Convergence rates for empirical Bayes tests for the shape parameter of Lomax distribution family

Abstract

In this paper, the empirical Bayes (EB) test problem for the shape parameter of the Lomax distribution family is investigated. By using the recursive kernel estimation of the density function and monotonicity, the empirical Bayes test functions are constructed. Under suitable conditions, the convergence rates of the EB tests are obtained. The convergence rates can be arbitrarily close to O(n^{-1}). Finally, an example is given to verify that prior distributions satisfying the conditions of the theorem exist.

Keywords

Lomax distribution family / empirical Bayes tests / recursive kernel estimation / monotone Bayes tests / convergence rates

References

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