Year: 2025
Type: article
Abstract: 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 $$\mathcal {G}=\{ G(\varvec{\theta }): \varvec{\theta } \in \Theta \}$$ G = { G ( θ ) : θ ∈ Θ } , we consider the testing problem $$ H_0: \Vert F - G(\varvec{\theta }_F) \Vert _p \ge \epsilon \quad \text {vs} \quad H_1: \Vert F - G(\varvec{\theta }_F) \Vert _p < \epsilon , $$ H 0 : ‖ F - G ( θ F ) ‖ p ≥ ϵ vs H 1 : ‖ F - G ( θ F ) ‖ p < ϵ , where $$\epsilon >0$$ ϵ > 0 is a margin of error and $$G(\varvec{\theta }_F)$$ G ( θ F ) denotes a representative of F within the parametric class. The approximate model is determined via an M-estimator of the parameters. The methodology also quantifies the percentage improvement of the proposed model relative to a non-informative (constant) benchmark. The test statistic is the $$\textrm{L}^p$$ L p -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.
Source: Statistics and Computing
Authors: Amparo Baíllo, Javier Cárcamo
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,890
OpenAlex ID: W4415747912