Big data fundamentally differs from traditional data, characterized by large volumes, high rates of missing values, and a lack of conformity to the normal distribution assumption for independent variables in traditional regression models. Consequently, there is a pressing need for new methodologies to enhance estimation accuracy and computational efficiency. Considering the hierarchical characteristics of data structure, we extend composite quantile regression (CQR) to accommodate hierarchical data assumptions and propose a hierarchical composite quantile regression (HCQR) model. In case of missing response variables, the regression coefficients are decomposed into individual and common components, where the inverse probability weighting is utilized for imputation. To enhance computational efficiency and achieve more accurate parameter estimates, we optimize the constructed function using the majorization-minimization algorithm. Numerical simulations of the proposed model under various missing rates reveal that our method not only improves parameter estimation accuracy but also effectively addresses non-normally distributed error terms. Finally, we apply the model to predict pancreatic cancer incidence, which provides valuable reference for the prediction and prevention of pancreatic cancer in clinical practice.

The probability mixture of beta and standard uniform distribution finds applications in various fields of natural and behavioral sciences, such as biology, epidemiology, bioinformatics and psychology. It is commonly used to model the mix of unadjusted p-values obtained from non-significant and significant hypotheses in multiple testing problems. Thus, some performance characteristics of the Benjamini–Hochberg procedure, such as its false discovery rate and power, can be verified. The focus of this work is to compare several techniques for estimating the unknown parameters in a Beta-Uniform mixture. In particular, we consider estimations based on the maximum likelihood (ML) and maximum product of spacings (MPS) methods. For numerical approximations of the ML estimators, the iterative expectation-maximization (EM) algorithm is adapted. Moreover, a generalization of the EM approximation is proposed for the computation of MPS estimations in the case of a general mixture of distributions. In addition, the method of moments is used as a benchmark estimation approach. Finally, the suggested procedures are analyzed via a simulation study and applied on a real-world example.

This paper proposes a new interpretable ensemble learning algorithm for survival data, an accelerated failure time boosting algorithm based on neural additive models (AFTBoost-NAMs), which is an extension of neural additive models and the gradient boosting algorithm to study survival data with right-censored data. The first step of the AFTBoost-NAMs algorithm is to replace the linear combination of covariates in the accelerated failure time model based on rank loss with the output function of the neural additive models, and the second step is the optimization of the model using the framework of the gradient boosting algorithm. Furthermore, to evaluate the performance of the new proposed AFTBoost-NAMs algorithm, we compare AFTBoost-NAMs with four other famous survival regression models on 4 simulated and 6 real datasets, using two evaluation measures, the concordance index and extended mean squared error. We use the prostate cancer dataset as an example to analyze the interpretability of the model. According to the comparison results in the testing dataset and global interpretation in the training dataset, the new proposed AFTBoost-NAMs performs well in terms of prediction accuracy and is effective in terms of interpretability.

Two-way ANOVA models are usually employed to see the homogeneity of row (column) effects. In various medical and psychological studies, prior information that these effects follow monotone orderings may be available; for example, the effects of the factors ‘Age’ and ‘Gender’ on low-density lipoprotein are observed to be monotonic with respect to both factors. Integrating this information yields computationally intensive yet powerful tests. Here we develop powerful procedures for testing simultaneous trends and constructing simultaneous confidence intervals for ordered effects in a two-way heteroscedastic additive ANOVA model. The likelihood ratio test and two union-intersection type tests are developed. For comparing various treatments, the reporting of confidence intervals for successive differences in effects that lead to the rejection of the null hypothesis is of interest. The proposed tests control type-I error rates, achieve high power, and remain robust under departures from normality. They also allow the construction of simultaneous confidence intervals. The test procedures developed here are implemented on cholesterol data of the patients classified according to age and gender and are seen to detect even small increments in effects of the factors. An ‘R’ software package has been developed to implement the proposed tests.

We propose a new goodness of fit test for the Lomax distribution using the fixed-point characterization developed using Stein's type identity. The theory of U-statistics is used for deriving the test statistic. The proposed test statistic is modified to incorporate the right-censored data. The asymptotic distribution of the test statistics is obtained. Monte Carlo simulation studies are conducted to evaluate the finite-sample performance of the test statistic. To assess the practical applicability of the test statistic, we analyzed four real datasets.

In order to better fit real-world datasets, studying asymmetric distribution is of great interest. In this work, we derive several mathematical properties of a general class of asymmetric distributions with positive support which shows up as a unified framework for Extreme Value Theory asymptotic results. The new model generalizes some well-known distribution models such as Generalized Gamma, Inverse Gamma, Weibull, Fréchet, Half-normal, Modified half-normal, Rayleigh, and Erlang. To highlight the applicability of our results, the performance of the analytical models is evaluated through real-life dataset modeling.

Asymmetry is a fundamental feature of data dealing with medical treatment in settings involving complex dependencies, such as cholesterol cardiology risk preventive studies. However, typical measures of dependence, like the correlation coefficient, are symmetric. This severe oversymmetrization brings several biases. To overcome this gap, we develop better dependence modeling and provide statistical guidelines for research on preventative cardiology, bone mineral density, and general medicine. By using pseudo-exponential, pseudo-normal, Marshall-Olkin bivariate exponential, and Hanagal bivariate Weibull models, we demonstrate the ability to discover important latent relationships emerging in recent studies in cardiology. For example, an excessively high level of HDL cholesterol can be dangerous, as can the use of different units for cholesterol and blood pressure measurements. These models eliminate erroneous oversymmetrization while providing greater flexibility than asymmetric copulas. We illustrate the usage of the newly developed dependence models on data from the Framingham Heart Study, the University of Victor Babes study, and the Study of Osteoporotic Fracture (SOF). We create new pseudo-exponential and pseudo-lognormal models and a graphical method for goodness-of-fit for certain bivariate models. We also derive the pseudo-exponential copula and densities for these models.

Accurately distinguishing between diseased and non-diseased states in clinical diagnostics is fundamental, particularly in complex cases with multiple disease stages or subtypes. This paper introduces a novel diagnostic metric, the Harmonic Mean of F-score and inverse (negative) F-score, developed to provide a more comprehensive assessment of diagnostic accuracy under tree or umbrella ordering for multi-subtype diseases (HTF). HTF integrates Specificity (TSp) and Negative Predictive Value (TNPV) into the Negative F-score (TNFγ), allowing for a robust evaluation of true negatives and negative test reliability. Also, the HTF metric was applied to estimate optimal cut-off points in tree ordering models, where subtypes categorize diseases. Through simulations, HTF measures demonstrated superior performance in certain situations compared to traditional methods. Applied to real-world multi-class (tree ordering) data using Lung Cancer data, the proposed measure consistently provided a more balanced evaluation of diagnostic accuracy. It frequently outperformed conventional metrics and delivered comparable results to the extended Youden index in tree-ordering settings. The versatility of HTF measure enables customization, allowing researchers and clinicians to adjust its parameters to prioritize specific elements of diagnostic performance based on the clinical context.

Mortality forecasting plays a central role in both demographic and actuarial studies. Classical approaches, such as the Lee-Carter (LC) model, typically rely on mortality rates as the primary measure. In recent years, compositional data analysis (CoDA), which respects summability and non-negativity constraints, has gained increasing attention for mortality forecasting. While the centred log-ratio (CLR) transformation is commonly used to map compositional data to real space, the α-transformation, a generalisation of log-ratio transformations, offers greater flexibility and adaptability. This study introduces the α-transformation as an alternative to the CLR transformation within a CoDA framework under a discrete-age setting for all-cause mortality forecasting, which has not been previously investigated. To enable a fair comparison of transformation choices, zero values in the data are imputed, although the α-transformation can inherently accommodate them. Using age-specific life table death counts for males and females in 31 selected European countries/regions from 1983 to 2018, the proposed method demonstrates comparable performance to the CLR transformation in most cases, with improved forecast accuracy in some instances. These findings highlight the potential of the α-transformation to enhance mortality forecasting within the CoDA framework.

This paper proposes a stochastic volatility model in which leverage evolves through a heterogeneous autoregressive (HAR) structure that combines daily and weekly return innovations. The resulting HARA specification can be viewed as a parsimonious restriction of multi-lag leverage drivers used in the stochastic volatility literature, delivering an interpretable multiscale decomposition of leverage dynamics and a closed-form leverage-propagation function. Parameters are estimated using data cloning, providing stable likelihood-based inference. Monte Carlo experiments confirm accurate recovery of the daily/weekly leverage components under both Gaussian and heavy-tailed innovations. Empirically, estimates for four international equity indices reveal substantial cross-asset heterogeneity in the horizon and persistence of leverage propagation. Benchmark comparisons are reported in an appendix as validation.