Mei-Mei Zen

Criterion-robust optimal designs for model discrimination and parameter estimation in Fourier regression models

Abstract Consider the problem of discriminating between two competitive Fourier regression on the circle [−π,π] and estimating parameters in the models. To find designs which are efficient for both model discrimination and parameter estimation, Zen and Tsai (some criterion-robust optimal designs for the dual problem of model discrimination and parameter estimation, Indian J. Statist. 64, 322–338) proposed a multiple-objective optimality criterion for polynomial regression models. In this work, taking the same Mγ-criterion, which puts weight γ (0⩽γ⩽1) for model discrimination and 1−γ for parameter estimation, and using the techniques of projection design, the corresponding Mγ-optimal design for Fourier regression models is explicitly derived in terms of canonical moments. The behavior of the Mγ-optimal designs is investigated under different weighted selection criterion. And the extreme value of the minimum Mγ-efficiency of any Mγ′-optimal design is obtained at γ′=γ ∗ , which results in the M γ ∗ -optimal design to be served as a criterion-robust optimal design for the problem.

More powerful tests for the sign testing problem about gamma scale parameters

For i=1, … , p, let denote independent random samples from gamma distributions with unknown scale parameters θi and known shape parameters ηi. Consider testing H0:θi≤θi0 for some i=1, … , p versus H1:θi>θi0 for all i=1, … , p, where θ10, … , θp0 are fixed constants. For any 0<α<0.4, we construct two new tests that have the same size as the likelihood ratio test (LRT) and are uniformly more powerful than it. Power comparisons of our tests with other tests are given. The proposed tests are intersection–union tests. We apply the results to test the variances of normal distributions and scale parameters of two-parameter exponential distributions. Finally, we illustrate our proposed tests with an example.

A Note on Criterion-Robust Optimal Designs for Model Discrimination and Parameter Estimation in Polynomial Regression Models

Consider the problem of discriminating between the polynomial regression models on [−1, 1] and estimating parameters in the models. Zen and Tsai (2002) proposed a multiple-objective optimality criterion, M γ-criterion, which uses weight γ (0 ≤ γ ≤ 1) for model discrimination and α = β = (1 − γ)/2 for parameter estimation in each model. In this article, we generalize it to a wider setup with different values of α and β. For instance, α = 2 β suggests that the “smaller” model is more likely to be the true model. Using similar techniques, the corresponding criterion-robust optimal design is investigated. A study for the original criterion-robust optimal design with α = β, through M-efficiency, shows that it is good enough for any wider setup.

Bayesian Analysis of a change-point Poisson Process

For a Poisson process with a change-point, a uniform prior is commonly used for the change-point, but it is more realistic to put a unimodal prior on it, which outlines an important feature of prior beliefs. We consider a couple of unimodal priors on the change-point first and use ML-II approach to obtain the empirical Bayes estimators in this paper. The Bayes factor is used for the selection of a suitable prior. The procedure is applied to the British coal-mining disaster data. Finally, a comparison among these empirical Bayes estimators is made by Monte Carlo integration. It turns out that the ML-II Beta prior fit the data most, which corresponds to the prior belief of unimodality.

A note on estimating the number of superimposed exponential signals by the cross-validation approach

In this paper, a procedure based on the delete-1 cross-validation is given for estimating the number of superimposed exponential signals, its limiting behavior is explored and it is shown that the probability of overestimating the true number of signals is greater than a positive constant for sufficiently large samples. Also a general procedure based on the cross-validation is presented when the deletion proceeds according to a collection of subsets of indices. The result is similar to the delete-1 cross-validation if the number of deletions is fixed. The simulation results are provided for the performance of the procedure when the collections of subsets of indices are chosen as those suggested by Shao [1]in a linear model selection problem.