If the population is rare and clustered, then simple random sampling gives a poor estimate of the population total. For such type of populations, adaptive cluster sampling is useful. But it loses control on the final sample size. Hence, the cost of sampling increases substantially. To overcome this problem, the surveyors often use auxiliary information which is easy to obtain and inexpensive. An attempt is made through the auxiliary information to control the final sample size. In this article, we have proposed two-stage negative adaptive cluster sampling design. It is a new design, which is a combination of two-stage sampling and negative adaptive cluster sampling designs. In this design, we consider an auxiliary variable which is highly negatively correlated with the variable of interest and auxiliary information is completely known. In the first stage of this design, an initial random sample is drawn by using the auxiliary information. Further, using Thompson’s (J Am Stat Assoc 85:1050–1059, 1990) adaptive procedure networks in the population are discovered. These networks serve as the primary-stage units (PSUs). In the second stage, random samples of unequal sizes are drawn from the PSUs to get the secondary-stage units (SSUs). The values of the auxiliary variable and the variable of interest are recorded for these SSUs. Regression estimator is proposed to estimate the population total of the variable of interest. A new estimator, Composite Horwitz–Thompson (CHT)-type estimator, is also proposed. It is based on only the information on the variable of interest. Variances of the above two estimators along with their unbiased estimators are derived. Using this proposed methodology, sample survey was conducted at Western Ghat of Maharashtra, India. The comparison of the performance of these estimators and methodology is presented and compared with other existing methods. The cost–benefit analysis is given.

Recently, Ahmed et al. (Commun Stat Theory Methods 47(2):324–343, 2018) have introduced the idea of simultaneously estimating means of two sensitive variables by collecting one scrambled response and another pseudo-response. In this paper, we extend their idea to the simultaneous estimation of two means by making use of the forced quantitative randomized response model of Gjestvang and Singh (Metrika 66(2):243–257, 2007) but then re-scrambling the scrambled scores. This idea of re-scrambling already scrambled responses seems completely new in the field of randomized response sampling. The performance of the proposed forced quantitative randomized response model has been investigated analytically as well as empirically.

In this paper, we explore sparsity and homogeneity of regression coefficients incorporating prior constraint information. The sparsity means that a small fraction of regression coefficients is nonzero, and the homogeneity means that regression coefficients are grouped and have exactly the same value in each group. A general pairwise fusion approach is proposed to deal with the sparsity and homogeneity detection when combining prior convex constraints. We develop a modified alternating direction method of multipliers algorithm to obtain the estimators and demonstrate its convergence. The efficiency of both sparsity and homogeneity detection can be improved by combining the prior information. Our proposed method is further illustrated by simulation studies and analysis of an ozone dataset.

In this paper, we study the expansions of Ricci flat metrics in harmonic coordinates about the infinity of ALE (Asymptotically Local Euclidean) manifolds.

We study the accuracy and performance of isogeometric analysis on implicit domains when solving time-independent Schrödinger equation. We construct weighted extended PHT-spline basis functions for analysis, and the domain is presented with same basis functions in implicit form excluding the need for a parameterization step. Moreover, an adaptive refinement process is formulated and discussed with details. The constructed basis functions with cubic polynomials and only $C^{1}$ continuity are enough to produce a higher continuous field approximation while maintaining the computational cost for the matrices as low as possible. A numerical implementation for the adaptive method is performed on Schrödinger eigenvalue problem with double-well potential using 3 examples on different implicit domains. The convergence and performance results demonstrate the efficiency and accuracy of the approach.

We characterize bounded and compact positive Toeplitz operators defined on the Bergman spaces over the Siegel upper half-space.