Conference Agenda

We propose a statistical methodology for anomaly detection in nonstationary EEG time series using adaptive sequential hypothesis testing. Wavelet-based time-frequency decompositions capture localized spectral variations, while abrupt deviations are identified using Cumulative Sum (CUSUM) statistics. To control false discoveries in high-dimensional comparisons, we employ an adaptive multiple testing correction that adjusts to data-driven null distributions. This approach ensures statistically rigorous detection of shifts in time-dependent signals while accommodating dynamic changes in EEG data.

This study presents a novel exact distributional representation for the product of two normal random variables, utilizing the non-central chi-square distribution. It demonstrates that the product of two normal variables exhibits the same distributional properties as the difference of two non-central chi-square random variables, under specific parameterizations. Through rigorous simulations across a variety of scenarios, the accuracy and robustness of this method are validated. The results show that the proposed approach surpasses traditional methods, which often rely on approximations or computationally expensive numerical integration. By offering a more precise and computationally efficient solution, this method is particularly valuable for applications in fields such as finance, econometrics, and risk management, where multiplicative effects are critical. The approach eliminates the need for complex infinite series or special functions, significantly reducing computation time while enhancing accuracy. This breakthrough opens new avenues for both theoretical developments and practical applications, providing a powerful tool for analyzing the product of normal random variables. The paper concludes by exploring potential extensions and implications for future research in various scientific and engineering disciplines.

In this talk, we examine Stress-Strength models where the random variables follow a Dagum distribution, with data subject to an adaptive Type-II progressively hybrid censoring scheme. This flexible censoring approach presents unique challenges for statistical analysis. We derive the maximum likelihood estimators and construct both asymptotic and bootstrap confidence intervals. The proposed procedure is evaluated through extensive Monte Carlo simulations, and a real dataset is analyzed for illustration.