Obtaining correct responses to sensitive questions in social and behavioural researches is an ancient problem in survey research with respondents misreporting on sensitive behaviours or giving false response to protect themselves. This paper develops an alternative unbiased estimator by modifying the dichotomous randomized response technique model to tackle this problem. The proposed estimator was compared numerically with conventional ones by considering different practicable and suitable design choices. Proposed model was also considered when sampling with unequal probabilities with or without replacement. It was observed that the proposed estimator performs efficiently than the conventional ones. As the proposed model captures progressively more people involved in the sensitive attribute, the model outperforms other models considered. Therefore, social and behavioural researchers can now obtain correct and valid responses from sensitive behavioural researches with ease in order to make informed and reliable decisions.

In the present paper, we propose an efficient scrambled estimator of population mean of quantitative sensitive study variable, using general linear transformation of non-sensitive auxiliary variable. Efficiency comparisons with the existing estimators have been carried out both theoretically and numerically. It has been found that our optimal scrambled estimator is always more efficient than most of the existing scrambled estimators and also it is more efficient than few other scrambled estimators under some conditions.

Feroze and Aslam (J Natl Sci Found Sri Lanka 42:325–334, 2014) and Sindhu et al. (J Mod Appl Stat Methods 13:259–286, 2014) have considered the Bayesian analysis of the two-component mixture of lifetime distributions under doubly censored samples. In this paper, the concept has been extended for the three-component mixture of lifetime (Rayleigh) distribution under doubly censored samples. The likelihood function for the mixture of lifetime models under doubly type-II censored samples has been introduced. Different priors and loss functions have been assumed for the derivation of Bayes estimators and posterior risks. The comparisons among various estimators have been made by analyzing the simulated and real data sets.

Macroeconomic situation is the overall performance of a country’s and regional economic situation. At present, the vast majority of macroeconomic indicators are obtained through sampling surveys, step-by-step reporting, statistical calculations, and other processes, which are publicly released by the Statistical Bureau. There are some shortcomings, such as lag and non-authenticity. Timely forecasting and early warning of macroeconomic trends are the important needs of government affairs. However, the timeliness of data has a direct impact on government decision-making. In this paper, the high frequency and relatively accurate big data sources are adopted to construct a multivariate regression prediction model for traditional national economic accounting indicators (such as industrial value added above the scale of Hefei), which is different from the traditional time series prediction model such as ARIMA model. Based on the macroeconomic prediction model of time series big data, multi-latitude data sources, sequential update, verification set screening model and other strategies are used to provide more reliable, timely, and easy-to-understand forecasting values of national economic accounting indicators. At the same time, the potential influencing factors of macroeconomic indicators are excavated to provide data and theoretical basis for macroeconomic analysis and decision-making.

Numerical integration over the implicitly defined domains is challenging due to topological variances of implicit functions. In this paper, we use interval arithmetic to identify the boundary of the integration domain exactly, thus getting the correct topology of the domain. Furthermore, a geometry-based local error estimate is explored to guide the hierarchical subdivision and save the computation cost. Numerical experiments are presented to demonstrate the accuracy and the potential of the proposed method.

There are no simple singular Whittaker modules over most of important algebras, such as simple complex finite-dimensional Lie algebras, affine Kac–Moody Lie algebras, the Virasoro algebra, the Heisenberg–Virasoro algebra and the Schrödinger–Witt algebra. In this paper, however, we construct simple singular Whittaker modules over the Schrödinger algebra. Moreover, simple singular Whittaker modules over the Schrödinger algebra are classified. As a result, simple modules for the Schrödinger algebra which are locally finite over the positive part are completely classified. We also give characterizations of simple highest weight modules and simple singular Whittaker modules.