This paper studies statistical inference for a Lindley random walk model when the increment process driving the walk is strictly stationary. Lindley random walks govern customer waiting times in many queueing models and several natural and business processes, including snow depths, frozen soil depths, inventory quantities, etc. The probabilistic properties of a Lindley walk with time-correlated stationary changes are first reviewed. We provide a streamlined argument that the process has a proper limiting distribution when the mean of the incremental changes is negative, and that the Lindley process is strictly stationary when starting from this stationary distribution. Next, the Markov characteristics of the process are explored when the change process has a Markov structure of first or higher order. A derivation of the model's likelihood is given when the change process is a Gaussian autoregressive time series. An efficient particle filtering method for evaluating and optimizing the likelihood with Gaussian changes is then devised and studied via simulation.

This paper proposes a robust economic-statistical design for Hotelling’s T 2 control chart to monitor linear profiles, accounting for uncertain parameters. Unlike previous studies assuming fixed inputs, this work applies an uncertainty interval approach to address parameter uncertainty when investigating the T 2 chart design. In this way the challenge of parameter uncertainty's adverse impact on the effectiveness of quality control models in practice is addressed. The key contribution of this study is formulating a T 2 control chart that maintains accuracy despite uncertainty. Results demonstrate the value of increased costs to mitigate uncertainty risks. The proposed approach also facilitates selecting appropriate protection levels against uncertainty. The paper examines practical challenges and applications of implementing the T 2 chart under real-world conditions affected by uncertainty. Overall, the proposed robust T 2 control chart design incorporates parameter ranges for monitoring linear profiles, contrasting with previous models assuming fixed parameters.

This paper investigates control charts for count data with a significant number of zeros. The proposed models are generalized to handle data exhibiting different types of dispersion, i.e. equidispersion, overdispersion, and underdispersion. To this effect, the zero-inflated Conway–Maxwell Poisson (ZICMP) distribution is employed. A Shewhart and an exponentially weighted moving average (EWMA) control chart are developed, referred to as ZICMP-Shewhart and ZICMP-EWMA charts, respectively. The ZICMP distribution incorporates various distributions, including the Conway–Maxwell–Poisson (COM-Poisson) and zero-inflated Poisson (ZIP), Geometric, and Bernoulli distributions, as special cases. Consequently, the flexibility and versatility of the ZICMP distribution enhance the applicability of the proposed control charts, thereby providing practitioners with an adaptable tool suitable for various scenarios.The control charts are examined for their ability to detect upward shifts in the process mean level, and their statistical performance is evaluated in terms of the average run-length (ARL). Through a simulation study, we demonstrate that the ZICMP-Shewhart chart is more effective for monitoring over-dispersed data, while the ZICMP-EWMA chart is more suitable for under-dispersed data. Finally, we provide two real-life examples to illustrate the applicability of the proposed charts.

This paper tackles the challenge of autoregressive modelling for bounded Z -valued count time series, a topic that has been largely overlooked in the existing literature. To bridge this gap, we introduce the trinomial difference bounded Z -valued autoregressive (TDBZAR) model utilizing the trinomial difference thinning operator, and we explore its stochastic properties in detail. Two notable advantages of the TDBZAR model are that the incorporated trinomial difference thinning operator ensures the conditional expectation takes a linear form and allows its 1-step transition probability to be expressed as the convolution of two independent trinomial difference distributions. This significantly simplifies the computation of both the conditional least squares (CLS) and conditional maximum likelihood (CML) estimates, making them more practical and straightforward. Second, we examine the two-step CLS and CML estimates, establishing their asymptotic properties. Third, we compare the performance of these estimators through simulation studies. Finally, we apply the proposed model to a real dataset to investigate which type of crime (rape or sex offense) was more prevalent in police reports from January 1990 to December 1998.

Quantile regression is a versatile statistical tool for modeling conditional quantiles, offering a comprehensive view of the relationship between explanatory and response variables. This technique is widely used in fields like economics, finance, environmental science, and psychology. This paper introduces a new quantile regression model based on the Owen distribution, which provides flexibility in capturing quantile-specific relationships. The model parameters are estimated using maximum likelihood estimation, with a detailed discussion on the estimation process. Diagnostic measures, including a pseudo- R 2 statistic, quantile residuals, and generalized Cook’s distance, are proposed to assess model adequacy and identify influential data points. Monte Carlo simulations are employed to evaluate the estimators' performance. The model’s effectiveness is illustrated through an application to Chilean household income data, highlighting its advantages over conventional quantile regression models. Implemented in the R programming language, this model is accessible for practical use, offering a valuable addition to the quantile regression field and suggesting promising directions for further research and application across disciplines.

Multivariate control charts are commonly used in manufacturing engineering to identify abnormal changes in the process. In a high-dimensional paradigm, where the number of variables (p) exceeds the number of Phase I subgroups (m), the sample covariance matrix is ill-conditioned and will become singular. This situation makes the classical T 2 control chart inefficient and even invalid to employ for monitoring a mean vector in statistical process control. This study proposes a new multivariate shrinkage-based diagonal T 2 control chart for high dimensional data, where p is very large compared to m with individual observation. A shrinkage estimator is used to estimate a diagonal covariance matrix to obtain an invertible, well-conditioned, and efficient estimate of the sample covariance matrix. The proposal's performance is also evaluated using the probability of detecting a shift. A simulation study reveals that the proposed control chart has an efficient sensitivity in detecting shifts for the high dimensional data. Results also show that m has a minor effect on the probability of shift detection for out-of-control data. In general, this probability improves for larger p, when shift is introduced in all p.

In this paper, we consider an integer-valued autoregressive (INAR) model. Based on the likelihood ratio scanning method (LRSM), the numbers and locations of the piecewise stationary INAR process change points are discussed. The minimum description length (MDL) function of the INAR model is given. Moreover, we also study the case when the sum of coefficients in each segment of the model tends to 1 and make adjustments to the MDL criterion in the LRSM. In this way, the accuracy of change point detection is improved. In the end, simulation experiments and real data analysis are conducted to illustrate the efficiency of the LRSM.

Due to situations where asymptotic results are not valid or when we do not know the true distributions of the data set, the bootstrap technique stands out as an effective alternative to make inferences about model parameters. In this context, we introduce the conditional parametric bootstrap, applied to time series data, specifically using the Generalized Linear Autoregressive Moving Average (GLARMA) model. Our interest is to use the procedure to correct possible biases and construct confidence intervals and hypothesis testing for the parameters of the GLARMA model. We conducted simulation studies to evaluate the performance of the procedure in finite samples. The results show that the proposed technique is promising and can be applied in practical situations. An example is the analysis of the monthly number of chronic obstructive pulmonary disease (COPD) cases, which illustrates the potential of the proposed approach in a real situation.

Quantile treatment effects (QTEs) characterize different causal effects of treatment on outcome distribution. Propensity score (PS) methods are commonly employed for estimating QTEs in non-randomized studies. Previous studies have shown that insufficient and unnecessary adjustment for covariates in PS models leads to bias and efficiency loss of treatment effects. Confounders may vary across different quantiles of outcome distribution. To allow for the selection of covariates related to outcome at interesting quantiles corresponding to QTE, we proposed quantile adaptive lasso (QAL) to select covariates that can provide unbiased and efficient QTE estimation. QAL utilized linear quantile regression models to construct penalty weights. Theoretical analyses showed that QAL enjoys several asymptotic properties. Simulations showed the superiority of QAL over existing methods in variable selection and QTE estimation. We applied QAL to datasets from the China Health and Retirement Longitudinal Study to explore the impact of smoking on the severity of depression.