损失,说明"已实现"模型比DCC-GARCH模型更具有应用价值.     

Estimating the Prediction Mean Squared Error in Gaussian Stochastic Processes with Exponential Correlation Structure

Given one or more realizations from the finite dimensional marginal distribution of a stochastic process, we consider the problem of estimating the squared prediction error when predicting the process at unobserved locations. An approximation taking into account the additional variability due to estimating parameters involved in the correlation structure was developed by Kackar & Harville (1984) and was revisited by Harville & Jeske (1992) as well as Zimmerman & Cressie (1992). The present paper discusses an extension of these methods. The approaches will be compared via an extensive simulation study for models with and without random error term. Effects due to the designs used for prediction and for model fitting as well as due to the strength of the correlation between neighbouring observations of the stochastic process are investigated. The results show that considering the additional variability in the predictor due to estimating the covariance structure is of great importance and should not be neglected in practical applications.     

Sampling Adjusted Analysis of Dynamic Additive Regression Models for Longitudinal Data

We consider a modelling approach to longitudinal data that aims at estimating flexible covariate effects in a model where the sampling probabilities are modelled explicitly. The joint modelling yields simple estimators that are easy to compute and analyse, even if the sampling of the longitudinal responses interacts with the response level. An incorrect model for the sampling probabilities results in biased estimates. Non-representative sampling occurs, for example, if patients with an extreme development (based on extreme values of the response) are called in for additional examinations and measurements. We allow covariate effects to be time-varying or time-constant. Estimates of covariate effects are obtained by solving martingale equations locally for the cumulative regression functions. Using Aalen's additive model for the sampling probabilities, we obtain simple expressions for the estimators and their asymptotic variances. The asymptotic distributions for the estimators of the non-parametric components as well as the parametric components of the model are derived drawing on general martingale results. Two applications are presented. We consider the growth of cystic fibrosis patients and the prothrombin index for liver cirrhosis patients. The conclusion about the growth of the cystic fibrosis patients is not altered when adjusting for a possible non-representativeness in the sampling, whereas we reach substantively different conclusions about the treatment effect for the liver cirrhosis patients.     

Time-varying associations between parental closeness,self-esteem,and sexual behavior across adolescence and emerging adulthood

This study applied the time-varying effect model (TVEM) to data from the National Longitudinal Study of Adolescent to Adult Health to explore how self-esteem mediated age-varying associations of closeness to mother and father and their child's sexual behavior through adolescence and emerging adulthood. Paternal closeness is associated with lesser odds of sexual behaviors for both female and male adolescents until age 20, whereas maternal closeness only predicts for female adolescents between ages 13 and 15. Self-esteem mediated the association between mother closeness and multiple partners in male adolescents between ages 14.5 and 16.5. Fathers have an impact on adolescent sexual behavior across adolescence and emerging adulthood, while mothers' roles are more important for female adolescents in early adolescence.     

Exploratory data structure comparisons: three new visual tools based on principal component analysis

Datasets are sometimes divided into distinct subsets, e.g. due to multi-center sampling, or to variations in instruments, questionnaire item ordering or mode of administration, and the data analyst then needs to assess whether a joint analysis is meaningful. The Principal Component Analysis-based Data Structure Comparisons (PCADSC) tools are three new non-parametric, visual diagnostic tools for investigating differences in structure for two subsets of a dataset through covariance matrix comparisons by use of principal component analysis. The PCADCS tools are demonstrated in a data example using European Social Survey data on psychological well-being in three countries, Denmark, Sweden, and Bulgaria. The data structures are found to be different in Denmark and Bulgaria, and thus a comparison of for example mean psychological well-being scores is not meaningful. However, when comparing Denmark and Sweden, very similar data structures, and thus comparable concepts of well-being, are found. Therefore, inter-country comparisons are warranted for these countries.     

基于时变相关系数的动态投资组合策略

在金融市场中个股收益率之间具有高度相关性,这种相关性的强弱程度随时间变化而改变.采用基于高频数据的已实现协方差刻画个股收益率间的相关性时变特征,真实反映投资组合中个股收益率间的相关情况,通过GARCH模型把投资组合的各期收益率的方差有效地连接起来,建立收益率方差之间的递推关系,从中分离出持续方差,构建总持续方差,进而把总持续方差作为二次规划模型的目标函数建立在控制风险扩散意义下的动态投资组合模型,求得该模型的解析解.实证结果表明,时变相关系数的引入将投资组合收益率在负半轴的波动幅度控制在较小的范围,说明基于时变相关系数建立的动态投资组合模型对控制风险的扩散具有实践意义.     

Sample Path Asymmetries in Non‐Gaussian Random Processes

We tackle an important although rarely addressed question of accounting for a variety of asymmetries frequently observed in stochastic temporal/spatial records. First, we review some measures intending to capture such asymmetries that have been introduced on various occasions in the past and then propose a family of measures that is motivated by Rice's formula for crossing level distributions of the slope. We utilize those asymmetry measures to demonstrate how a class of second‐order models built on the skewed Laplace distributions can account for sample path asymmetries. It is shown that these models are capable of mimicking not only distributional skewness but also more complex geometrical asymmetries in the sample path such as tilting, front‐back slope asymmetry and time irreversibility. Simple moment‐based estimation techniques are briefly discussed to allow direct application to modelling and fitting actual records.