Weak Convergence of Processes Related to Likelihood Ratios
The Annals of Statistics · 1977 · Volume 5 · Issue 2
Abstract
Material in Chapter VI of Hajek and Sidak's book is extended to a sequential analysis setting: conditions are given under which a sequence of log-likelihood-ratio processes (log-likelihood-ratios for sequential sampling, represented as jump processes in continuous time) converges weakly to a Wiener process with drift, the drift parameter depending on which hypothesis, in a suitable neighborhood of a null hypothesis, prevails. Conditions for convergence of other "test statistic" processes, related to likelihood ratios, are also given. Asymptotic sequential tests can thereby be constructed. Some "two-sample problem" examples are treated.
Keywords
60F05, 62E20, 62L10, Le Cam's lemmas, likelihood ratios, sequential analysis, Sign test, two-sample problem, weak convergence
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