On optimal tests for isotropy against the symmetric wrapped stable-circular uniform mixture family

The family of Symmetric Wrapped Stable (SWS) distributions can be widely used for modelling circular data. Mixtures of Circular Uniform (CU) with the former also have applications as a larger family of circular distributions to incorporate possible outliers. Restricting ourselves to such a mixture, we derive the locally most powerful invariant (LMPI) test for the hypothesis of isotropy or randomness of directions-expressed in terms of the null value of the mixing proportion, p, in the model. Global monotonicity of the power function of the test is established. The test is also consistent. Power values of the test for some selected parameter combinations, obtained through simulation reveal quite encouraging performances even for moderate sample sizes. The P 3 approach (SenGupta, 1991; Pal & SenGupta, 2000) for unknown p and rho and the non-regular case of unknown a, the index parameter, are also discussed. A real-life example is presented to illustrate the inadequacy of the circular normal distribution as a circular model. This example is also used to demonstrate the applications of the LMPI test, optimal P 3 test and a Daviesmotivated test (Davies, 1977, 1987). Finally, a goodness-of-fit test performed on the data establishes the plausibility of the above SWS-CU mixture model for real-life problems encountered in practical situations.     

On the construction of orthogonal factorial designs of resolution 11

A new method of construction of orthogonal resolution IV designs for symmetrical and asymmetrical factorials has been presented. Many new series of orthogonal factorial designs of resolution IV can be obtained by the above general method.     

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.     

A new unrelated question randomized response model

In this paper, we extend the work of Gjestvang and Singh [A new randomized response model, J. R. Statist. Soc. Ser. B (Methodological) 68 (2006), pp. 523–530] to propose a new unrelated question randomized response model that can be used for any sampling scheme. The interesting thing is that the estimator based on one sample is free from the use of known proportion of an unrelated character, unlike Horvitz et al. [The unrelated question randomized response model, Social Statistics Section, Proceedings of the American Statistical Association, 1967, pp. 65–72], Greenberg et al. [The unrelated question randomized response model: Theoretical framework, J. Amer. Statist. Assoc. 64 (1969), pp. 520–539] and Mangat et al. [An improved unrelated question randomized response strategy, Calcutta Statist. Assoc. Bull. 42 (1992), pp. 167–168] models. The relative efficiency of the proposed model with respect to the existing competitors has been studied.     

A Revisit to the Behrens–Fisher Problem: Comparison of Five Test Methods

We revisit the well-known Behrens–Fisher problem and apply a newly developed ‘Computational Approach Test’ (CAT) to test the equality of two population means where the populations are assumed to be normal with unknown and possibly unequal variances. An advantage of the CAT is that it does not require the explicit knowledge of the sampling distribution of the test statistic. The CAT is then compared with three widely accepted tests—Welch–Satterthwaite test (WST), Cochran–Cox test (CCT), ‘Generalized p-value’ test (GPT)—and a recently suggested test based on the jackknife procedure, called Singh–Saxena–Srivastava test (SSST). Further, model robustness of these five tests are studied when the data actually came from t-distributions, but wrongly perceived as normal ones. Our detailed study based on a comprehensive simulation indicate some interesting results including the facts that the GPT is quite conservative, and the SSST is not as good as it has been claimed in the literature. To the best of our knowledge, the trends observed in our study have not been reported earlier in the existing literature.     

Measuring and Analysing Community Action for Health: An Indicator-Based Typology and Its Application to the Case of Barcelona

Social welfare systems face major challenges, particularly in a context of social transformation, austerity and growing inequalities. This process is highly visible in the health sector. In this context, many voices ask for public sector reforms and community action for health as a relevant practice. However, analyses and evaluations of this kind of practices are still limited, particularly beyond the cases of single community health actions or interventions. We still need to identify key indicators for measuring and characterising what community action for health consists of, as well as to what degree this kind of intervention has been developed across a city. Based on a research about 49 neighborhoods in Barcelona, this paper creates an index to measure and characterize community action for health, using different indicators: citizen engagement programs in community health, organizational transformation of the health and social protection systems, stable participatory structures with specific teams, and urban health policies. We apply the index to the case of Barcelona and build a map of community action for health in the city using 4 categories: strong community health development (one neighbourhood), middle (9 neighborhoods), emergent (25 neighborhoods) and without specific community health promotion (14 neighbourhoods). We find that community action for health is extensive within the city of Barcelona, have great potential as a response to the need for change in the relationship between the public (health) sector and the citizenry, but is still implemented unequally across the urban territory in terms of types and methods.     

Likelihood inference based on EM algorithm for the destructive length-biased Poisson cure rate model with Weibull lifetime

In this article, we consider the destructive length-biased Poisson cure rate model, proposed by Rodrigues et al., that presents a realistic and interesting interpretation of the biological mechanism for the recurrence of tumor in a competing causes scenario. Assuming the lifetime to follow the Weibull distribution and censoring mechanism to be non-informative, the necessary steps of the EM algorithm for the determination of the MLEs of the model parameters are developed here based on right censored data. The standard errors of the MLEs are obtained by inverting the observed information matrix. A simulation study is then carried out to examine the method of inference developed here. Finally, the proposed methodology is illustrated with a real melanoma dataset.