2008/08/06 by Alessandro De Gregorio, Stefano M. Iacus, De Gregorio, Alessandro +2
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Applications (stat.AP) #FOS: Computer and information sciences #FOS: Mathematics #Probability (math.PR) #Statistical Mechanics and Entropy #Statistical Methods and Inference #Statistics Theory (math.ST) #Stochastic processes and financial applications #math.PR #math.ST #stat.AP #stat.TH
paper · pdf · doi:10.48550/arxiv.0808.0853
arxiv created 2008/08/06 · openalex publication_date 2008/08/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we propose the use of ϕ-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process \de Xt = b(Xt, θ)\de t + σ(Xt, θ)\de Wt, from discrete observations \Xti, i=0, ..., n\ with ti = iΔn, i=0, 1, >..., n, under the asymptotic scheme Δn→0, nΔn→∞ and nΔn2→ 0. The class of ϕ-divergences is wide and includes several special members like Kullback-Leibler, Rényi, power and α-divergences. We derive the asymptotic distribution of the test statistics based on ϕ-divergences. The limiting law takes different forms depending on the regularity of ϕ. These convergence differ from the classical results for independent and identically distributed random variables. Numerical analysis is used to show the small sample properties of the test statistics in terms of estimated level and power of the test.