Some hypothesis tests based on random projection

Two new non-parametric tests are proposed based on continuous one-dimensional random projections. The first one addresses central symmetry and the second addresses independence. These tests are implemented for finite and infinite dimensional (functional) data sets. Both tests are distribution-free and universally consistent. Additionally, different techniques are proposed to improve the power of the tests. Promising results have been obtained by comparing the new tests with existing ones using simulation study. Real data in Banach spaces have been used to develop an application.

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