Work and breastfeeding decisions are jointly determined for higher socioeconomic status US mothers

We study postpartum decisions about paid work and breastfeeding using a simultaneous equations model. For our sample of higher socioeconomic status mothers, we find a joint decision process for three sets of decisions modeled: work leave duration and duration of any, as well as of exclusive, breastfeeding, and daily work hours and daily breastfeedings at infant age 3 months. We find that returning to paid work 1 week earlier reduces any breastfeeding duration by about two-thirds of a week while extending breastfeeding by a week delays work participation by about one-third of a week. We find larger elasticities for decisions involving daily work hours and number of breastfeedings at 3 months than for work leave duration and any breastfeeding duration and the smallest elasticities for duration of exclusive breastfeeding and work leave. This marks the first study to find a joint decision-making process for postpartum work and breastfeeding decisions and suggests that, in addition to increased leave impacting breastfeeding behaviors, successful breastfeeding promotion policies can have nontrivial impacts on the US labor market.     

Optimum covariate designs in partially balanced incomplete block (PBIB) design set-ups

The use of covariates in block designs is necessary when the covariates cannot be controlled like the blocking factor in the experiment. In this paper, we consider the situation where there is some flexibility for selection in the values of the covariates. The choice of values of the covariates for a given block design attaining minimum variance for estimation of each of the parameters has attracted attention in recent times. Optimum covariate designs in simple set-ups such as completely randomised design (CRD), randomised block design (RBD) and some series of balanced incomplete block design (BIBD) have already been considered. In this paper, optimum covariate designs have been considered for the more complex set-ups of different partially balanced incomplete block (PBIB) designs, which are popular among practitioners. The optimum covariate designs depend much on the methods of construction of the basic PBIB designs. Different combinatorial arrangements and tools such as orthogonal arrays, Hadamard matrices and different kinds of products of matrices viz. Khatri–Rao product, Kronecker product have been conveniently used to construct optimum covariate designs with as many covariates as possible.     

Cell-to-switch level planning in mobile wireless networks for efficient management of radio resources

A major step in effectively managing radio resources in a cellular network is to design an appropriate scheme for assigning cells to a location area (LA), serviced by a switch, and allocate resources for individual switches. However, this assignment is already proven in the literature to be an NP-hard problem [Merchant A, Sengupta B. Assignment of cells to switches in PCS networks. IEEE/ACM Transactions on Networking 3(5) (1995) 521–6] that requires efficient heuristic search techniques for obtaining real-time solutions. This work presents a state-space search technique, which is a variant of best first search heuristic technique. The algorithm called the block depth first search (BDFS), allocates cells to switches during switch level resource planning. Under various simulated performance criteria, we compare the performance of the proposed technique with other similar procedures in the literature. Our results indicate that the BDFS outperforms the meta-heuristic procedures in terms of both efficiency and quality of solutions. Hence, we conclude that our proposed technique can be effectively used for switch level planning leading to an efficient management of scarce radio resource in cellular networks.     

Optimum designs for parameter estimation in a mixture experiment with two correlated responses

In this paper, we investigate a mixture problem with two responses, which are functions of the mixing proportions, and are correlated with known dispersion matrix. We obtain D- and A-optimal designs for estimating the parameters of the response functions, when none or some of the regression coefficients of the two functions are the same. It is shown that when no prior knowledge about the regression coefficients is available, the D-optimal design is independent of the dispersion matrix, while the A-optimal design depends on it, provided the response functions are of different degree. On the other hand, when some of the regression coefficients are known to be the same for both the functions, the D-optimal design depends on the dispersion matrix when the two response functions are not of the same degree.     

Combinatorial Equivalence of Fractional Factorial Designs

Two symmetrical fractional factorial designs are said to be combinatorially equivalent if one design can be obtained from another by reordering the runs, relabeling the factors and relabeling the levels of one or more factors. This article presents concepts of ordered distance frequency matrix, distance frequency vector, and reduced distance frequency vector for a design. Necessary conditions for two designs to be combinatorial equivalent based on these concepts are presented. A new algorithm based on the results obtained is proposed to check combinatorial non-equivalence of two factorial designs and several illustrating examples are provided.     

Optimum mixture designs in a restricted region

In a mixture experiment, the response depends on the proportions of the mixing components. Canonical models of different degrees and also other models have been suggested to represent the mean response. Optimum designs for estimation of the parameters of the models have been investigated by different authors. In most cases, the optimum design includes the vertex points of the simplex as support points of the design, which are not mixture combinations in the true non-trivial sense. In this paper, optimum designs have been obtained when the experimental region is an ellipsoidal subspace of the entire factor space which does not cover the vertex points of the simplex.     

IPPS Sampling Plans Excluding Adjacent Units

The concept of inclusion probability proportional to size sampling plans excluding adjacent units separated by at most a distance of m (≥ 1) units {IPPSEA plans} is introduced. IPPSEA plans ensure that the first-order inclusion probabilities of units are proportional to size measures of the units, while the second-order inclusion probabilities are zero for pairs of adjacent units separated by a distance of m units or less. IPPSEA plans have been obtained by making use of binary, proper, and unequireplicated block designs and linear programing approach. The performance of IPPSEA plans using Horvitz–Thompson estimator of population total has been compared with existing sampling plans such as simple random sampling without replacement (SRSWOR), balanced sampling plans excluding adjacent units {BSA (m) plans}, probability proportional to size with replacement, Hartley and Rao's plan (1962 Hartley , H. O. , Rao , J. N. K. ( 1962 ). Sampling with unequal probabilities and without replacement . Ann. Math. Statist. 33 : 350 – 374 .[Crossref] , [Google Scholar]), Rao et al.'s strategy (1962 Rao , J. N. K. , Hartley , H. O. , Cochran , W. G. ( 1962 ). On a simple procedure of unequal probability sampling without replacement . J. Roy. Statist. Soc. B 24 : 482 – 491 . [Google Scholar]), and Sampford's IPPS plan (1967 Sampford , M. R. ( 1967 ). On sampling without replacement with unequal probabilities of selection . Biometrika 54 ( 3 ): 499 – 513 .[Crossref], [PubMed] , [Google Scholar]) using a real life population. Unbiased estimation of Horvitz–Thompson estimator of population total is not possible in these types of plans because some of the second-order inclusion probabilities are zero. To resolve this problem, one approximate variance estimation technique has been suggested.     

Designs Robust against Violation of Normality Assumption in the Standard F-test

In this article, designs are found for which the F-test of analysis of variance is insensitive to violation of normality assumption. Atiqullah (1962 Atiquallah, M. (1962). The estimation of residual variance in quadratically balanced least-squares problems and the robustness of the F-test. Biometrika 49: 83–91.[Crossref], [Web of Science ®] , [Google Scholar]) proved that the F-test for treatments adjusting for blocks in the intra-block analysis of a balanced incomplete block design is robust against non-normality in the observations. Here an attempt has been made to identify other designs robust in this sense. In particular, it is observed that for testing relevant hypothesis, a partially balanced incomplete block design in block design setup, under certain conditions, is robust. Robustness of a balanced treatment incomplete block design and a partially balanced treatment incomplete block design (Biswas, 2012 Biswas, A. (2012). Block designs robust against the presence of an aberration in a treatment-control setup. Commun Statist.Theor Methods 41: 920–933.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), in treatment-control design setup, is also studied. Moreover, a new measure of robustness is introduced for further study. The performance of the F-test in presence of non-normality in the observations for a quadratically balanced design is also examined.     

D-Optimum Designs for Optimum Mixture in a Quadratic Log Contrast Model

Optimal designs for estimating the optimum mixing proportions in a quadratic mixture model was first investigated by Pal and Mandal (2006). In this article, similar investigation is carried out when mean response in a mixture experiment is described by a quadratic log contrast model. It is found that in a symmetric subspace of the finite dimensional simplex, there exists a D-optimal design that puts weights at the centroid of the sub-space and the vertices of the experimental domain. The optimality is checked by numerical computation using Equivalence Theorem.     

D-Optimal Designs for Covariate Models

The problem of finding D-optimal designs in the presence of a number of covariates has been considered in the one-way set-up. This is an extension of Dey and Mukerjee (2006 Dey , A. , Mukerjee , R. ( 2006 ). D-optimal designs for covariate models . Statistics 40 : 297 – 305 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) in the sense that for fixed replication numbers of each treatment, an alternative upper bound to the determinant of the information matrix has been found through completely symmetric C-matrices for the regression coefficients; this upper bound includes the upper bound given in Dey and Mukerjee (2006 Dey , A. , Mukerjee , R. ( 2006 ). D-optimal designs for covariate models . Statistics 40 : 297 – 305 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) obtained through diagonal C-matrices. Because of the fact that a smaller class of C-matrices was used at the intermediate stage where the replication numbers were fixed, ultimately some optimal designs remained unidentified there. These designs have been identified here and thereby the conjecture made in Dey and Mukerjee (2006 Dey , A. , Mukerjee , R. ( 2006 ). D-optimal designs for covariate models . Statistics 40 : 297 – 305 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) has been settled.