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The Interpretable Components (IC) use restrictions in order to have a better interpretation of the coefficients related to a Principal Component (PC). The efficiency of a (IC) due to a (PC) is made in relation to the angle formed between the Components, it being desirable the lowest value. In this context, an alternative to enrich this validation is the use of measures and circular distances so far not applied for this purpose. Given this motivation, this paper aims to propose the use of these measures to evaluate the robustness of the (IC) compared to samples contaminated with outliers, using measures and circular distances. According to various scenarios evaluated through Monte Carlo simulation, it was concluded that the use of these measures are recommended to validate the (PC) and when considering the Toeplitz correlation structure, IC were more robust in relation to the presence of outliers. [ABSTRACT FROM AUTHOR]

We define the delayed Lévy-driven continuous-time autoregressive process via the inverse of the stable subordinator. We derive correlation structure for the observed non-stationary delayed Lévy-driven continuous-time autoregressive processes of order p, emphasizing low orders, and we show they exhibit long-range dependence property. Distributional properties are discussed as well. [ABSTRACT FROM AUTHOR]

Generalized estimating equations (GEE) incorporate a working correlation structure that is important because the more accurately this structure reflects the true structure, the more efficiently regression parameters may be estimated. Numerous criteria have therefore been proposed to select a working structure, although no criterion will always work better than all other criteria. In practice, it will be unknown which criterion will work best. Therefore, in this manuscript we propose how to utilize information from multiple criteria. We demonstrate the benefits of our proposed approach via a simulation study in a variety of settings and then in an application example. [ABSTRACT FROM AUTHOR]

The aim of this study is to investigate the impact of correlation structure, prevalence and effect size on the risk prediction model by using the change in the area under the receiver operating characteristic curve (ΔAUC), net reclassification improvement (NRI), and integrated discrimination improvement (IDI). In simulation study, the dataset is generated under different correlation structures, prevalences and effect sizes. We verify the simulation results with the real-data application. In conclusion, the correlation structure between the variables should be taken into account while composing a multivariable model. Negative correlation structure between independent variables is more beneficial while constructing a model. [ABSTRACT FROM AUTHOR]

We propose a novel methodology to define, analyze and forecast market states. In our approach, market states are identified by a reference sparse precision matrix and a vector of expectation values. In our procedure, each multivariate observation is associated to a given market state accordingly to a minimization of a penalized Mahalanobis distance. The procedure is made computationally very efficient and can be used with a large number of assets. We demonstrate that this procedure is successful at clustering different states of the markets in an unsupervised manner. In particular, we describe an experiment with one hundred log-returns and two states in which the methodology automatically associates states prevalently to pre- and post-crisis periods with one state gathering periods with average positive returns and the other state periods with average negative returns, therefore discovering spontaneously the common classification of 'bull' and 'bear' markets. In another experiment, with again one hundred log-returns and two states, we demonstrate that this procedure can be efficiently used to forecast off-sample future market states with significant prediction accuracy. This methodology opens the way to a range of applications in risk management and trading strategies in the context where the correlation structure plays a central role. [ABSTRACT FROM AUTHOR]

Generalized estimating equations (GEE) is one of the most commonly used methods for regression analysis of longitudinal data, especially with discrete outcomes. The GEE method accounts for the association among the responses of a subject through a working correlation matrix and its correct specification ensures efficient estimation of the regression parameters in the marginal mean regression model. This study proposes a predicted residual sum of squares (PRESS) statistic as a working correlation selection criterion in GEE. A simulation study is designed to assess the performance of the proposed GEE PRESS criterion and to compare its performance with its counterpart criteria in the literature. The results show that the GEE PRESS criterion has better performance than the weighted error sum of squares SC criterion in all cases but is surpassed in performance by the Gaussian pseudo-likelihood criterion. Lastly, the working correlation selection criteria are illustrated with data from the Coronary Artery Risk Development in Young Adults study. [ABSTRACT FROM AUTHOR]

Identifying an informative correlation structure is important in improving estimation efficiency for longitudinal data. We approximate the empirical estimator of the correlation matrix by groups of known basis matrices that represent different correlation structures, and transform the correlation structure selection problem to a covariate selection problem. To address both the complexity and the informativeness of the correlation matrix, we minimize an objective function that consists of two parts: the difference between the empirical information and a model approximation of the correlation matrix, and a penalty that penalizes models with too many basis matrices. The unique feature of the proposed estimation and selection of correlation structure is that it does not require the specification of the likelihood function, and therefore it is applicable for discrete longitudinal data. We carry out the proposed method through a groupwise penalty strategy, which is able to identify more complex structures. The proposed method possesses the oracle property and selects the true correlation structure consistently. In addition, the estimator of the correlation parameters follows a normal distribution asymptotically. Simulation studies and a data example confirm that the proposed method works effectively in estimating and selecting the true structure in finite samples, and it enables improvement in estimation efficiency by selecting the true structures. [ABSTRACT FROM AUTHOR]

The cost for conducting a “thorough QT/QTc study” is substantial and an unsuccessful outcome of the study can be detrimental to the safety profile of the drug, so sample size calculations play a very important role in ensuring adequate power for a thorough QT study. Current literature offers some help in designing such studies, but these methods have limitations and mostly apply only in the context of linear mixed models with compound symmetry covariance structure. It is not evident that such models can satisfactorily be employed to represent all kinds of QTc data, and the existing literature inadequately addresses whether there is a change in sample size and power for more general covariance structures for the linear mixed models. We assess the use of some of the existing methods to design a thorough QT study through data arising from a GlaxoSmithKline (GSK)-conducted thorough QT study, and explore newer models for sample size calculation. We also provide a new method to calculate the sample size required to detect assay sensitivity with adequate power. [ABSTRACT FROM AUTHOR]

In many practical applications of nonparametric regression, it is desirable to allow for the possibility that the noise is correlated. In this article, we focus on wavelet-based nonparametric function estimation and propose two distinct methods for estimating the correlation structure of the noise, one based in the time domain and the other based in the wavelet domain. Once the correlation structure has been estimated, there are various methods that may be used for reconstructing the unknown signal; we focus here on the empirical Bayes block shrinkage method proposed by Wang and Wood (2006). A simulation study is described. Our numerical results indicate that the proposed methods do a good job of reconstructing the signal even when the noise is highly correlated. [ABSTRACT FROM AUTHOR]

Estimation of longitudinal data covariance structure poses significant challenges because the data usually are collected at irregular time points. A viable semiparametric model for covariance matrixes has been proposed that allows one to estimate the variance function non-parametrically and to estimate the correlation function parametrically by aggregating information from irregular and sparse data points within each subject. But the asymptotic properties of the quasi-maximum likelihood estimator (QMLE) of parameters in the covariance model are largely unknown. We address this problem in the context of more general models for the conditional mean function, including parametric, nonparametric, or semiparametric. We also consider the possibility of rough mean regression function and introduce the difference-based method to reduce biases in the context of varying-coefficient partially linear mean regression models. This provides a more robust estimator of the covariance function under a wider range of situations. Under some technical conditions, consistency and asymptotic normality are obtained for the QMLE of the parameters in the correlation function. Simulation studies and a real data example are used to illustrate the proposed approach. [ABSTRACT FROM AUTHOR]

A generic template for clinical trials simulations that are typically required by statisticians is developed. Realistic clinical trials data sets are created using a unifying model that allows general correlation structures for endpoint*timepoint data and nonnormal distributions (including time-to-event), and computationally efficient algorithms are presented. The model allows for patient dropout and noncompliance. A grid-enabled SAS-based system has been developed to implement this model; details are presented summarizing the system development. An example illustrating use of the system is given. [ABSTRACT FROM AUTHOR]

Efficiency of analysis using generalized estimation equations is enhanced when intracluster correlation structure is accurately modeled. We compare two existing criteria (a quasi-likelihood information criterion, and the Rotnitzky—Jewell criterion) to identify the true correlation structure via simulations with Gaussian or binomial response, covariates varying at cluster or observation level, and exchangeable or AR(1) intracluster correlation structure. Rotnitzky and Jewell's approach performs better when the true intracluster correlation structure is exchangeable, while the quasi-likelihood criteria performs better for an AR(l) structure. [ABSTRACT FROM AUTHOR]

Two kinds of estimation variance functions for estimating a local average (LA) of a stationary (homogeneous) random field (RF) are derived. One is local estimation (LE) and the other is general estimation (GE) of LA. The former is for estimating LA at the observation location, and the latter is for obtaining LA at any arbitrary location within the RF. The geotechnical implications of these two estimations are that LE is for estimating LA of geotechnical parameters at the spot where the investigations are made, whereas GE is for estimating LA at any arbitrary location within the same layer. The behavior of the two estimation variance functions differs greatly, controlled by the number of observations (i.e. sample size) and the normalized layer thickness (layer thickness divided by autocorrelation distance of RF). Based on the derived estimation variance functions, methods for determining reliable characteristic values of geotechnical parameters and necessary sample size are proposed. The methods are based on the same framework as that of the traditional statistical theory, i.e. confidence interval of estimated parameters. However, the assumption of independently and identically distributed (i.i.d.) samples in the traditional statistical theory is replaced by the assumption of correlated samples from a stationary RF. The results obtained from the proposed methods for LE and GE differ from each other as well as from the traditional results, which has significant implications for geotechnical parameter estimation in geotechnical engineering practice. [ABSTRACT FROM AUTHOR]

Gaussian traffic models are capable of representing a broad variety of correlation structures, ranging from short-range dependent (e.g., Ornstein–Uhlenbeck type) to long-range dependent (e.g., fractional Brownian motion, with Hurst parameter H exceeding ). This note focuses on queues fed by a large number (n) of Gaussian sources, emptied at constant service rate nc. In particular, we consider the probability of exceeding buffer level nb, as a function of b. This probability decaying (asymptotically) exponentially in n, the essential information is contained in the exponential decay rate I(b). The main result of this note describes the duality relation between the shape of I( ⋅ ) and the correlation structure. More specifically, it is shown that the curve I( ⋅ ) is convex at some buffer size b if and only if there are negative correlations on the time scale at which the overflow takes place. [ABSTRACT FROM AUTHOR]