Alternative Estimators for Randomized Response Techniques in Multi-Character Surveys

Tail estimates are developed for power law probability distributions with exponential tempering, using a conditional maximum likelihood approach based on the upper-order statistics. Tempered power law distributions are intermediate between heavy power-law tails and Laplace or exponential tails, and are sometimes called “semi-heavy” tailed distributions. The estimation method is demonstrated on simulated data from a tempered stable distribution, and for several data sets from geophysics and finance that show a power law probability tail with some tempering.     

SB-Robust Estimators of the Parameters of the Wrapped Normal Distribution

In this article, we study the SB-robustness of various estimators of the mean direction (μ) and the concentration parameter (ρ) of the wrapped normal distribution. The functional corresponding to the sample mean direction is seen to be not SB-robust as an estimator of μ at the family of wrapped normal distributions with varying ρ, whereas the γ-trimmed mean direction is SB-robust at the same family of distributions for the different dispersion measures considered in this article. We also study the SB-robustness of the moment estimator of ρ and also that for a newly introduced trimmed estimator of ρ.     

Multiple-start balanced modified systematic sampling in the presence of linear trend

ABSTRACT

In this paper, we propose a sampling design termed as multiple-start balanced modified systematic sampling (MBMSS), which involves the supplementation of two or more balanced modified systematic samples, thus permitting us to obtain an unbiased estimate of the associated sampling variance. There are five cases for this design and in the presence of linear trend only one of these cases is optimal. To further improve results for the other cases, we propose an estimator that removes linear trend by applying weights to the first and last sampling units of the selected balanced modified systematic samples and is thus termed as the MBMSS with end corrections (MBMSSEC) estimator. By assuming a linear trend model averaged over a super-population model, we will compare the expected mean square errors (MSEs) of the proposed sample means, to that of simple random sampling (SRS), linear systematic sampling (LSS), stratified random sampling (STR), multiple-start linear systematic sampling (MLSS), and other modified MLSS estimators. As a result, MBMSS is optimal for one of the five possible cases, while the MBMSSEC estimator is preferred for three of the other four cases.     

Effect of adjustment for sex composition in the measurement of fertility on intrinsic rates

The inconsistencies inherent in the one-sex models created a need for the construction of what are known as marriage functions, especially for the measurement of fertility. But attempts to develop marriage functions have been frustrated by the inability of the proposed functions to meet certain consistency conditions and also by difficulties in empiracally determining function parameters. Among several functions proposed so far, Das Gupta's (1972) "effective population" deserves special mention. He uses both sexes in its formulation, and has shown that the constancy of fertility rates based on such a function together with the constancy of survivorship probabilities of both sexes would result in a stable population. It is suggested in this article that the major source of the problem in a two-sex model seems to be the requirement that the model has to be specific both for sex and age. The ideal of incorporating the relative composition of one sex in the age-specific rates of the other, thereby creating a function dependent on both sexes, is advanced in this article. Such functions, defined explicitly for births, can be easily translated into age-specific birth rates. In addition to simplicity in the definition and form, the conditions leading toward stability can also be established. Interestingly enough, the intrinsic rate for this two-sex model lies in the interval determined by the rates obtained from the two one-sex models.     

Managing ‘American Islam’

Focusing on the case of Islam in post-9/11 United States, this article highlights the particularity of how US secularism is enacted by the state. In much sociological theory, the United States has been understood to be a neutral and non-interfering state with regard to religion, thereby fostering a pluralist religious context of free consumer choice. Some Muslim reformists have argued that this context makes the US highly fertile ground upon which to reform Islam and to improve women's status in Islam. This article argues that, in the context of the US-led ‘war on terror’, the government has drawn on and amplified this discourse in the service of producing a representation of the US as tolerant, while also seeking to promote a concept of ‘true’ Islam and produce patriotic Muslim citizens. At the center of this discourse are contested portrayals of Muslim women as symbolic of a modern and liberated Islam that is uniquely ‘American’ and opposed to other presumably oppressive Islams. While this context may in fact promote the reform of Islam, it does so with state involvement rather than as a result of state neutrality.     

Assessment of hospital services and patient reactions

This paper deals with the study of assessment of hospital services and patient reactions carried out amongst 473 respondents, both in-door (3 wards) and out-door patients in M.L.B. Medical College Hospital, Jhansi (Uttar Pradesh). The patients were from three wards medical, surgical and gynaecological wards and consisted of 373 discharged and 100 out-door patients.     

Bayesian hierarchical model for protein identifications

In proteomics, identification of proteins from complex mixtures of proteins extracted from biological samples is an important problem. Among the experimental technologies, mass spectrometry (MS) is the most popular one. Protein identification from MS data typically relies on a ‘two-step’ procedure of identifying the peptide first followed by the separate protein identification procedure next. In this setup, the interdependence of peptides and proteins is neglected resulting in relatively inaccurate protein identification. In this article, we propose a Markov chain Monte Carlo based Bayesian hierarchical model, a first of its kind in protein identification, which integrates the two steps and performs joint analysis of proteins and peptides using posterior probabilities. We remove the assumption of independence of proteins by using clustering group priors to the proteins based on the assumption that proteins sharing the same biological pathway are likely to be present or absent together and are correlated. The complete conditionals of the proposed joint model being tractable, we propose and implement a Gibbs sampling scheme for full posterior inference that provides the estimation and statistical uncertainties of all relevant parameters. The model has better operational characteristics compared to two existing ‘one-step’ procedures on a range of simulation settings as well as on two well-studied datasets.     

Combining monotonicity and strong equity: construction and representation of orders on infinite utility streams

This paper studies the nature of social welfare orders (SWO) on infinite utility streams, satisfying the efficiency principle known as monotonicity and the consequentialist equity principle known as strong equity. It provides a complete characterization of domain sets for which there exists such a SWO which is in addition representable by a real valued function. It then shows that for those domain sets for which there is no such SWO which is representable, the existence of such a SWO necessarily entails the existence of a non-Ramsey set, a non-constructive object.     

Testing for Spatial Isotropy Under General Designs

Spatial modeling is typically composed of a specification of a mean function and a model for the correlation structure. A common assumption on the spatial correlation is that it is isotropic. This means that the correlation between any two observations depends only on the distance between those sites and not on their relative orientation. The assumption of isotropy is often made due to a simpler interpretation of correlation behavior and to an easier estimation problem under an assumed isotropy. The assumption of isotropy, however, can have serious deleterious effects when not appropriate. In this paper we formulate a test of isotropy for spatial observations located according to a general class of stochastic designs. Distribution theory of our test statistic is derived and we carry out extensive simulations which verify the efficacy of our approach. We apply our methodology to a data set on longleaf pine trees from an oldgrowth forest in the southern United States.