Computational Statistics最新文献

We consider mixtures of longitudinal trajectories, where one trajectory contains measurements over time of the variable of interest for one individual and each individual belongs to one cluster. The number of clusters as well as individual cluster memberships are unknown and must be inferred. We propose an original Bayesian clustering framework that allows us to obtain an exact finite-sample model selection criterion for selecting the number of clusters. Our finite-sample approach is more flexible and parsimonious than asymptotic alternatives such as Bayesian information criterion or integrated classification likelihood criterion in the choice of the number of clusters. Moreover, our approach has other desirable qualities: (i) it keeps the computational effort of the clustering algorithm under control and (ii) it generalizes to several families of regression mixture models, from linear to purely non-parametric. We test our method on simulated datasets as well as on a real world dataset from the Alzheimer’s disease neuroimaging initative database.

Finite mixture of Gaussians are often used to classify two- (units and variables) or three- (units, variables and occasions) way data. However, two issues arise: model complexity and capturing the true cluster structure. Indeed, a large number of variables and/or occasions implies a large number of model parameters; while the existence of noise variables (and/or occasions) could mask the true cluster structure. The approach adopted in the present paper is to reduce the number of model parameters by identifying a sub-space containing the information needed to classify the observations. This should also help in identifying noise variables and/or occasions. The maximum likelihood model estimation is carried out through an EM-like algorithm. The effectiveness of the proposal is assessed through a simulation study and an application to real data.

Longitudinal studies have been conducted in various fields, including medicine, economics and the social sciences. In this paper, we focus on longitudinal ordinal data. Since the longitudinal data are collected over time, repeated outcomes within each subject may be serially correlated. To address both the within-subjects serial correlation and the specific variance between subjects, we propose a Bayesian cumulative probit random effects model for the analysis of longitudinal ordinal data. The hypersphere decomposition approach is employed to overcome the positive definiteness constraint and high-dimensionality of the correlation matrix. Additionally, we present a hybrid Gibbs/Metropolis-Hastings algorithm to efficiently generate cutoff points from truncated normal distributions, thereby expediting the convergence of the Markov Chain Monte Carlo (MCMC) algorithm. The performance and robustness of our proposed methodology under misspecified correlation matrices are demonstrated through simulation studies under complete data, missing completely at random (MCAR), and missing at random (MAR). We apply the proposed approach to analyze two sets of actual ordinal data: the arthritis dataset and the lung cancer dataset. To facilitate the implementation of our method, we have developed BayesRGMM, an open-source R package available on CRAN, accompanied by comprehensive documentation and source code accessible at https://github.com/kuojunglee/BayesRGMM/.

The main objective of this paper is to discuss selected computational aspects of robust estimation in the linear model with the emphasis on R-estimators. We focus on numerical algorithms and computational efficiency rather than on statistical properties. In addition, we formulate some algorithmic properties that a “good” method for R-estimators is expected to satisfy and show how to satisfy them using the currently available algorithms. We illustrate both good and bad properties of the existing algorithms. We propose two-stage methods to minimize the effect of the bad properties. Finally we justify a challenge for new approaches based on interior-point methods in optimization.

This paper introduces a new nonparametric estimator of the regression based on local quasi-interpolation spline method. This model combines a B-spline basis with a simple local polynomial regression, via blossoming approach, to produce a reduced rank spline like smoother. Different coefficients functionals are allowed to have different smoothing parameters (bandwidths) if the function has different smoothness. In addition, the number and location of the knots of this estimator are not fixed. In practice, we may employ a modest number of basis functions and then determine the smoothing parameter as the minimizer of the criterion. In simulations, the approach achieves very competitive performance with P-spline and smoothing spline methods. Simulated data and a real data example are used to illustrate the effectiveness of the method proposed in this paper.

Estimating the reliability of multicomponent systems is crucial in various engineering and reliability analysis applications. This paper investigates the multicomponent stress strength reliability estimation using lower record values, specifically for the exponentiated Pareto distribution. We compare classical estimation techniques, such as maximum likelihood estimation, with Bayesian estimation methods. Under Bayesian estimation, we employ Markov Chain Monte Carlo techniques and Tierney–Kadane’s approximation to obtain the posterior distribution of the reliability parameter. To evaluate the performance of the proposed estimation approaches, we conduct a comprehensive simulation study, considering various system configurations and sample sizes. Additionally, we analyze real data to illustrate the practical applicability of our methods. The proposed methodologies provide valuable insights for engineers and reliability analysts in accurately assessing the reliability of multicomponent systems using lower record values.

This study proposes a new linear dimension reduction technique called Maximizing Adjusted Covariance (MAC), which is suitable for supervised classification. The new approach is to adjust the covariance matrix between input and target variables using the within-class sum of squares, thereby promoting class separation after linear dimension reduction. MAC has a low computational cost and can complement existing linear dimensionality reduction techniques for classification. In this study, the classification performance by MAC was compared with those of the existing linear dimension reduction methods using 44 datasets. In most of the classification models used in the experiment, the MAC dimension reduction method showed better classification accuracy and F1 score than other linear dimension reduction methods.

Extensions of quantile regression modeling for time series analysis are extensively employed in medical and health studies. This study introduces a specific class of transformed quantile-dispersion regression models for non-stationary time series. These models possess the flexibility to incorporate the time-varying structure into the model specification, enabling precise predictions for future decisions. Our proposed modeling methodology applies to dynamic processes characterized by high variation and possible periodicity, relying on a non-linear framework. Additionally, unlike the transformed time series model, our approach directly interprets the regression parameters concerning the initial response. For computational purposes, we present an iteratively reweighted least squares algorithm. To assess the performance of our model, we conduct simulation experiments. To illustrate the modeling strategy, we analyze time-series measurements of influenza infection and daily COVID-19 deaths.

In this manuscript, we consider a finite multivariate nonparametric mixture model where the dependence between the marginal densities is modeled using the copula device. Pseudo expectation–maximization (EM) stochastic algorithms were recently proposed to estimate all of the components of this model under a location-scale constraint on the marginals. Here, we introduce a deterministic algorithm that seeks to maximize a smoothed semiparametric likelihood. No location-scale assumption is made about the marginals. The algorithm is monotonic in one special case, and, in another, leads to “approximate monotonicity”—whereby the difference between successive values of the objective function becomes non-negative up to an additive term that becomes negligible after a sufficiently large number of iterations. The behavior of this algorithm is illustrated on several simulated and real datasets. The results suggest that, under suitable conditions, the proposed algorithm may indeed be monotonic in general. A discussion of the results and some possible future research directions round out our presentation.

We present a technique for learning via aggregation in supervised classification. The new method improves classification performance, regardless of which classifier is at its core. This approach exploits the information hidden in subspaces by combinations of aggregating variables and is applicable to high-dimensional data sets. We provide algorithms that randomly divide the variables into smaller subsets and permute them before applying a classification method to each subset. We combine the resulting classes to predict the class membership. Theoretical and simulation analyses consistently demonstrate the high accuracy of our classification methods. In comparison to aggregating observations through sampling, our approach proves to be significantly more effective. Through extensive simulations, we evaluate the accuracy of various classification methods. To further illustrate the effectiveness of our techniques, we apply them to five real-world data sets.