In robust ridge regression, the ridge biasing parameter k is typically estimated as the ratio of the Huber variance factor to the M-estimator of the regression coefficients. However, the presence of outliers or heavy-tailed error distributions compromises the consistency of the ordinary least squares error variance, particularly in the presence of multicollinearity among predictors. To overcome these limitations, we propose a novel class of hybrid estimation framework that integrates ridge regression with a scale-based error variance estimator and M-estimation. This strategy enhances estimation efficiency by inflating the error variance in a principled manner to better accommodate both outliers and multicollinearity. Extensive simulation studies and a real data application demonstrate that the proposed approach consistently outperforms existing methods in terms of achieving lower average mean squared error.

In this article, we propose a novel variable selection approach in the framework of high-dimensional linear models where the columns of the design matrix are highly correlated. It consists in rewriting the initial high-dimensional linear model to remove the correlation between the columns of the design matrix and applying a generalized Elastic Net criterion since it can be seen as an extension of the generalized Lasso. The properties of our approach, called gEN (generalized Elastic Net), are investigated both from a theoretical and a numerical point of view. More precisely, we provide a new condition called GIC (generalized irrepresentable condition), which generalizes the EIC (elastic net irrepresentable condition) of Jia and Yu (2010), under which we prove that our estimator can recover the positions of the null and non null entries of the coefficients when the sample size tends to infinity. We also assess the performance of our methodology using synthetic data and compare it with alternative approaches. Our numerical experiments show that our approach improves the variable selection performance in many cases.

. This article introduces a new kernel for pattern classification. The consolidation kernel is designed to deal with a topological difficulty: a data set where some of the clouds of points associated with the different categories are parted in multiple clusters, possibly distant one from the other. It brings together such clusters. It is incorporated in a multi-class support vector machine. A comparative experimental study highlights its appealing properties.

. Bootstrap methods are widely used statistical techniques known for their simplicity and good properties. This paper introduces a novel bootstrap method called the parametric predictive bootstrap (PP-B), which relies on parametric models and is designed for predictive inference. The PP-B method is evaluated in various scenarios and typically used with other bootstrap methods to assess its performance in estimation and prediction inference. Comparisons of PP-B with other bootstrap methods are made in terms of the coverage probabilities of confidence and prediction intervals. Simulation results indicate that PP-B excels in predictive inference due to its explicitly predictive nature.

This paper proposes one-stage multiple comparisons for exponential mean lifetimes with the average based on the doubly censored samples under heteroscedasticity. This approach is suggested for situations where obtaining an additional sample for the second stage is impractical. These intervals facilitate the identification of treatments in experimental designs that are either better than the average, worse than the average, or not significantly different from the average, particularly relevant in agriculture and pharmaceutical industries. The methodology employs both one-sided and two-sided confidence intervals for conducting these multiple comparisons. Additionally, the paper includes statistical tables of critical values and provides an example involving the comparison of four drugs in leukemia treatment to illustrate the proposed procedures.

. In this article, we derive the local asymptotic normality (LAN) property for periodic GARCH and periodic threshold GARCH models with periodically time-varying parameters. For this purpose, we adapt a framework that works under quite natural and economic conditions. This property is fundamental and prepares the way for efficient and adaptive estimation in a semiparametric setting for future consideration. The simulation experiment is carried out for studying the distribution of the likelihood ratio under different underlying error distributions.

Since De Finetti first introduced the concept of dividend in 1957, an increasing number of scholars have started to study different dividend strategies. With the advent of barrier dividend strategies and band dividend strategies, ratcheting dividend strategies have also become a new research direction in recent years. This type of dividend strategy stipulates that once the level of dividend increases, it will not decline. The problem of determining the optimal dividend strategy can be formulated as a Hamilton-Jacobi-Bellman equation (hereinafter referred to as the HJB equation). This article explores the problem of one-fold optimal ratcheting dividend strategies by solving the HJB equation and leveraging the fluctuation theory of the Lévy processes. The research is conducted separately under the Brownian risk model, the classical risk model, and the classical risk model with drift. Additionally, a proof of the optimality of the ratcheting dividend strategy is provided.

. This article investigates estimation of semiparametric varying-coefficient spatial autoregressive models with measurement errors. By combining two different types of instrumental variables and subsequently relaxing the assumptions associated with them to enhance their practical applicability, a sieve three-stage least squares (S-3SLS) estimation method is proposed. Furthermore, the asymptotic normality of the proposed estimator is derived under mild conditions. Simulation studies consistently demonstrate that the proposed methodology exhibits robust performance under finite sample sizes, irrespective of the presence or absence of spatial dependence within the underlying model.

. In this article, we study the Wiener-Poisson risk model under high-frequency data. An estimator for the Gerber-Shiu function is constructed by combining the threshold method with the Fourier-cosine method. We establish that the proposed estimator achieves a convergence rate of order O P ( log ⁡ ( n h n ) ( h n α + 1 n h n ) ) , where n+1 is the number of observations from process (1.1), h n is the time step, and α ∈ ( 0 , 1 2 ) . Finally, we verify the effectiveness of our estimator through some simulation studies.

. In this article, we introduce several test statistics for goodness-of-fit tests of the Pareto distribution using progressively Type-II censored data. While one test statistic is derived from the complete sufficient statistic and the maximum product of spacings estimator of the Pareto distribution parameter, the others are based on progressively Type-II censored spacings. These test statistics are scale-invariant, and their null distributions are independent of the parameter of the Pareto distribution. We evaluate the performance of these test statistics against different alternatives with monotonic and non-monotonic hazard rate functions and compare their power with an existing goodness-of-fit test statistic through a wide range of Monte Carlo simulations. Our findings indicate that the proposed test statistics perform well in many cases. Finally, we provide two examples to illustrate the proposed tests.