Empirical results demonstrate the ability of the proposed tests to adapt to the unknown hardness of the problem instance. As an example, assume we are testing a sequence of numbers against Benfords. 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. There are tools to test continuous distributions, such as normality tests. 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. by assuming a distribution for the effect size under the alternative hypothesis. 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. article, we propose a sequential probability ratio test that combines. For a multinomial distribution, the parameters are the proportions of occurrence of each outcome. ![]() A hypothesis test formally tests if the population parameters are different from the hypothesized values. 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. Multinomial distribution parameters hypothesis test. 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. In the experimental setup belonging to the test, n items fall into k categories with certain probabilities (sample size n with k categories). It is tested if a given observation is likely to have occurred under the assumption of an ab-initio model. Batch tests run the risk of allocating too many (resp. The Exact Multinomial Test is a Goodness-of-fit test for discrete multivariate data. The empirical work in this volume employs the multinomial logit model and, occasionally, variants of this model-the maximum model and the sequential logit model. 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.
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