Statistics are derived for testing a sequence of observations from an exponential-type distribution for no change in parameter against possible two-sided alternatives involving parameter changes at unknown points. The test statistic can be chosen to have high power against certain of a variety of alternatives. Conditions on functionals on $C\lbrack 0,1\rbrack$ are given under which one can assert that the large sample distribution of the test statistic under the null-hypothesis or an alternative from a range of interesting hypotheses is that of a functional on Brownian Motion. We compute and tabulate distributions for functionals defined by nonnegative weight functions of the form $\psi(s) = as^k, k > -2$. The functionals for $-1 \geqq k > -2$ are not continuous in the uniform topology on $C\lbrack 0, 1\rbrack$.
@article{1176342816,
author = {MacNeill, Ian B.},
title = {Tests for Change of Parameter at Unknown Times and Distributions of Some Related Functionals on Brownian Motion},
journal = {Ann. Statist.},
volume = {2},
number = {1},
year = {1974},
pages = { 950-962},
language = {en},
url = {http://dml.mathdoc.fr/item/1176342816}
}
MacNeill, Ian B. Tests for Change of Parameter at Unknown Times and Distributions of Some Related Functionals on Brownian Motion. Ann. Statist., Tome 2 (1974) no. 1, pp. 950-962. http://gdmltest.u-ga.fr/item/1176342816/