2024/10/28 by Amparo Baı́llo, Javier Cárcamo, Baíllo, Amparo +1
Decision Sciences · #62F40 #62G10 #62G20 #Applications (stat.AP) #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Risk and Safety Analysis #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2410.20918
openalex publication_date 2024/10/28 · openalex created_date 2024/11/14 · openalex updated_date 2026/07/30
We introduce the almost goodness-of-fit test, a procedure to assess whether a (parametric) model provides a good representation of the probability distribution generating the observed sample. Specifically, given a distribution function F and a parametric family G=\ G(\boldsymbolθ) : \boldsymbolθ ∈ Θ\, we consider the testing problem H0: ‖ F - G(\boldsymbolθF) ‖p ≥ ε vs H1: ‖ F - G(\boldsymbolθF) ‖p lt; ε, where ε>0 is a margin of error and G(\boldsymbolθF) denotes a representative of F within the parametric class. The approximate model is determined via an M-estimator of the parameters. %The objective is the approximate validation of a distribution or an entire parametric family up to a pre-specified threshold value. The methodology also quantifies the percentage improvement of the proposed model relative to a non-informative (constant) benchmark. The test statistic is the Lp-distance between the empirical distribution function and that of the estimated model. We present two consistent, easy-to-implement, and flexible bootstrap schemes to carry out the test. The performance of the proposal is illustrated through simulation studies and analysis and real-data applications.