Computational Statistics最新文献

This paper develops a nonparametric method for estimating the spectral density of multivariate stationary time series using basis expansion. A likelihood-based approach is used to fit the model through the minimization of a penalized Whittle negative log-likelihood. Then, a Newton-type algorithm is developed for the computation. In this method, we smooth the Cholesky factors of the multivariate spectral density matrix in a way that the reconstructed estimate based on the smoothed Cholesky components is consistent and positive-definite. In a simulation study, we have illustrated and compared our proposed method with other competitive approaches. Finally, we apply our approach to two real-world problems, Electroencephalogram signals analysis, (El Nitilde{n}o) Cycle.

Broken adaptive ridge (BAR) is a penalized regression method that performs variable selection via a computationally scalable surrogate to (L_0) regularization. The BAR regression has many appealing features; it converges to selection with (L_0) penalties as a result of reweighting (L_2) penalties, and satisfies the oracle property with grouping effect for highly correlated covariates. In this paper, we investigate the BAR procedure for variable selection in a semiparametric accelerated failure time model with complex high-dimensional censored data. Coupled with Buckley-James-type responses, BAR-based variable selection procedures can be performed when event times are censored in complex ways, such as right-censored, left-censored, or double-censored. Our approach utilizes a two-stage cyclic coordinate descent algorithm to minimize the objective function by iteratively estimating the pseudo survival response and regression coefficients along the direction of coordinates. Under some weak regularity conditions, we establish both the oracle property and the grouping effect of the proposed BAR estimator. Numerical studies are conducted to investigate the finite-sample performance of the proposed algorithm and an application to real data is provided as a data example.

The support vector machine (SVM) is a powerful classifier used for binary classification to improve the prediction accuracy. However, the nondifferentiability of the SVM hinge loss function can lead to computational difficulties in high-dimensional settings. To overcome this problem, we rely on the Bernstein polynomial and propose a new smoothed version of the SVM hinge loss called the Bernstein support vector machine (BernSVC). This extension is suitable for the high dimension regime. As the BernSVC objective loss function is twice differentiable everywhere, we propose two efficient algorithms for computing the solution of the penalized BernSVC. The first algorithm is based on coordinate descent with the maximization-majorization principle and the second algorithm is the iterative reweighted least squares-type algorithm. Under standard assumptions, we derive a cone condition and a restricted strong convexity to establish an upper bound for the weighted lasso BernSVC estimator. By using a local linear approximation, we extend the latter result to the penalized BernSVC with nonconvex penalties SCAD and MCP. Our bound holds with high probability and achieves the so-called fast rate under mild conditions on the design matrix. Simulation studies are considered to illustrate the prediction accuracy of BernSVC relative to its competitors and also to compare the performance of the two algorithms in terms of computational timing and error estimation. The use of the proposed method is illustrated through analysis of three large-scale real data examples.

We propose a random forest based estimation procedure for Quantile-Oriented Sensitivity Analysis—QOSA. In order to be efficient, a cross-validation step on the leaf size of trees is required. Our full estimation procedure is tested on both simulated data and a real dataset. Our estimators use either the bootstrap samples or the original sample in the estimation. Also, they are either based on a quantile plug-in procedure (the R-estimators) or on a direct minimization (the Q-estimators). This leads to 8 different estimators which are compared on simulations. From these simulations, it seems that the estimation method based on a direct minimization is better than the one plugging the quantile. This is a significant result because the method with direct minimization requires only one sample and could therefore be preferred.

Abstract

Rating migration matrix is a crux to assess credit risks. Modeling and predicting these matrices are then an issue of great importance for risk managers in any financial institution. As a challenger to usual parametric modeling approaches, we propose a new structured dictionary learning model with auto-regressive regularization that is able to meet key expectations and constraints: small amount of data, fast evolution in time of these matrices, economic interpretability of the calibrated model. To show the model applicability, we present a numerical test with both synthetic and real data and a comparison study with the widely used parametric Gaussian Copula model: it turns out that our new approach based on dictionary learning significantly outperforms the Gaussian Copula model.

Abstract

The ability of individuals to recall events is influenced by the time interval between the monitoring time and the occurrence of the event. In this article, we introduce a non-recall probability function that incorporates this information into our modeling framework. We model the time-to-event using the Weibull distribution and adopt a latent variable approach to handle situations where recall is not possible. In the classical framework, we obtain point estimators using expectation-maximization algorithm and construct the observed Fisher information matrix using missing information principle. Within the Bayesian paradigm, we derive point estimators under suitable choice of priors and calculate highest posterior density intervals using Markov Chain Monte Carlo samples. To assess the performance of the proposed estimators, we conduct an extensive simulation study. Additionally, we utilize age at menarche and breastfeeding datasets as examples to illustrate the effectiveness of the proposed methodology.

A goodness-of-fit test for the Functional Linear Model with Scalar Response (FLMSR) with responses Missing at Random (MAR) is proposed in this paper. The test statistic relies on a marked empirical process indexed by the projected functional covariate and its distribution under the null hypothesis is calibrated using a wild bootstrap procedure. The computation and performance of the test rely on having an accurate estimator of the functional slope of the FLMSR when the sample has MAR responses. Three estimation methods based on the Functional Principal Components (FPCs) of the covariate are considered. First, the simplified method estimates the functional slope by simply discarding observations with missing responses. Second, the imputed method estimates the functional slope by imputing the missing responses using the simplified estimator. Third, the inverse probability weighted method incorporates the missing response generation mechanism when imputing. Furthermore, both cross-validation and LASSO regression are used to select the FPCs used by each estimator. Several Monte Carlo experiments are conducted to analyze the behavior of the testing procedure in combination with the functional slope estimators. Results indicate that estimators performing missing-response imputation achieve the highest power. The testing procedure is applied to check for linear dependence between the average number of sunny days per year and the mean curve of daily temperatures at weather stations in Spain.

Abstract

Despite many statistical applications brush the question of data quality aside, it is a fundamental concern inherent to external data collection. In this paper, data quality relates to the confidence one can have about the covariate values in a regression framework. More precisely, we study how to integrate the information of data quality given by a ((n times p)) -matrix, with n the number of individuals and p the number of explanatory variables. In this view, we suggest a latent variable model that drives the generation of the covariate values, and introduce a new algorithm that takes all these information into account for prediction. Our approach provides unbiased estimators of the regression coefficients, and allows to make predictions adapted to some given quality pattern. The usefulness of our procedure is illustrated through simulations and real-life applications. Kindly check and confirm whether the corresponding author is correctly identified.Yes

State estimation for large-scale non-Gaussian dynamic systems remains an unresolved issue, given nonscalability of the existing particle filter algorithms. To address this issue, this paper extends the Langevinized ensemble Kalman filter (LEnKF) algorithm to non-Gaussian dynamic systems by introducing a latent Gaussian measurement variable to the dynamic system. The extended LEnKF algorithm can converge to the right filtering distribution as the number of stages become large, while inheriting the scalability of the LEnKF algorithm with respect to the sample size and state dimension. The performance of the extended LEnKF algorithm is illustrated by dynamic network embedding and dynamic Poisson spatial models.

In the analysis of qualification stage data from FIRST Robotics Competition (FRC) championships, the ratio (1.67–1.68) of the number of observations (110–114 matches) to the number of parameters (66–68 robots) in each division has been found to be quite small for the most commonly used winning margin power rating (WMPR) model. This usually leads to imprecise estimates and inaccurate predictions in such three-on-three matches that FRC tournaments are composed of. With the recognition of a clustering feature in estimated robot strengths, a more flexible model with latent clusters of robots was proposed to alleviate overparameterization of the WMPR model. Since its structure can be regarded as a dimension reduction of the parameter space in the WMPR model, the identification of clusters of robot strengths is naturally transformed into a model selection problem. Instead of comparing a huge number of competing models ((7.76times 10^{67}) to (3.66times 10^{70})), we develop an effective method to estimate the number of clusters, clusters of robots and robot strengths in the format of qualification stage data from the FRC championships. The new method consists of two parts: (i) a combination of hierarchical and non-hierarchical classifications to determine candidate models; and (ii) variant goodness-of-fit criteria to select optimal models. In contrast to existing hierarchical classification, each step of our proposed non-hierarchical classification is based on estimated robot strengths from a candidate model in the preceding non-hierarchical classification step. A great advantage of the proposed methodology is its ability to consider the possibility of reassigning robots to other clusters. To reduce overestimation of the number of clusters by the mean squared prediction error criteria, corresponding Bayesian information criteria are further established as alternatives for model selection. With a coherent assembly of these essential elements, a systematic procedure is presented to perform the estimation of parameters. In addition, we propose two indices to measure the nested relation between clusters from any two models and monotonic association between robot strengths from any two models. Data from the 2018 and 2019 FRC championships and a simulation study are also used to illustrate the applicability and superiority of our proposed methodology.