A two-stage rank test using density estimation

A Two-stage Rank Test Using Density Estimation

For the one-sample problem, a two-stage rank test is derived which realizes a required power against a given local alternative, for all sufficiently smooth underlying distributions. This is achieved using asymptotic expansions resulting in a precision of order m-~, where m is the size of the first sample. The size of the second sample is derived through a number of estimators of e.g. integrated...

Two-stage estimation using copula function

‎Maximum likelihood estimation of multivariate distributions needs solving a optimization problem with large dimentions (to the number of unknown parameters) but two‎- ‎stage estimation divides this problem to several simple optimizations‎. ‎It saves significant amount of computational time‎. ‎Two methods are investigated for estimation consistency check‎. ‎We revisit Sankaran and Nair's bivari...

Two Stage Rank Estimation of Quantile Index Models

This paper estimates a class of models which satisfy a monotonicity condition on the conditional quantile function of the response variable. This class includes as a special case the monotonic transformation model with the error term satisfying a conditional quantile restriction, thus allowing for very general forms of conditional heteroscedasticity. Furthermore, the monotonicity condition enab...

A Pooled Two-Sample Median Test Based on Density Estimation

Optimal estimation of low rank density matrices

The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system. The goal of the paper is to develop minimax lower bounds on error rates of estimation of low rank density matrices in trace regression models used in quantum state tomography (in particular, in the case of Pauli measurements) with explicit dependence of the bounds on t...