Comparison of Four New General Classes of Search Designs

A factor screening experiment identifies a few important factors from a large list of factors that potentially influence the response. If a list consists of m factors each at three levels, a design is a subset of all possible 3 ^m runs. This paper considers the problem of finding designs with small numbers of runs, using the search linear model introduced in Srivastava (1975). The paper presents four new general classes of these 'search designs', each with 2 m −1 runs, which permit, at most, two important factors out of m factors to be searched for and identified. The paper compares the designs for 4 ≤ m ≤ 10, using arithmetic and geometric means of the determinants, traces and maximum characteristic roots of particular matrices. Two of the designs are found to be superior in all six criteria studied. The four designs are identical for m = 3 and this design is an optimal design in the class of all search designs under the six criteria. The four designs are also identical for m = 4 under some row and column permutations.     

Efficient designs based on orthogonal arrays of type I and type II for experiments using units ordered over time or space

For a wide variety of applications, experiments are based on units ordered over time or space. Models for these experiments generally may include one or more of: correlations, systematic trends, carryover effects and interference effects. Since the standard optimal block designs may not be efficient in these situations, orthogonal arrays of type I and type II, which were introduced in 1961 by C.R. Rao [Combinatorial arrangements analogous to orthogonal arrays, Sankhya A 23 (1961) 283–286], have been recently used to construct optimal and efficient designs for many of these experiments. Results in this area are unified and the salient features are outlined.     

Empirical Bayes estimation in finite population sampling under functional measurement error models

The paper considers simultaneous estimation of finite population means for several strata. A model-based approach is taken, where the covariates in the super-population model are subject to measurement errors. Empirical Bayes (EB) estimators of the strata means are developed and an asymptotic expression for the MSE of the EB estimators is provided. It is shown that the proposed EB estimators are “first order optimal” in the sense of Robbins [1956. An empirical Bayes approach to statistics. In: Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, University of California Press, Berkeley, pp. 157–164], while the regular EB estimators which ignore the measurement error are not.     

A Class of Efficient Non-parametric K-sample Tests for Multivariate Counting Processes with Frailties

A K -sample testing problem is studied for multivariate counting processes with time-dependent frailty. Asymptotic distributions and efficiency of a class of non-parametric test statistics are established for certain local alternatives. The concept of efficiency is to show that for every non-parametric test in this class, there is a parametric submodel for which the optimal test has the same asymptotic power as the non-parametric one. The theory is applied to analyse a diabetic retinopathy study data set. A simulation study is also presented to illustrate the theory     

Sensitivity of the Optimum to Perturbations of the Profit or Weight of an Item in the Binary Knapsack Problem

In the binary single constraint Knapsack Problem, denoted KP, we are given a knapsack of fixed capacity c and a set of n items. Each item j, j = 1,...,n, has an associated size or weight w_j and a profit p_j. The goal is to determine whether or not item j, j = 1,...,n, should be included in the knapsack. The objective is to maximize the total profit without exceeding the capacity c of the knapsack. In this paper, we study the sensitivity of the optimum of the KP to perturbations of either the profit or the weight of an item. We give approximate and exact interval limits for both cases (profit and weight) and propose several polynomial time algorithms able to reach these interval limits. The performance of the proposed algorithms are evaluated on a large number of problem instances.     

Estimating function method for product autoregressive models

The first-order product autoregressive (PAR(1)) model introduced by McKenzie in 1982 McKenzie, E. D. (1982). Product autoregression: A time series characterization of the gamma distribution. Journal of Applied Probability 19:463–468. [Google Scholar] did not attract the attention of practitioners due to the unavailability of a proper estimation method. This article proposes an estimating function (EF) method to fill the gap. In particular, we suggest an optimal combination of linear and quadratic EFs to overcome the problem of parameter identification. The procedure is applied to Weibull and Gamma PAR(1) models. Simulation and data analysis show that the proposed method performs better than the existing methods.     

Optimality Of Some Two-Stage Sampling Methods

Two-stage sampling plans in which the estimator is computed from the second sample only, and has a guaranteed precision irrespective of the parameter value, are considered. We prove the following optimality property for existing strategies in binomial and Poisson populations: there exists no other

strategy, of the same form, that guarantees the same precision, without increasing the expected sample size for some parameter valucs. The method of proof is illustrnted by proving a similar result for normal populations     

The ℓ1 oblique procrustes problem

In this paper, we reconsider the well-known oblique Procrustes problem where the usual least-squares objective function is replaced by a more robust discrepancy measure, based on the ₁ norm or smooth approximations of it.We propose two approaches to the solution of this problem. One approach is based on convex analysis and uses the structure of the problem to permit a solution to the ₁ norm problem. An alternative approach is to smooth the problem by working with smooth approximations to the ₁ norm, and this leads to a solution process based on the solution of ordinary differential equations on manifolds. The general weighted Procrustes problem (both orthogonal and oblique) can also be solved by the latter approach. Numerical examples to illustrate the algorithms which have been developed are reported and analyzed.     

Model Averaging for Prediction With Fragmentary Data

ABSTRACT

One main challenge for statistical prediction with data from multiple sources is that not all the associated covariate data are available for many sampled subjects. Consequently, we need new statistical methodology to handle this type of “fragmentary data” that has become more and more popular in recent years. In this article, we propose a novel method based on the frequentist model averaging that fits some candidate models using all available covariate data. The weights in model averaging are selected by delete-one cross-validation based on the data from complete cases. The optimality of the selected weights is rigorously proved under some conditions. The finite sample performance of the proposed method is confirmed by simulation studies. An example for personal income prediction based on real data from a leading e-community of wealth management in China is also presented for illustration.     

E-optimal designs for three treatments

E-optimality is studied for three treatments in an arbitrary n-way heterogeneity setting. In some cases maximal trace designs cannot be E-optimal. When there is more than one E-optimal design for a given setting, the best with respect to all reasonable criteria is determined.