The case-cohort design is a cost-efficient two-phase design for analyzing survival data when key risk factors are expensive to assess and the event rate is low. Traditionally, subcohorts are selected via simple random sampling, which might not fully utilize available information. This paper introduces an efficient sampling design using balanced sampling for subcohort selection within the case-cohort design. A notable benefit of employing balanced sampling is the automatic calibration of auxiliary variables available for the entire cohort. Under a Cox model, it has been demonstrated that the calibration of sampling weights, utilizing auxiliary variables highly correlated with the main risk factor, significantly enhances the efficiency of regression coefficient estimators. Extensive simulation experiments show the reduced variabilities under the proposed approach in comparison to those under both simple random sampling. The proposed design and estimation procedure are further illustrated using the well-established National Wilms Tumor Study dataset.

Our goal is to provide a valid point of reference for the theoretical study and the practical use of the Non-central Dirichlet distribution. An Achilles' heel of such model is the limited mathematical manageability of its joint density function, which is the main obstacle to the conduct of a further exploration of it. This paper is thus intended to enrich the little range of the already existing findings referring to this distribution by offering new insights into its analysis. An operating procedure to employ the Non-central Dirichlet as a model to be fitted to data consisting of vectors of proportions subject to the unit-sum constraint is illustrated. Simulation studies are performed to confirm the validity of the derived moments formula and to investigate the finite-sample performance of the asymptotic properties of the Maximum-Likelihood estimators and the Likelihood-Ratio tests used to accomplish the abovementioned applied matters.

This article studies a method about how to design efficient Bayesian sampling plans based on samples collected from two-component exponential distributions. First, based on a complete sampling, for a general loss function, a Bayes decision function δ A is derived, and then a Bayesian sampling plan (BSP) is constructed. The monotonicity of δ A is studied. By applying this monotonicity, a curtailment procedure to the preceding Bayes decision function is constructed. By applying this curtailment procedure, an on-line new Bayes decision function δ C , and then an efficient Bayesian sampling plan (EBSP) are constructed. It is shown that for each fixed sample size n, δ C and δ A are equivalent in the sense that for every sampling process, the decisions made by δ C and δ A are the same. It is also proved that the Bayes risk of EBSP is less than or equal to that of BSP. This indicates that EBSP is more efficient than the BSP. Comparisons among some BSPs and the proposed EBSP are given. The numerical results indicate that, in terms of Bayes risks, the EBSP significantly outperforms the BSP.

This paper addresses the optimal design problem for constant-stress accelerated degradation tests using inverse Gaussian (IG) process models. Unlike previous studies that primarily focussed on optimizing stress levels and sample sizes, this research uniquely emphasizes the critical role of measurement timing as a design variable. We investigate D-, A-, and V -optimal designs for IG processes, both with and without random effects. Our study derives analytical solutions for optimal measurement time schedules in IG processes characterized by linear degradation paths and provides numerical solutions for those with nonlinear degradation paths. To streamline the search for optimal time schedules, we employ a lower-dimensional parameterization method that mitigates the substantial computational burden. This approach facilitates the generation of multiple measurement times using only a limited number of design variables. The numerical results highlight the significant impact of optimal time scheduling on enhancing the efficiency and effectiveness of accelerated degradation test designs.

A data-driven surrogate mimics the behavior of a black-box simulation model using selected input-output data points. Highly nonlinear models challenge many surrogate techniques in engineering design. This study proposes a reliable surrogate for training small-scale problems (two or three input variables). A combination of local and semi-global interpolators is introduced to approximate responses for new sample points in the design space. The local predictor uses a linear combination of two adjacent points, while the semi-global predictor employs K-means clustering, averaging samples in each cluster, and weighting clusters based on Euclidean distances. The trade-off between predictors is optimized using jackknife resampling error minimized via Genetic Algorithm (GA). Performance comparisons with Kriging, Radial Basis Function (RBF), and Support Vector Machine (SVM) confirm the proposed surrogate’s accuracy and robustness using five benchmark functions and two engineering problems. Results demonstrate superior interpolation of nonlinear functions with reduced error and improved robustness.

In the scenario of data streams, the variable set in a model often changes according to the data conditions, which makes traditional statistical methods fail in general. In this paper, we propose an online updating method under heterogeneous updating generalized linear models, inspired by the idea of imputation methods for missing variables and the relationship between simplified and imputed models. Wherein, we focus on correcting the overall deviations of the likelihood equations rather than addressing specific individual data. This method only requires storing summary statistics from past data blocks rather than accessing the raw data, making it efficient and feasible in the online framework. We establish the asymptotic properties of online updating statistics, demonstrating that our new method achieves estimation efficiency without limitation on the number of data blocks. Finally, comprehensive simulation experiments illustrate the performance of the proposed method.

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.

The Stochastic Volatility Jump Diffusion (SVJD) model is a common tool used for option pricing. Existing literature has employed many techniques in order to estimate the parameters of this model, including both Bayesian and frequentist approaches. In 2010, Duan and Yeh [Jump and volatility risk premiums implied by VIX. J Econ Dyn Control. 2010;34(11):2232–2244] used a frequentist approach with maximum likelihood estimation that included the VIX, the Chicago Board Options Exchange (CBOE) Volatility Index, which carries real time S&P 500 option price information in addition to the S&P 500 data. In this paper, we combine the previous Bayesian approach in Cape et al. [Estimating Heston's and Bates' models parameters using Markov Chain Monte Carlo simulation. J Stat Comput Simul. 2015;85(11):2295–2314] with the inclusion of VIX by Duan and Yeh. We provide the derivations of the conditional posterior distributions of the SVJD model's parameters and a guide to a Markov Chain Monte Carlo (MCMC) algorithm used to estimate the parameters. We apply the algorithm to the historical S&P 500 and VIX data and provide the subsequent parameter estimates. We offer these tools for others performing similar research with our R code available upon request.

Classification in high dimensions has been highlighted for the past two decades since Fisher's linear discriminant analysis (LDA) is not optimal in a smaller sample size n comparing the number of covariates p, i.e. p>n, which is mostly due to the singularity of the sample covariance matrix. Rather than modifying how to estimate the sample covariance and sample mean vector in constructing a classifier, we build two types of high-dimensional classifiers using data splitting, i.e. single data splitting (SDS) and multiple data splitting (MDS). Moreover, we introduce a weighted version of MDS classifier that improves classification performance as illustrated in numerical studies. Each of the split data sets has a smaller size of covariates compared to the sample size so that LDA is applicable, and classification results can be combined with respect to minimizing the misclassification rate. We present theoretical justification backing up our proposed methods by comparing misclassification rates with LDA in high dimension. We also conduct a wide range of simulations and analyse four microarray data sets, which demonstrates that our proposed methods outperform some existing methods or at least yield comparable performances.

This paper focuses on analysing dependent truncated data. To address this, we draw inspiration from some literatures and employ the Archimedean copula model to establish a correlation between the truncation time and the survival time. Building on this, we refer to the U-statistics and the copula-graphic method to estimate the association parameter and the survival function. Subsequently, we proceed to build a quantile regression model and develop an estimation procedure for the quantile regression parameters using the counting process method. To further validate the efficacy of our approach, we conduct simulation experiments with specific settings of quantiles and correlations. In conclusion, we apply our method to analyse two datasets: one pertaining to HIV transfusion infections and the other related to retirement centres.