Computational Statistics最新文献

Finite mixture models have been widely used to model and analyze data from heterogeneous populations. In practical scenarios, these types of data often confront upper and/or lower detection limits due to the constraints imposed by experimental apparatuses. Additional complexity arises when measures of each mixture component significantly deviate from the normal distribution, manifesting characteristics such as multimodality, asymmetry, and heavy-tailed behavior, simultaneously. This paper introduces a flexible model tailored for censored data to address these intricacies, leveraging the finite mixture of skew-t distributions. An Expectation Conditional Maximization Either (ECME) algorithm, is developed to efficiently derive parameter estimates by iteratively maximizing the observed data log-likelihood function. The algorithm has closed-form expressions at the E-step that rely on formulas for the mean and variance of truncated skew-t distributions. Moreover, a method based on general information principles is presented for approximating the asymptotic covariance matrix of the estimators. Results obtained from the analysis of both simulated and real datasets demonstrate the proposed method’s effectiveness.

The main goal in this study was to determine confidence intervals for average age, average seniority, and average money-savings, for faculty members in a university retirement system using a simulation model. The simulation—built-in Arena—considers age, seniority, and the probability of continuing in the institution as the main input random variables in the model. An annual interest rate of 7% and an average annual salary increase of 3% were considered. The scenario simulated consisted of the teacher and the university making contributions, the faculty 5% of his salary, and the university 5% of the teacher’s salary. Since the base salaries with which teachers join to university are variable, we considered a monthly salary of MXN 23 181.2, corresponding to full-time teachers with middle salaries. The results obtained by a simulation of 30 replicates showed that the confidence intervals for the average age at retirement were (55.0, 55.2) years, for the average seniority (22.1, 22.3) years, and for the average savings amount (329 795.2, 341 287.0) MXN. Moreover, the risk that a retiree of 62 years of age and more of 25 years of work, is alive after his savings runs out is approximately 98% and this happens at 64 years of age.

Abstract

Fitting concentric ellipses is a crucial yet challenging task in image processing, pattern recognition, and astronomy. To address this complexity, researchers have introduced simplified models by imposing geometric assumptions. These assumptions enable the linearization of the model through reparameterization, allowing for the extension of various fitting methods. However, these restrictive assumptions often fail to hold in real-world scenarios, limiting their practical applicability. In this work, we propose two novel estimators that relax these assumptions: the Least Squares method (LS) and the Gradient Algebraic Fit (GRAF). Since these methods are iterative, we provide numerical implementations and strategies for obtaining reliable initial guesses. Moreover, we employ perturbation theory to conduct a first-order analysis, deriving the leading terms of their Mean Squared Errors and their theoretical lower bounds. Our theoretical findings reveal that the GRAF is statistically efficient, while the LS method is not. We further validate our theoretical results and the performance of the proposed estimators through a series of numerical experiments on both real and synthetic data.

The increased predictive power of machine learning models comes at the cost of increased complexity and loss of interpretability, particularly in comparison to parametric statistical models. This trade-off has led to the emergence of eXplainable AI (XAI) which provides methods, such as local explanations (LEs) and local variable attributions (LVAs), to shed light on how a model use predictors to arrive at a prediction. These provide a point estimate of the linear variable importance in the vicinity of a single observation. However, LVAs tend not to effectively handle association between predictors. To understand how the interaction between predictors affects the variable importance estimate, we can convert LVAs into linear projections and use the radial tour. This is also useful for learning how a model has made a mistake, or the effect of outliers, or the clustering of observations. The approach is illustrated with examples from categorical (penguin species, chocolate types) and quantitative (soccer/football salaries, house prices) response models. The methods are implemented in the R package cheem, available on CRAN.

The current status censoring takes place in survival analysis when the exact event times are not known, but each individual is monitored once for their survival status. The current status data often arise in medical research, from situations that involve multiple causes of failure. Examining current status competing risks data, commonly encountered in epidemiological studies and clinical trials, is more advantageous with Bayesian methods compared to conventional approaches. They excel in integrating prior knowledge with the observed data and delivering accurate results even with small samples. Inspired by these advantages, the present study is pioneering in introducing a Bayesian framework for both modelling and analysis of current status competing risks data together with covariates. By means of the proportional hazards model, estimation procedures for the regression parameters and cumulative incidence functions are established assuming appropriate prior distributions. The posterior computation is performed using an adaptive Metropolis–Hastings algorithm. Methods for comparing and validating models have been devised. An assessment of the finite sample characteristics of the estimators is conducted through simulation studies. Through the application of this Bayesian approach to prostate cancer clinical trial data, its practical efficacy is demonstrated.

We consider continuous-time Markov chains that describe the stochastic evolution of a dynamical system by a transition-rate matrix Q which depends on a parameter (theta ). Computing the probability distribution over states at time t requires the matrix exponential (exp ,left( tQright) ,), and inferring (theta ) from data requires its derivative (partial exp ,left( tQright) ,/partial theta ). Both are challenging to compute when the state space and hence the size of Q is huge. This can happen when the state space consists of all combinations of the values of several interacting discrete variables. Often it is even impossible to store Q. However, when Q can be written as a sum of tensor products, computing (exp ,left( tQright) ,) becomes feasible by the uniformization method, which does not require explicit storage of Q. Here we provide an analogous algorithm for computing (partial exp ,left( tQright) ,/partial theta ), the differentiated uniformization method. We demonstrate our algorithm for the stochastic SIR model of epidemic spread, for which we show that Q can be written as a sum of tensor products. We estimate monthly infection and recovery rates during the first wave of the COVID-19 pandemic in Austria and quantify their uncertainty in a full Bayesian analysis. Implementation and data are available at https://github.com/spang-lab/TenSIR.

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.