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

[gcafiso <gcafiso@unict.it>]

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

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