Computational Statistics最新文献

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.

Abstract

The data distribution is often associated with a priori-known probability, and the occurrence probability of interest events is small, so a large amount of imbalanced data appears in sociology, economics, engineering, and various other fields. The existing over- and under-sampling methods are widely used in imbalanced data classification problems, but over-sampling leads to overfitting, and under-sampling ignores the effective information. We propose a new sampling design algorithm called the neighbor grid of boundary mixed-sampling (NGBM), which focuses on the boundary information. This paper obtains the classification boundary information through grid boundary domain identification, thereby determining the importance of the samples. Based on this premise, the synthetic minority oversampling technique is applied to the boundary grid, and random under-sampling is applied to the other grids. With the help of this mixed sampling strategy, more important classification boundary information, especially for positive sample information identification is extracted. Numerical simulations and real data analysis are used to discuss the parameter-setting strategy of the NGBM and illustrate the advantages of the proposed NGBM in the imbalanced data, as well as practical applications.

Abstract

This paper considers the sparse estimation problem of regression coefficients in the linear model. Note that the global–local shrinkage priors do not allow the regression coefficients to be truly estimated as zero, we propose three threshold rules and compare their contraction properties, and also tandem those rules with the popular horseshoe prior and the horseshoe+ prior that are normally regarded as global–local shrinkage priors. The hierarchical prior expressions for the horseshoe prior and the horseshoe+ prior are obtained, and the full conditional posterior distributions for all parameters for algorithm implementation are also given. Simulation studies indicate that the horseshoe/horseshoe+ prior with the threshold rules are both superior to the spike-slab models. Finally, a real data analysis demonstrates the effectiveness of variable selection of the proposed method.

Abstract

Bernstein Polynomial (BP) bases can uniformly approximate any continuous function based on observed noisy samples. However, a persistent challenge is the data-driven selection of a suitable degree for the BPs. In the absence of noise, asymptotic theory suggests that a larger degree leads to better approximation. However, in the presence of noise, which reduces bias, a larger degree also results in larger variances due to high-dimensional parameter estimation. Thus, a balance in the classic bias-variance trade-off is essential. The main objective of this work is to determine the minimum possible degree of the approximating BPs using probabilistic methods that are robust to various shapes of an unknown continuous function. Beyond offering theoretical guidance, the paper includes numerical illustrations to address the issue of determining a suitable degree for BPs in approximating arbitrary continuous functions.

Regression modelling often presents a trade-off between predictiveness and interpretability. Highly predictive and popular tree-based algorithms such as Random Forest and boosted trees predict very well the outcome of new observations, but the effect of the predictors on the result is hard to interpret. Highly interpretable algorithms like linear effect-based boosting and MARS, on the other hand, are typically less predictive. Here we propose a novel regression algorithm, automatic piecewise linear regression (APLR), that combines the predictiveness of a boosting algorithm with the interpretability of a MARS model. In addition, as a boosting algorithm, it automatically handles variable selection, and, as a MARS-based approach, it takes into account non-linear relationships and possible interaction terms. We show on simulated and real data examples how APLR’s performance is comparable to that of the top-performing approaches in terms of prediction, while offering an easy way to interpret the results. APLR has been implemented in C++ and wrapped in a Python package as a Scikit-learn compatible estimator.