The fused lasso signal approximator (FLSA) obtains sparse and blocky estimates of the piecewise constant mean model with two tuning parameters for the total variation (TV)-norm and ${\ell }_1$-norm penalties. The FLSA can be divided into the fusion procedure for finding block structures and the soft-thresholding procedure for identifying non-zero block signals. In this paper, we first prove that Bayesian information criterion-type criteria guarantee that the FLSA obtains the minimally over-fitted block estimates. Second, we propose a new procedure to select the soft-thresholding level that controls the false discovery rate of the estimated signals for identifying non-zero signals under the aimed level based on the preliminary test statistics. We show that the soft-thresholded fusion estimators improve the preliminary test statistics regarding false discovery rates. We apply the FLSA with the proposed selection procedure to the COVID-19 pandemic dataset in Korea to identify the change points.

In the era of Big Data, a tremendous amount of usable data is produced every day. Count data is an essential component. The first-order integer-valued autoregressive (INAR(1)) model is one of the most effective tools for evaluating count data. In this study, we provide an improved INAR(1) model with explanatory variables. This model can well characterize the type of data where the variance of innovation is influenced by other time-varying factors. We introduce a two-step penalized conditional least squares (2SPCLS) method for unknown parameter estimation and variable selection. This method facilitates the selection of explanatory variables in the model, allowing us to more effectively address a modeling challenge. The asymptotical properties have been thoroughly investigated. This paper demonstrates, via a simulation study, that the 2SPCLS approach can accurately and effectively select the zero parameters. Finally, we perform a real-time series analysis, suggesting that this method can be used to solve problems in real life.

In this paper, we present an arithmetic short rate model based on generalized Langevin equations. The innovative feature of the model is that it accounts for memory effects in interest rate markets via the involved Langevin processes. In this setup, we provide a representation for the related zero-coupon bond price and infer its risk-neutral time dynamics. We also deduce the associated forward rate dynamics, the latter being of Heath–Jarrow–Morton type. We further establish a measure change to the risk-adjusted forward measure and propose a market-consistent calibration procedure. We finally derive a pricing formula for a European call option written on the zero-coupon bond by Fourier transform methods.

Balakrishnan et al. (Communications in Statistics Simulation and Computation 46 (2017) 4082–4097) proposed a skew logistic distribution by making use of the cumulative distribution function (CDF) of the folded logistic distribution. They made use of moments of order statistics from the standard folded logistic distribution to obtain the single and product moments of order statistics from the skew logistic distribution. Subsequently, Mac’Oduol et al. (Communications in Statistics—Theory and Methods 49 (2020) 4413–4429) proposed quantile splicing for the construction of two-piece distributions using quantile functions of symmetric distributions as building blocks. This paper presents the derivation of a general formula for the L-moments of such two-piece distributions. In addition, quantile splicing and its results are then specialized to the Tukey lambda distribution, and an example is used to illustrate the results developed.

The exponential weighted moving average (EWMA) control chart is commonly used in industry to monitor process performance for small changes in objective values. In everyday life, a large amount of data is generated by a technique where a monitoring statistic displays an undefined probability distribution; in this case, nonparametric control charts are used to examine nonconformities from the procedure aim. We aim for an existing nonparametric modified arcsine EWMA (NPMASE) sign control chart in this study. This control chart is accessible based on a single sample; however, the repetitive sampling scheme is less well-known and has received less attention, but it outperforms other sampling schemes. An NPMASE control chart based on repetitive sampling (namely RSMASE) is used here to improve the detectability of small process shifts. The performance of the resulting chart is examined in terms of popular run-length properties such as mean run-length (ARL), median run-length (MDRL), and standard deviation run-length (SDRL). The early RSMASE chart demonstrates the efficiency of shift detection abilities, followed by the NPMASE and nonparametric arcsine EWMA (NPASE) control charts. An actual-life application based on a soft-drink beverage data set for the industrial implementation of the newly designed chart is also explained.

This article considers the inference for a competing risks model with a partially observed failure cause when latent failure times follow Burr XII distributions. Inference is obtained under a generalized progressive hybrid censoring. Estimations of unknown parameters under different restrictions are provided using frequentist and Bayesian approaches. Subsequently, interval estimators are also derived. Bayesian estimators are developed for order-restricted parameters and are compared with corresponding likelihood estimators. The case of unrestricted parameters is considered as well. The performance of all estimators is evaluated based on a simulation study, and a real data set is also presented for illustrative purposes.

With the continuous development of economy and technology, the application of spatial data has become increasingly widespread. Handling complex spatial data, outlier detection has become an important problem in the study of spatial models. This article proposes a method for simultaneously performing outlier detection and variable selection in the spatial Durbin model. This method combines relevant theories of spatial statistics and enables accurate identification and location of outliers, as well as variable selection of estimation coefficients, by modeling and analyzing spatial data. The experimental results indicate that the proposed method effectively detects outliers in spatial data while maintaining accuracy, and has high interpretability and generalization value. Furthermore, a practical case is presented to demonstrate the method’s effectiveness in real-world scenarios.

The bivariate Gaussian distribution has been a key model for many developments in statistics. However, many real-world phenomena produce data that follow asymmetric distributions, and consequently bivariate normal model becomes inappropriate in such situations. Bidimensional log-symmetric models have attractive properties and can be considered as good alternatives in such situations. In this paper, we discuss bivariate log-symmetric distributions and their characterizations. We establish several distributional properties and also discuss the maximum likelihood estimation of model parameters. A Monte Carlo simulation study is performed for examining the performance of the developed parameter estimation method. A real data set is finally analyzed to illustrate the proposed model and the associated inferential method.