Kolmogorov-Smirnov test for nested alternatives?

["Bill Shipley" <bill.shipley@usherbrooke.ca>]

Hello.  The Kolmogorov-Smirnov test in S-PLUS allows one to test for a significant deviation of an empirical distribution from a predicted distribution.  Consider a case where one has a series of nested alternative predicted distributions - alternative exponential distributions with increasing numbers of estimated parameters:

 

p(i) =(1/Z)exp(-lamda0 -lambda1*t_i1-lamda2*t_i2...)  where Z is a normalization constant and t_i1 etc are attributes of each group i and the lamda coefficients are estimated from the empirical data.

 

I would like to conduct a series of sequential tests in which

(I)

 I compare an empirical distribution of proportions over a set of groups to the predicted distributions assuming (1) all lamda values greater than 0 (i.e. lamda1, lamda 2 etc.) are zero; (2)all lamda values greater that 1 (i.e. lamda2, lamda3 etc.) are zero

 

(II) Compare the improvement in fit as I increase the number of lamda values that are freely estimated in order to detect non-significant improvement in fit.

 

Is it possible to do step (ii) using a Kolmogorov-Smirnov procedure? 

Bill Shipley