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From |
Gianluca Cafiso <gcafiso@unict.it> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: bootstrap test, combined bootstrap datasets, statistical properties of the bootstrap |

Date |
Fri, 11 Jun 2010 13:47:57 +0200 |

Dear Stas, sorry for this very late answer, but the e-mail server which I use for statalist stopped working for a while. My doubt regards which Critical Values I should use to test Ho:'df_L >0'. Where: 1- df_Lb = df_TFb * df_GCb; 2- the distribution of df_L is generated as the product of the bootstrap distribution of df_TF times the bootstrap distribution of df_GC. If I want to test this hypothesis for either df_TF or df_GC, the ?Bias ?Corrected and Accelerated Confidence Interval? (BCa-CI) is reliable when the bootstrap distribution is not normal. Then, if the upper-limit of the BCa-CI (95% quantile) were less than 0, I would reject Ho: df_TF>0 (or df_GC). I wonder whether I can use the BCa-CI even for df_L. I am not sure about this since its distribution is not generated in a bootstrap process, but it is the ex-post product of two different bootstrap distributions. I am worried about the robustness of the BCa-CI with respect to this case. Furthermore, I am not sure that I am able to use the BCa-CI to test the hypothesis. Indeed, I do not believe that the acceleration for df_L is given by the product of the accelerations of df_TF and df_GC. ______________ As for the points that you listed in your reply: 1 &2 ? Strictly speaking, I am not dealing with time series. ?diff? is to test the difference between the same population taken at two different times. 3 ? Yes, I do not have a point null. But why should this be problematic? Is the percentile method or the BCa-CI for hypothesis testing restricted to the case of a point null? I didn?t find anything about this in the literature. My null refers to zero and I check how the bootstrap distribution is positioned with respect to zero. I do not understand why you mention an asymptotic test. As far as I know, the all point of the bootstrap is to exploit the bootstrap distribution without resort to asymptotic theory. However, I am not a statistician. Let me know if I am missing something. These considerations are drawn from Cameron + Trivedi 2005 ??Microeconometrics?, paragraph 11.2.6, 11.2.7. Many thanks. Gianluca ___________________________________________________________ Dr. Gianluca Cafiso Research Fellow, University of Catania - Economics Department. Corso Italia 55, 95129 Catania, Italy. e-mail: gcafiso@unict.it tel.: +39 095 7537 745 ---------------------------------------------------------------- Universita' di Catania - A.P.Se.Ma. Servizio di Posta Elettronica * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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