Comparison of two methods in estimating standard error of simulated moments estimators for generalized linear mixed models

We consider standard error of the method of simulated moment (MSM) estimator for generalized linear mixed models (GLMM). Parametric bootstrap (PB) has been used to estimate the covariance matrix, in which we use the estimates to generate the simulated moments. To avoid the bias introduced by estimating the parameters and to deal with the correlated observations, (Lu, 2012) proposed a multi-stage block nonparametric bootstrap to estimate the standard errors. In this research, we compare PB and nonparametric bootstrap methods (NPB) in estimating the standard errors of MSM estimators for GLMM. Simulation results show that when the group size is large, NPB and PB perform similarly; when group size is medium, NPB performs better than PB in estimating the mean. A data application is considered to illustrate the methods discussed in this paper, using productivity of plantation roses. The data application finds that the person caring for the roses is associated with the productivity of those beds. Furthermore, we did an initial study in applying random forests to predict the productivity of the rose beds

On the Properties of Simulation-based Estimators in High Dimensions

Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase with the sample size bringing standard inferential procedures to incur significant loss in terms of performance. Moreover, the complexity of statistical models is also increasing thereby entailing important computational challenges in constructing new estimators or in implementing classical ones. A trade-off between numerical complexity and statistical properties is often accepted. However, numerically efficient estimators that are altogether unbiased, consistent and asymptotically normal in high dimensional problems would generally be ideal. In this paper, we set a general framework from which such estimators can easily be derived for wide classes of models. This framework is based on the concepts that underlie simulation-based estimation methods such as indirect inference. The approach allows various extensions compared to previous results as it is adapted to possibly inconsistent estimators and is applicable to discrete models and/or models with a large number of parameters. We consider an algorithm, namely the Iterative Bootstrap (IB), to efficiently compute simulation-based estimators by showing its convergence properties. Within this framework we also prove the properties of simulation-based estimators, more specifically the unbiasedness, consistency and asymptotic normality when the number of parameters is allowed to increase with the sample size. Therefore, an important implication of the proposed approach is that it allows to obtain unbiased estimators in finite samples. Finally, we study this approach when applied to three common models, namely logistic regression, negative binomial regression and lasso regression

Multilevel functional principal component analysis

The Sleep Heart Health Study (SHHS) is a comprehensive landmark study of sleep and its impacts on health outcomes. A primary metric of the SHHS is the in-home polysomnogram, which includes two electroencephalographic (EEG) channels for each subject, at two visits. The volume and importance of this data presents enormous challenges for analysis. To address these challenges, we introduce multilevel functional principal component analysis (MFPCA), a novel statistical methodology designed to extract core intra- and inter-subject geometric components of multilevel functional data. Though motivated by the SHHS, the proposed methodology is generally applicable, with potential relevance to many modern scientific studies of hierarchical or longitudinal functional outcomes. Notably, using MFPCA, we identify and quantify associations between EEG activity during sleep and adverse cardiovascular outcomes.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS206 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

The multi-fractal model of asset returns : its estimation via GMM and its use for volatility forecasting

Multi-fractal processes have been proposed as a new formalism for modeling the time series of returns in finance. The major attraction of these processes is their ability to generate various degrees of long memory in different powers of returns - a feature that has been found to characterize virtually all financial prices. Furthermore, elementary variants of multi-fractal models are very parsimonious formalizations as they are essentially one-parameter families of stochastic processes. The aim of this paper is to provide the characteristics of a causal multi-fractal model (replacing the earlier combinatorial approaches discussed in the literature), to estimate the parameters of this model and to use these estimates in forecasting financial volatility. We use the auto-covariances of log increments of the multi-fractal process in order to estimate its parameters consistently via GMM (Generalized Method of Moment). Simulations show that this approach leads to essentially unbiased estimates, which also have much smaller root mean squared errors than those obtained from the traditional ?scaling? approach. Our empirical estimates are used in out-of-sample forecasting of volatility for a number of important financial assets. Comparing the multi-fractal forecasts with those derived from GARCH and FIGARCH models yields results in favor of the new model: multi-fractal forecasts dominate all other forecasts in one out of four cases considered, while in the remaining cases they are head to head with one or more of their competitors. --multi-fractality , financial volatility , forecasting