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We study the optimal design problem under second-order least squares estimation which is known to outperform ordinary least squares estimation when the error distribution is asymmetric. First, a general approximate theory is developed, taking due cognizance of the nonlinearity of the underlying information matrix in the design measure. This yields necessary and sufficient conditions that a D- or A-optimal design measure must satisfy. The results are then applied to find optimal design measures when the design points are binary. The issue of reducing the support size of the optimal design measure is also addressed.

In some socio-economic surveys, data are collected on sensitive or stigmatizing issues such as tax evasion, criminal conviction, drug use, etc. In such surveys, direct questioning of respondents is not of much use and the randomized response technique is used instead. A few researchers have studied the issue of privacy protection or respondent jeopardy for surveys on dichotomous populations, where the objective is to estimate the proportion of persons bearing the sensitive trait. However, not much is yet known about respondent protection when the variable under study takes discrete numerical values and the objective of the survey is to estimate the population mean of this variable. In this article we study this issue. We first propose a randomization device for this situation and give the corresponding estimation procedure. We next propose a measure of privacy and show that given a certain stipulated level of this privacy measure, we can determine the parameter of the randomization device so as to maximize the efficiency of estimation, while guaranteeing the desired level of privacy protection. In particular, our study also covers the case of polychotomous populations and we can estimate the proportions of individuals belonging to the different classes. Consequently, results for dichotomous populations follow as corollaries., Comment: 12 pages

Key predistribution schemes for distributed sensor networks have received significant attention in the recent literature. In this paper we propose a new construction method for these schemes based on combinations of duals of standard block designs. Our method is a broad spectrum one which works for any intersection threshold. By varying the initial designs, we can generate various schemes and this makes the method quite flexible. We also obtain explicit algebraic expressions for the metrics for local connectivity and resiliency. These schemes are quite efficient with regard to connectivity and resiliency and at the same time they allow a straightforward shared-key discovery., Comment: Indian Statistical Institute Kolkata Tech., November 10, 2010 (Revised version)

We propose a new scheme for sharing symmetric key operations among a set of participants according to a (t,n) threshold access structure. We focus on anonymity properties of this scheme and show that this scheme provides improved values of anonymity measures than the existing ones. In particular, the scheme can provide optimal and equitable participant anonymity when it is based on balanced perfect hash families.

Anti-collusion digital fingerprinting codes have been of significant current interest in the context of deterring unauthorized use of multimedia content by a coalition of users. In this article, partially cover-free families of sets are considered and these are employed to obtain such codes. Compared to the existing methods of construction, our methods ensure gains in terms of accommodating more users and/or reducing the number of basis vectors.

We show that the balanced crossover designs given by Patterson [Biometrika 39 (1952) 32--48] are (a) universally optimal (UO) for the joint estimation of direct and residual effects when the competing class is the class of connected binary designs and (b) UO for the estimation of direct (residual) effects when the competing class of designs is the class of connected designs (which includes the connected binary designs) in which no treatment is given to the same subject in consecutive periods. In both results, the formulation of UO is as given by Shah and Sinha [Unpublished manuscript (2002)]. Further, we introduce a functional of practical interest, involving both direct and residual effects, and establish (c) optimality of Patterson's designs with respect to this functional when the class of competing designs is as in (b) above., Comment: Published at http://dx.doi.org/10.1214/009053605000000723 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)