Computational Statistics最新文献

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.

Interpretability and stability are two important characteristics required for the application of high dimensional data in statistics. Although the former has been favored by many existing forecasting methods to some extent, the latter in the sense of controlling the fraction of wrongly discovered features is still largely underdeveloped. Under the accelerated failure time model, this paper introduces a controlled variable selection method with the general framework of Model-X knockoffs to tackle high dimensional data. We provide theoretical justifications on the asymptotic false discovery rate (FDR) control. The proposed method has attracted significant interest due to its strong control of the FDR while preserving predictive power. Several simulation examples are conducted to assess the finite sample performance with desired interpretability and stability. A real data example from Acute Myeloid Leukemia study is analyzed to demonstrate the utility of the proposed method in practice.

Exploratory analysis and visualization of multiple time series data are essential for discovering the underlying dynamics of a series before attempting modeling and forecasting. This study extends two dimension reduction methods - principal component analysis (PCA) and sliced inverse regression (SIR) - to multiple time series data. This is achieved through the innovative path point approach, a new addition to the symbolic data analysis framework. By transforming multiple time series data into time-dependent intervals marked by starting and ending values, each series is geometrically represented as successive directed segments with unique path points. These path points serve as the foundation of our novel representation approach. PCA and SIR are then applied to the data table formed by the coordinates of these path points, enabling visualization of temporal trajectories of objects within a reduced-dimensional subspace. Empirical studies encompassing simulations, microarray time series data from a yeast cell cycle, and financial data confirm the effectiveness of our path point approach in revealing the structure and behavior of objects within a 2D factorial plane. Comparative analyses with existing methods, such as the applied vector approach for PCA and SIR on time-dependent interval data, further underscore the strength and versatility of our path point representation in the realm of time series data.

Hidden Markov models are a class of probabilistic graphical models used to describe the evolution of a sequence of unknown variables from a set of observed variables. They are statistical models introduced by Baum and Petrie in Baum (JMA 101:789–810) and belong to the class of latent variable models. Initially developed and applied in the context of speech recognition, they have attracted much attention in many fields of application. The central objective of this research work is upon an extension of these models. More accurately, we define multiparameter hidden Markov models, using multiple observation processes and the Riesz distribution on the space of symmetric matrices as a natural extension of the gamma one. Some basic related properties are discussed and marginal and posterior distributions are derived. We conduct the Forward-Backward dynamic programming algorithm and the classical Expectation Maximization algorithm to estimate the global set of parameters. Using simulated data, the performance of these estimators is conveniently achieved by the Matlab program. This allows us to assess the quality of the proposed estimators by means of the mean square errors between the true and the estimated values.

In clinical trials of longitudinal continuous outcomes, reference based imputation (RBI) has commonly been applied to handle missing outcome data in settings where the estimand incorporates the effects of intercurrent events, e.g. treatment discontinuation. RBI was originally developed in the multiple imputation framework, however recently conditional mean imputation (CMI) combined with the jackknife estimator of the standard error was proposed as a way to obtain deterministic treatment effect estimates and correct frequentist inference. For both multiple and CMI, a mixed model for repeated measures (MMRM) is often used for the imputation model, but this can be computationally intensive to fit to multiple data sets (e.g. the jackknife samples) and lead to convergence issues with complex MMRM models with many parameters. Therefore, a step-wise approach based on sequential linear regression (SLR) of the outcomes at each visit was developed for the imputation model in the multiple imputation framework, but similar developments in the CMI framework are lacking. In this article, we fill this gap in the literature by proposing a SLR approach to implement RBI in the CMI framework, and justify its validity using theoretical results and simulations. We also illustrate our proposal on a real data application.