Order-of-addition (OofA) experiments are widely utilized in diverse fields, such as industry and pharmacy. The two most commonly employed models are the pairwise ordering model and the component-position model. However, in certain experimental problems, the response only depends on the adjacency relationship (AR) between components, rather than their absolute or relative positions. This is referred to as the AR problem. Among the different types of AR problems, spatial AR and sequential AR are frequently discussed, yet research on sequential AR remains rather limited. In this paper, we introduce OofAM, a method grounded in OofA experiments to tackle the sequential AR problem. The proposed method encompasses a novel model, designs with certain theoretical properties, along with some analytical techniques for inferring the optimal orders. As a first attempt to apply OofA experiments to solve the sequential AR problem, OofAM is both straightforward and information-efficient. Moreover, case studies demonstrate that the proposed method outperforms other methods in terms of efficiency, especially for large-scale problems.

Control Chart Pattern Recognition (CCPR) plays a crucial role in maintaining product quality. This paper presents some recognition models that utilizes a custom convolutional network alongside pretrained VGG19, MobileNet, and LeNet networks to identify Control Chart Patterns (CCP) for autocorrelated processes. The suggested architectures autonomously extract features from input data, in contrast to conventional methods that necessitate manual feature engineering. This study addresses the challenge of training deep networks with insufficient training data by employing transfer learning to refine a VGG19, MobileNet, and LeNet model, for a new CCPR task. The comparison of the performance between pre-trained networks and the extended convolutional network as a 2D CNN, which does not utilize transfer learning, indicates that pre-trained networks attain superior recognition accuracies with a smaller training data. On the other hand, the pretrained VGG19 demonstrates superior performance when compared to 1D CNN and conventional machine learning techniques, highlighting the advantages of utilizing transfer learning. Additionally, the utilization of pre-trained models addresses the challenge of the intricate design involved in the feature extraction component of deep networks that possess numerous hyperparameters. The suggested method has demonstrated significant potential for identifying CCPs, as evidenced by comparative experimental findings and a real-world case study.

Pooling data from multiple studies enhances statistical power and precision for quantifying biomarker-disease associations. However, inter-study variability in biomarker measurements exists, requiring calibration to a reference assay to standardize biomarker data across contributing studies before pooling. In this study, we develop a novel Bayesian Biomarker Pooling (BBP) method to aggregate biomarker data from multiple study sources, which considers the reference measurements of biospecimens that have not been re-assayed as unobservable latent variables. We establish a two-level model of studies and biospecimens to delineate the relationships among reference measurements, local measurements, and outcomes. Furthermore, we compare the proposed BBP method with several prevalent methodologies: the internalized method, the full calibration method, the two-stage method, the naïve method, and the x-only method. Our results demonstrate that the BBP method outperforms the other methods. This advantage is particularly pronounced in scenarios involving high noise and strong effects. As an illustrative example, we apply these methods in a pooling analysis to evaluate the association between Human Epidermal Growth Factor Receptor 2 (HER2) gene expression levels and breast cancer risk. The full package is available online at https://github.com/luyiyun/bayesian_biomark_pooling.

Markov Regime-Switching (MRS) models are widely used for modeling equity return time series. Yet standard MRS models may inadequately capture the mean reversion behavior of long-term equity returns and exhibit unstable parameter estimation due to their reliance on normality assumptions within each regime. These limitations in model adequacy can compromise the accuracy of risk exposure measurements for invested assets. To address these issues, we propose a constrained robust MRS (CRMRS) model, which integrates an order restriction and sparse constraints on regime means and transition probabilities to better capture mean reversion while employing a general ρ-based least favorable distribution to improve distributional flexibility across regimes. We assess the method's performance through finite-sample simulations under various scenarios in the presence or absence of atypical values. Furthermore, we empirically validate the improvements in model adequacy and risk exposure measurement using monthly returns from the S&P/TSX Composite Index, the benchmark for Canadian equity performance, where S&P and TSX stand for Standard & Poor's and the Toronto Stock Exchange, respectively. Our findings demonstrate that the proposed CRMRS-Huber produces stable parameter estimates and superior approximations of higher-order moments, such as skewness and kurtosis, and provides balanced intermediate risk evaluation across all cases.

We introduce two ratio-based robust test statistics, max-robust-sum (MRS) and sum-robust-sum (SRS), which compare the largest suspected outlier(s) to a trimmed partial sum of the sample. They are designed to enhance the robustness of outlier detection in samples with exponential or Pareto tails. These statistics are invariant to scale parameters and offer improved overall resistance to masking and swamping by recalibrating the denominator to reduce the influence of the largest observations. In particular, the proposed tests are shown to substantially reduce the masking problem in inward sequential testing, thereby re-establishing the inward sequential testing method – formerly relegated since the introduction of outward testing – as a competitive alternative to outward testing, without requiring multiple testing correction. The analytical null distributions of the statistics are derived, and a comprehensive comparison of the test statistics is conducted through simulation, evaluating the performance of the proposed tests in both block and sequential settings, and contrasting their performance with classical statistics across various data scenarios. In five case studies – financial crashes, nuclear power generation accidents, stock market returns, epidemic fatalities, and city sizes – significant outliers are detected and related to the concept of ‘Dragon King’ events, defined as meaningful outliers that arise from a unique generating mechanism.

The relationship between covariates and outcomes can change over time, regardless of whether these covariates are time-varying or static. For instance, the influence of circulating biomarkers like white blood cell counts on the efficacy of standard chemotherapy in cancer patients may shift throughout the treatment duration. Traditional models with constant coefficients may fail to capture these dynamic interactions. Additionally, when multiple covariates are present, their interactions within and across time periods can become complex. To address these issues, we introduce a Lasso-Network constrained time-varying linear mixed-effects model (TVLMM) accompanied by an efficient two-stage parameter estimation algorithm that tracks the evolution of fixed-effect coefficients over time. We validate our approach through extensive simulations that highlight its effectiveness and computational efficiency in high-dimensional settings. Our method is further applied to real data from a randomized clinical trial of patients with metastatic colorectal cancer (mCRC), treated with standard chemotherapy with or without panitumumab. This case study demonstrates how our approach adeptly captures the time-varying impacts of critical circulating biomarkers on treatment outcomes, specifically tumor size reduction.

In this paper, we study the functional linear multiplicative model based on the least product relative error criterion. Under some regularization conditions, we establish the consistency and asymptotic normality of the estimator. Further, we investigate the optimal subsampling for this model with massive data. Both the consistency and asymptotic distribution of the subsampling estimator are first derived. Then, we obtain the optimal subsampling probabilities based on the A-optimality criterion. Moreover, the useful alternative subsampling probabilities without computing the inverse of the Hessian matrix are also proposed, which are easier to implement in practise. Finally, numerical studies and real data analysis are carried out to evaluate the performance of the proposed approaches.

Fuzzy set theory has become increasingly popular for deriving uni- and multi-dimensional poverty estimates. In recent years, various authors have proposed different approaches to defining membership functions, resulting in the development of various fuzzy poverty indices. This paper introduces a new R package called FuzzyPovertyR, designed for estimating fuzzy poverty indices. The package is demonstrated by using it to estimate three fuzzy poverty indices – one multi- and two uni-dimensional – at the regional level (NUTS 2) in Italy. The package allows users to select from a range of membership functions and includes tools for estimating the variance of these indices by the ad-hoc Jack-Knife repeated replication procedure or by naive and calibrated non-parametric bootstrap methods.

When analyzing real data sets, statisticians often face the question that the data are heterogeneous and it may not necessarily be possible to model this heterogeneity directly. One natural option in this case is to use the methods based on finite mixtures. The key question in these techniques often is what is the best number of mixtures or, depending on the focus of the analysis, the best number of sub-populations when the model is otherwise fixed. Moreover, when the distribution of the response variable deviates from meeting the assumptions, it's common to employ an appropriate transformation to align the distribution with the model's requirements. To solve the problem in the mixture regression context we propose a technique based on the scaled Box-Cox transformation for normal mixtures. The specific focus here is on mixture regression for longitudinal data, the so-called trajectory analysis. We present interesting practical results as well as simulation experiments to demonstrate that our method yields reasonable results. Associated R-programs are also provided.

This study presents diagnostic techniques for Heckman selection models estimated using the EM algorithm. The focus is on the selection t and normal models, based on the bivariate Student's-t and bivariate normal distributions, respectively. The Heckman selection model is a key econometric tool for estimating relationships while addressing selection bias. Relying on the EM-type algorithm, we develop global and local influence analyses based on the conditional expectation of the complete-data log-likelihood function, exploring four perturbation schemes for local influence analysis. To assess the effectiveness of the proposed diagnostic measures in identifying influential observations, we conducted a simulation study, complemented by two real-data applications that demonstrate how these techniques can effectively identify influential points. The proposed algorithms and methodologies are incorporated into the R package HeckmanEM.