Grade estimation of chi-square divergence

Abstract

For F₁, F₂ being distribution functions such that F₂ is absolutely continuous w.r.t. F₁ and F₁ is continuous, the chi-square divergence between F₂ and F₁ equal to is considered. Its estimator based on the modified kernel estimate of the grade density g is introduced. Asymptotic normality of is established, asymptotic variance turns out to be larger than for the estimator of χ² in the case when the i.i.d. sample from g is observable. Finally, choice of smoothing parameter is discussed based on calculation of the asymptotic mean square error for some approximation of χ².

Keywords:

• asymptotic mean square error
• bandwidth
• chi-square divergence
• grade density
• modified kernel estimate
• separation measure