Nested Group Testing Procedure

We investigated the false-negative,true-negative,false-positive,and true-positive predictive values from a general group testing procedure for a heterogeneous population.We show that its false(true)-negative predictive value of a specimen is larger(smaller),and the false(true)-positive predictive value is smaller(larger)than that from individual testing procedure,where the former is in aversion.Then we propose a nested group testing procedure,and show that it can keep the sterling characteristics and also improve the false-negative predictive values for a specimen,not larger than that from individual testing.These characteristics are studied from both theoretical and numerical points of view.The nested group testing procedure is better than individual testing on both false-positive and false-negative predictive values,while retains the efficiency as a basic characteristic of a group testing procedure.Applications to Dorfman’s,Halving and Sterrett procedures are discussed.Results from extensive simulation studies and an application to malaria infection in microscopy-negative Malawian women exemplify the findings.

Estimation of partial derivative functionals with application to human mortality data analysis

To better describe and understand the time dynamics in functional data analysis,it is often desirable to recover the partial derivatives of the random surface.A novel approach is proposed based on marginal functional principal component analysis to derive the representation for partial derivatives.To obtain the Karhunen-Lo`eve expansion of the partial derivatives,an adaptive estimation is explored.Asymptotic results of the proposed estimates are established.Simulation studies show that the proposed methods perform well in finite samples.Application to the human mortality data reveals informative time dynamics in mortality rates.

Robust inference in linear mixed model with skew normal-symmetric error

Linear mixed effects models with general skew normal-symmetric （SNS） error are considered and several properties of the SNS distributions are obtained. Under the SNS settings, ANOVA-type estimates of variance components in the model are unbiased, the ANOVA-type F-tests are exact F-tests in SNS setting, and the exact confidence intervals for fixed effects are constructed. Also the power of ANOVA-type F-tests for components are free of the skewing function if the random effects normally distributed. For illustration of the main results, simulation studies on the robustness of the models are given by comparisons of multivariate skew-normal, multivariate skew normal-Laplace, multivariate skew normal-uniform, multivariate skew normal-symmetric, and multivariate normal distributed errors. A real example is provided for the illustration of the proposed method.