A bootstrap test for single index models

• Autor(a) principal: Härdle, Wolfgang
• Data de Publicação: 2001
• Outros Autores: Mammen, Enno, Proença, Isabel
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.5/28082
• topic: Bootstrap; Kernel Estimate; Single Index Model Specification Test

Single index model are frequently used econometrics and biometrics. Logit and Probit models are special cases with fixed link functions. in this paper we consider a bootstrap specification test that detects nonparametric deviations of the link function. The bootstrap is used with the aim to find a more accurate distribution under the null than the normal approximation. We prove that the statistic and the statistic and its bootstrapped version have the same asymptotic distribution. In a simulation study we show that the bootstrap is able to capture the negative bias and the skewness of the test statistic. It yields better approximations to the true critical values and consequently it has accurate level than the normal approximation.