Computational Statistics & Data Analysis最新文献

The focus is on the statistical analysis of matrix-valued time series, where data is collected over a network of sensors, typically at spatial locations, over time. Each sensor records a vector of features at each time point, creating a vectorial time series for each sensor. The goal is to identify the dependency structure among these sensors and represent it with a graph. When only one feature per sensor is observed, vector auto-regressive (VAR) models are commonly used to infer Granger causality, resulting in a causal graph. The first contribution extends VAR models to matrix-variate models for the purpose of graph learning. Additionally, two online procedures are proposed for both low and high dimensions, enabling rapid updates of coefficient estimates as new samples arrive. In the high-dimensional setting, a novel Lasso-type approach is introduced, and homotopy algorithms are developed for online learning. An adaptive tuning procedure for the regularization parameter is also provided. Given that the application of auto-regressive models to data typically requires detrending, which is not feasible in an online context, the proposed AR models are augmented by incorporating trend as an additional parameter, with a particular focus on periodic trends. The online algorithms are adapted to these augmented data models, allowing for simultaneous learning of the graph and trend from streaming samples. Numerical experiments using both synthetic and real data demonstrate the effectiveness of the proposed methods.

n-gram profiles have been successfully and widely used to analyse long sequences of potentially differing lengths for clustering or classification. Mainly, machine learning algorithms have been used for this purpose but, despite their predictive performance, these methods cannot discover hidden structures or provide a full probabilistic representation of the data. A novel class of Bayesian generative models designed for n-gram profiles used as binary attributes have been designed to address this. The flexibility of the proposed modelling allows to consider a straightforward approach to feature selection in the generative model. Furthermore, a slice sampling algorithm is derived for a fast inferential procedure, which is applied to synthetic and real data scenarios and shows that feature selection can improve classification accuracy.

Covariate models, such as polynomial regression models, generalized linear models, and heteroscedastic models, are widely used in statistical applications. The importance of such models in statistical analysis is abundantly clear by the ever-increasing rate at which articles on covariate models are appearing in the statistical literature. Because of their flexibility, covariate models are increasingly being exploited as a convenient way to model data that consist of both a response variable and one or more covariate variables that affect the outcome of the response variable. Efficient and robust estimates for broadly defined semiparametric covariate models are investigated, and for this purpose the minimum distance approach is employed. In general, minimum distance estimators are automatically robust with respect to the stability of the quantity being estimated. In particular, minimum Hellinger distance estimation for parametric models produces estimators that are asymptotically efficient at the model density and simultaneously possess excellent robustness properties. For semiparametric covariate models, the minimum Hellinger distance method is extended and a minimum profile Hellinger distance estimator is proposed. Its asymptotic properties such as consistency are studied, and its finite-sample performance and robustness are examined by using Monte Carlo simulations and three real data analyses. Additionally, a computing algorithm is developed to ease the computation of the estimator.

In this paper, we address direction estimation in single-index models, with a focus on heavy-tailed data applications. Our method utilizes cumulative divergence to directly capture the conditional mean dependence between the response variable and the index predictor, resulting in a model-free property that obviates the need for initial link function estimation. Furthermore, our approach allows heavy-tailed predictors and is robust against the presence of outliers, leveraging the rank-based nature of cumulative divergence. We establish theoretical properties for our proposal under mild regularity conditions and illustrate its solid performance through comprehensive simulations and real data analysis.

Selecting the appropriate number of clusters is a critical step in applying clustering algorithms. To assist in this process, various cluster validity indices (CVIs) have been developed. These indices are designed to identify the optimal number of clusters within a dataset. However, users may not always seek the absolute optimal number of clusters but rather a secondary option that better aligns with their specific applications. This realization has led us to introduce a Bayesian cluster validity index (BCVI), which builds upon existing indices. The BCVI utilizes either Dirichlet or generalized Dirichlet priors, resulting in the same posterior distribution. The proposed BCVI is evaluated using the Calinski-Harabasz, CVNN, Davies–Bouldin, silhouette, Starczewski, and Wiroonsri indices for hard clustering and the KWON2, Wiroonsri–Preedasawakul, and Xie–Beni indices for soft clustering as underlying indices. The performance of the proposed BCVI with that of the original underlying indices has been compared. The BCVI offers clear advantages in situations where user expertise is valuable, allowing users to specify their desired range for the final number of clusters. To illustrate this, experiments classified into three different scenarios are conducted. Additionally, the practical applicability of the proposed approach through real-world datasets, such as MRI brain tumor images are presented. These tools are published as a recent R package ‘BayesCVI’.

Innovative inference procedures for analyzing time series data are introduced. The methodology covers density approximation and composite hypothesis testing based on Whittle's estimator, which is a widely applied M-estimator in the frequency domain. Its core feature involves the cumulant generating function of Whittle's score obtained using an approximated distribution of the periodogram ordinates. A testing algorithm not only significantly expands the applicability of the state-of-the-art saddlepoint test, but also maintains the numerical accuracy of the saddlepoint approximation. Connections are made with three other prevalent frequency domain techniques: the bootstrap, empirical likelihood, and exponential tilting. Numerical examples using both simulated and real data illustrate the advantages and accuracy of the saddlepoint methods.

The one-sample test and two-sample test for the mean of high-dimensional functional time series are considered in this study. The proposed tests are built on the dimension-wise max-norm of the sum of squares of diverging projections. The null distribution of the test statistics is investigated using normal approximation, and the asymptotic behavior under the alternative is studied. The approach is robust to the cross-series dependence of unknown forms and magnitude. To approximate the critical values, a blockwise wild bootstrap method for functional time series is employed. Both fully and partially observed data are analyzed in theoretical research and numerical studies. Evidence from simulation studies and an IT stock data case study demonstrates the usefulness of the test in practice. The proposed methods have been implemented in a R package.