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We instantiate the above strategy for several commonly used distance measures to obtain sequential versions of Kolmogorov-Smirnov (KS) test, $\chi^2$-test and kernel-MMD test. We propose a general strategy for selecting these payoff functions as predictable estimates of the witness function associated with the variational representations of certain statistical distance measures. Within this framework, we show that designing consistent tests can be transformed into the task of selecting payoff functions that result in high growth rate of the wealth of the bettor in the repeated betting game. Our design strategy builds upon the principle of testing-by-betting, which, in the context of hypothesis testing, establishes the equivalence between gathering evidence against the null, and multiplying an initial wealth by a large factor by repeatedly betting on the observations with payoff functions bought for their expected value under the null. Our work addresses both of these issues by proposing a general framework for designing consistent level $\alpha$ sequential nonparametric two-sample (as well as one-sample) tests. harder) problem instances, whereas the strong parametric assumptions are often not satisfied in many practical tasks, thus limiting the applicability of parametric sequential tests. Mathematically, we have k possible mutually exclusive outcomes, with corresponding probabilities p1.
#Sequential testing multinomial distributiuon trial
The null hypothesis states that the proportions equal the hypothesized values, against the alternative hypothesis that at least one of the proportions is not equal to its hypothesized value. The multinomial distribution models the outcome of n experiments, where the outcome of each trial has a categorical distribution, such as rolling a k -sided dice n times. For a multinomial distribution, the parameters are the proportions of occurrence of each outcome. As the number of reads increases, the distribution of the T statistic converges to a Chi-square with degrees of freedom equal to (P-1)(K-1), when the number of. Sequential tests on a multinomial distribution and a Markov chain, Stochastic Processes and their Applications 6, 17. MATH Article MathSciNet Google Scholar Weiss, L. A hypothesis test formally tests if the population parameters are different from the hypothesized values. A sequential test of the equality of probabilities in a multinomial distribution, Journal of the American Statistical Association 57, 769774. Batch tests run the risk of allocating too many (resp. Multinomial distribution parameters hypothesis test. Most of the prior works (with some exceptions) have studied this problem either in the batch setting (or the fixed-sample size setting) or in a sequential but parametric setting. Two-sample testing, also known as homogeneity testing, is a fundamental problem in statistics, where the goal is to decide whether two independent samples are drawn from the same distribution or not.