t-test for mixtures

[Xao Ping <xao_ping@yahoo.com>]

Dear All:

Many thanks to Tim Hesterberg for his immediate response.

I need to clarify some details in my initial formulation of the problem.

Yes, the number and sizes of sub-components, i.e., n1, n2,...are fixed and known and identical for samples X and Y.

 

The problem with using the permutation techniques is that, in the context of my research, the numbers n1, n2, ... are generally small,  and therefore the accuracies of the permutation p-values are inevitably poor.

 

Is there any way to derive the distribution of t-statistic (or something else) analytically for mixture of normals? I've tried but failed (so far). May be it is impossible.

 

Thanks

 

Xao  

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