
Minimax Nonparametric Parallelism Test
Testing the hypothesis of parallelism is a fundamental statistical probl...
read it

Hypothesis Testing For Densities and HighDimensional Multinomials: Sharp Local Minimax Rates
We consider the goodnessoffit testing problem of distinguishing whethe...
read it

Kernel based method for the ksample problem
In this paper we deal with the problem of testing for the equality of k ...
read it

WaldKernel: Learning to Aggregate Information for Sequential Inference
Sequential hypothesis testing is a desirable decision making strategy in...
read it

Adaptive minimax testing in inverse Gaussian sequence space models
In the inverse Gaussian sequence space model with additional noisy obser...
read it

Kernel density decomposition with an application to the social cost of carbon
A kernel density is an aggregate of kernel functions, which are itself d...
read it

Local minimax rates for closeness testing of discrete distributions
We consider the closeness testing (or twosample testing) problem in the...
read it
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.
READ FULL TEXT
Comments
There are no comments yet.