
Minimax Nonparametric Parallelism Test
Testing the hypothesis of parallelism is a fundamental statistical probl...
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Hypothesis Testing For Densities and HighDimensional Multinomials: Sharp Local Minimax Rates
We consider the goodnessoffit testing problem of distinguishing whethe...
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Kernel based method for the ksample problem
In this paper we deal with the problem of testing for the equality of k ...
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On uniform consistency of nonparametric tests II
For Kolmogorov test we find natural conditions of uniform consistency of...
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WaldKernel: Learning to Aggregate Information for Sequential Inference
Sequential hypothesis testing is a desirable decision making strategy in...
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Classification Logit Twosample Testing by Neural Networks
The recent success of generative adversarial networks and variational le...
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Efficient twosample functional estimation and the superoracle phenomenon
We consider the estimation of twosample integral functionals, of the ty...
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Minimax Nonparametric Twosample Test
We consider the problem of comparing probability densities between two groups. To model the complex pattern of the underlying densities, we formulate the problem as a nonparametric density hypothesis testing problem. The major difficulty is that conventional tests may fail to distinguish the alternative from the null hypothesis under the controlled type I error. In this paper, we model logtransformed densities in a tensor product reproducing kernel Hilbert space (RKHS) and propose a probabilistic decomposition of this space. Under such a decomposition, we quantify the difference of the densities between two groups by the component norm in the probabilistic decomposition. Based on the Bernstein width, a sharp minimax lower bound of the distinguishable rate is established for the nonparametric twosample test. We then propose a penalized likelihood ratio (PLR) test possessing the Wilks' phenomenon with an asymptotically Chisquare distributed test statistic and achieving the established minimax testing rate. Simulations and real applications demonstrate that the proposed test outperforms the conventional approaches under various scenarios.
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