Asymptotic rate of discrimination of random processes. (English) Zbl 0701.62093
Asymptotic statistics, 4th Prague Symp., Prague/Czech. 1988, 101-109 (1989).
Summary: [For the entire collection see Zbl 0692.00015.]
We evaluate the Rényi distance of discrete time random processes with the same covariance structure, in particular of autoregressive processes with different means. This distance is applied in evaluating the asymptotics of tests of simple hypotheses about such processes. We present a generalized theorem of Stein concerning the second kind error of most powerful tests of level \(0<\alpha <1\) and a generalized theorem of Chernoff concerning the mixed error of Bayes tests with arbitrary prior weight.
We evaluate the Rényi distance of discrete time random processes with the same covariance structure, in particular of autoregressive processes with different means. This distance is applied in evaluating the asymptotics of tests of simple hypotheses about such processes. We present a generalized theorem of Stein concerning the second kind error of most powerful tests of level \(0<\alpha <1\) and a generalized theorem of Chernoff concerning the mixed error of Bayes tests with arbitrary prior weight.
MSC:
| 62M99 | Inference from stochastic processes |
| 62F05 | Asymptotic properties of parametric tests |
| 62B10 | Statistical aspects of information-theoretic topics |
| 62M07 | Non-Markovian processes: hypothesis testing |
