Edgeworth expansions for nonparametric distribution estimation with applications

✍ Scribed by Pilar H. García-Soidán; Wenceslao González-Manteiga; JoséM. Prada-Sánchez

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 963 KB
• Volume: 65
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(97)00059-1

✦ Synopsis

In this paper, we will investigate thc nonparametric estimation of the distribution function F of an absolutely continuous random variable. Two methods are analyzed: the first one based on the empirical distribution function, expressed in terms of i.i.d, lattice random variables and, secondly, the kernel method, which inw)lves nonlattice random vectors dependent on the sample size n; this latter procedure produces a smooth distribution estimator that will be explicitly corrected to reduce the effect of bias or variance. For both methods, the non-Studentized and Studentized statistics are considered as well as their bootstrap counterparts and asymptotic expansions are constructed to approximate their distribution functions via the Edgeworth expansion techniques. On this basis, we will obtain confidence intervals for F(xl and state the coverage error order achieved in each case. ( 1997 Elsevier Science B.V.