Applied Mathematics and Statistics Seminar by Milan Stehlik: Exact Distributions of LR Tests and their Applications in Statistical Inference for Small Sample Sizes

Speaker: Milan Stehlik, Institute of Statistics, University of Valparaíso, Chile; Data Science and AI, Universidad Andrés Bello, Chile

 

Title: Exact Distributions of LR Tests and their Applications in Statistical Inference for Small Sample Sizes

 

Abstract: Asymptotic large-sample paradigms frequently fail in modern translational, biostatistical, and ecological applications where experimental datasets are inherently small yet high-dimensional. This talk addresses the dual challenges of constructing reliable parametric and nonparametric models, and executing exact statistical tests under severe sample-size constraints and data irregularities such as censoring or truncation. We introduce exact likelihood ratio tests within the exponential family and for the generalized gamma distribution, characterizing their underlying properties. Furthermore, we derive general forms of distributions for exact likelihood ratio testing of homogeneity and scale. The practical utility of this methodology is illustrated through various applications and examples, including mixtures, missing data, and censored data. Finally, we explore the geometry of lifetime data in relation to I-divergence decomposition, discuss small-sample frailty testing via homogeneity tests, and provide a framework for exact and robust normality testing.