We present fmmpy, an open-source Python library that implements the Frequency Modulated Möbius (FMM) model for robust decomposition of oscillatory signals into interpretable components. Beyond addressing the computational limitations of earlier implementations, fmmpy provides a significantly more flexible and general framework for applying the FMM model in diverse real-world scenarios. The package incorporates optimized algorithms and robust parameter constraint handling, showing how its improved flexibility and efficiency make it feasible to address problems that were previously too complex or slow to solve. This makes the FMM model more accessible and adaptable for diverse applications in biomedical, engineering, and other signal processing fields. To demonstrate its practical utility, we present two representative use cases: ECG analysis and signal spectrography, showing how the enhanced algorithms enable novel insights and solutions in these domains.

In this paper, a novel hybrid framework, called the Sparse and Pruned Approach to Random Forest (SPARF), is proposed that enhances prediction accuracy by automatically pruning the ensemble of trees generated by the RF algorithm. Unlike traditional RF, the proposed framework applies non-concave penalties, namely SCAD and GSCAD, to identify and eliminate redundant trees. The core innovation lies in integrating SCAD-based techniques with RF and aggregating remaining trees. This model leverages the sparsity of SCAD and GSCAD to provide an interpretable model with high predictive accuracy. The performance of this method is evaluated on two real datasets and Monte Carlo simulation, where a combined RF, SCAD, and GSCAD model is created to reduce and automatically select RF trees. In real-world datasets, the SPARF-SC model achieves an approximately 9.68% reduction in RMSE compared to RF, while SPARF-GSC achieves a reduction of approximately 8.46% in RMSE.

An algorithm to solve the optimal univariate stratification problem is proposed that consistently outperforms competing algorithms in a range of numerical experiments. Here the number of strata L and the sample size n are pre-specified, and the algorithm seeks the boundaries for the strata that minimize the variance of the estimator for the total of the stratification variable, under exact optimal allocation of the sample to the resulting strata. The algorithm combines ideas from the Tabu Search metaheuristic with an exact method for allocating the sample to the strata. Numerical experiments were carried out with 40 populations, varying numbers of strata (6) and sample sizes (2) – yielding a total of 40 × 6 × 2 = 480 scenarios. Our results were compared to those obtained by four competing algorithms, including the well-known algorithm by Kozak and two algorithms based on alternative metaheuristics. The comparison showed that our proposed algorithm outperformed all the competitors considered, producing a high percentage of good-quality solutions.

This paper considers a double-stage Bayesian shrinkage estimation for the scale parameter of a two-parameter exponential distribution when prior information exists as an initial value under progressively type-II censored samples. The mean squared error (MSE) of the proposed estimator is derived under Weighted Squared Error Loss (WSEL) function and it is shown that this estimator dominates the corresponding classical Bayesian estimator. Some graphical representations are also given for the illustration purpose. Simulation study and an numerical example are given to illustrate the proposed method.

The digital age has brought an explosion of data through technology adoption and smart devices. Our research tackles the specific challenge of multicollinearity in analysis of massive datasets. This issue can make statistical models unstable, where small data changes lead to dramatic shifts in results. To address this, we have developed a new statistical method called the Ridge-Guided Independent Component Regression (RICR) and propose an estimator based upon RICR, i.e. Independent Component Ridge Regression Estimator (ICRRE). This method combines two existing approaches – Ordinary Ridge Regression (ORR) and Independent Component Regression (ICR) – to better handle both multicollinearity and high dimensions of data. We mathematically prove that RIC-based estimator outperforms both the ICR- and ORR-based estimators by establishing the conditions under which it produces superior results. To validate our approach, we conducted extensive simulations comparing these methods. We also tested ICRRE's real-world performance using cotton yield data.

Monte Carlo simulation is used to demonstrate improved estimation performance of proposed distance-type estimators for lifetime models under progressive Type-I interval censoring. We propose novel distance-based estimators for lifetime models under progressive Type-I interval censoring. These estimators minimize the discrepancy between observed and model-based conditional failure probabilities using either quadratic or Mahalanobis distances, providing natural alternatives to maximum likelihood estimators (MLEs). Through extensive Monte Carlo simulations, we demonstrate that the Mahalanobis estimator outperforms MLE, particularly under heavy censoring or sparse data. The quadratic estimator also yields competitive results, especially under model misspecification. Two real data examples illustrate the practical advantages of the proposed approach.

Interval-censored data is a common type of failure time data in survival analysis. However, in practice, there is often a dependent relationship between the failure time and the observation time, and ignoring this dependency can lead to biased inferences. To address this issue, this study describes the dependent relationship between the failure time and the observation time using the copula model and establishes a copula-based joint model. Existing research on dependent censored data has focused on cases where covariate effects take relatively simple forms, however, in practical studies, it has been observed that the effects of covariates are more complex. Consequently, this study assumes that the failure time follows an additive-multiplicative hazards model, which includes covariates with multiplicative effects as well as covariates with additive effects, providing greater flexibility. Additionally, we propose a penalized sieve maximum likelihood estimation method. Furthermore, a Newton Multiple Iteration (Newton-MI) algorithm, adept at handling parameter non-negativity constraints, is employed to estimate the model parameters. Extensive simulations validate the proposed method's favorable statistical properties. Finally, we apply the proposed model and methods to a tumor dataset.

This paper focuses on the estimation of partial functional linear model (PFLM) with right-censored response. Using functional principal component basis functions to approximate the unknown slope function, combined with inverse probability weighting, we can obtain the estimation of unknown coefficients by minimizing the weighted composite quantile loss function. A data-driven strategy is developed to select the optimal weight vector. Theoretical results establish the asymptotic normality of the parameter estimator and derive the optimal convergence rate for the slope function estimator. Further, simulation studies demonstrate that the proposed method is robust and outperforms the quantile regression and the least-squares in the presence of outliers or heavy-tailed errors. Finally, we apply the proposed methodology to the Alzheimer's Disease Neuroimaging Initiative (ADNI) data to illustrate its usefulness in practice.

This paper studies the pointwise estimation of copula density c under a censoring model. We use the wavelet method to construct a corresponding linear wavelet estimator with the new weight, and provide the risk bound for the pointwise error of the estimator on the Besov space B ∞ s . The results show that our convergence rate is optimal. Finally, the numerical results evaluate the feasibility and effectiveness of our proposed estimator.

Precision medicine aims to optimize treatment by identifying patient subgroups most likely to benefit from specific interventions. To support this goal, we introduce fkbma, an R package that implements a Bayesian model averaging approach with free-knot B-splines for identifying tailoring variables and treatment-sensitive subgroups. The package employs a reversible jump Markov chain Monte Carlo algorithm to flexibly model treatment effect heterogeneity while accounting for uncertainty in both variable selection and non-linear relationships. It provides a comprehensive framework for detecting predictive biomarkers and enabling robust subgroup identification in clinical trials and observational studies. This paper details the statistical methodology underlying fkbma, outlines its computational implementation, and demonstrates its application through simulated data examples. The flexibility of the package makes it a valuable tool for precision medicine research, offering a principled approach to treatment personalization.