T. V. Ramanathan

Acceptance sampling plans by variables for a class of symmetric distributions

The estimation of percentage defectives using a normal sampling plan will not be appropriate when the assumption of normality is violated. In this paper, we propose a sampling plan based on a more general symmetric family of distributions with the parameters estimated using the modified maximum likelihood (MML) procedures introduced by Tiku and Suresh . This sampling plan works well for most of the symmetric non-normal distributions. Some numerical study has also been carried out to show the superiority of the proposed plan.

Design of a Community Ownership and Preparedness Index: using data to inform the capacity development of community-based groups

Background Community mobilisation is an important component of a participatory approach to health and development interventions. However, it is challenging to define, measure and assess community participation and ownership of a programme, especially at scale. Methods An iterative cross-sectional survey was designed for implementation across a representative sample of community-based groups, using a weighted index that captured both qualitative and quantitative data in a standardised form. These data were aggregated at the level of individual groups, as well as state-wide or across the whole programme. Community participation in the survey is a primary feature of the methodology and was integral to the process of designing the index and administering the survey. Results The survey provided programme management and communities with objective tools for monitoring community mobilisation across a large-scale and complex intervention covering 32 districts in India. The implementation of the survey engaged communities in an open discussion of their goals and capabilities and helped them to challenge the power dynamics between themselves and other stakeholders. Conclusions It is possible to translate the theoretical premises of participatory development into a tool that both measures and fosters meaningful participation. The active participation of community members in the collection and analysis of data on their mobilisation suggests that monitoring of participation can be undertaken to inform a scaled-up programme and can be a useful intervention in its own right.

Monitoring community mobilisation and organisational capacity among high-risk groups in a large-scale HIV prevention programme in India: selected findings using a Community Ownership and Preparedness Index

Background In a participatory approach to health and development interventions, defining and measuring community mobilisation is important, but it is challenging to do this effectively, especially at scale. Methods A cross-sectional, participatory monitoring tool was administered in 2008–2009 and 2009–2010 across a representative sample of 25 community-based groups (CBGs) formed under the Avahan India AIDS Initiative, to assess their progress in mobilisation, and to inform efforts to strengthen the groups and make them sustainable. The survey used a weighted index to capture both qualitative and quantitative data in numeric form. The index permitted broad, as well as highly detailed, analysis of community mobilisation, relevant at the level of individual groups, as well as state-wide and across the whole programme. Results The survey demonstrated that leadership and programme management were the strongest areas among the CBGs, confirming the programmes investment in these areas. Discussion of the Round 1 results led to efforts to strengthen governance and democratic decision making in the groups, and progress was reflected in the Round 2 survey results. CBG engagement with state authorities to gain rights and entitlements and securing the long-term financial stability of groups remain a challenge. Conclusion The survey has proven useful for informing the managers of programmes about what is happening on the ground, and it has opened spaces for discussion within community groups about the nature of leadership, decision making and their goals, which is leading to accelerated progress. The tool provided useful data to manage community mobilisation in Avahan.

Nonparametric estimation of a time-varying GARCH model

In this paper, a non-stationary time-varying GARCH (tvGARCH) model has been introduced by allowing the parameters of a stationary GARCH model to vary as functions of time. It is shown that the tvGARCH process is locally stationary in the sense that it can be locally approximated by stationary GARCH processes at fixed time points. We develop a two-step local polynomial procedure for the estimation of the parameter functions of the proposed model. Several asymptotic properties of the estimators have been established, including the asymptotic optimality. It is found that the tvGARCH model performs better than many of the standard GARCH models for various real data sets.

A comparison of the technical efficiencies of health districts and hospitals in Botswana

An attempt is made here to construct and present relative efficiency indices for the services rendered by health districts and specific hospitals in Botswana, using Stochastic Frontier Regression analysis and Data Envelopment Analysis. The analysis indicated that three districts - Kweneng East, Kgalagadi and Boteti - have efficiency scores below the optimum level. Among the 13 hospitals considered, Tsabong Primary Hospital was found to have an efficiency score of less than one. Since the health services involve a number of factors, these indices ought to serve as indicators for further scrutiny of those units (health districts and hospitals) that fall below the optimum efficiency level. The data used for the analysis are from the published material by the Central Statistics Office, Botswana for the year 1997. Health is considered one of the major concerns of the government of Botswana. As a consequence, the authors feel that this study will be useful to policy makers and health planners in giving them some kind of relative ranking among health districts and hospitals.

Integer autoregressive models with structural breaks

Even though integer-valued time series are common in practice, the methods for their analysis have been developed only in recent past. Several models for stationary processes with discrete marginal distributions have been proposed in the literature. Such processes assume the parameters of the model to remain constant throughout the time period. However, this need not be true in practice. In this paper, we introduce non-stationary integer-valued autoregressive (INAR) models with structural breaks to model a situation, where the parameters of the INAR process do not remain constant over time. Such models are useful while modelling count data time series with structural breaks. The Bayesian and Markov Chain Monte Carlo (MCMC) procedures for the estimation of the parameters and break points of such models are discussed. We illustrate the model and estimation procedure with the help of a simulation study. The proposed model is applied to the two real biometrical data sets.

Asymmetric Volatility Models with Structural Breaks

This article develops an asymmetric volatility model that takes into consideration the structural breaks in the volatility process. Break points and other parameters of the model are estimated using MCMC and Gibbs sampling techniques. Models with different number of break points are compared using the Bayes factor and BIC. We provide a formal test and hence a new procedure for Bayes factor computation to choose between models with different number of breaks. The procedure is illustrated using simulated as well as real data sets. The analysis shows an evidence to the fact that the financial crisis in the market from the first week of September 2008 has caused a significant break in the structure of the return series of two major NYSE indices viz., S & P 500 and Dow Jones. Analysis of the USD/EURO exchange rate data also shows an evidence of structural break around the same time.

On the distribution of shrinkage parameters of Liu-type estimators

In this paper, we derive the density and distribution functions of the estimator of the shrinkage parameters of the Liu and generalized Liu estimators associated with the normal linear regression model. We indicate how these distributions can be used in arriving at a confidence interval for the optimal value of the shrinkage parameter. Since the distributions are difficult to handle, we have carried out some numerical computations to illustrate them.

Rank tests for testing randomness of a regression coefficient in a linear regression model

We propose a class of nonparametric tests for testing non-stochasticity of the regression parameterβ in the regression modelyi=βxi+ɛi,i=1, ...,n. We prove that the test statistics are asymptotically normally distributed both underH0 and under contiguous alternatives. The asymptotic relative efficiencies (in the Pitman sense) with respect to the best parametric test have also been computed and they are quite high. Some simulation studies are carried out to illustrate the results.

Modified Expected Shortfall: A New Robust Coherent Risk Measure

The coherent risk measure expected shortfall is a popular alternative to value-at-risk. However, the estimated value may miscommunicate the actual risk, especially when huge losses are present in the return series. This may force the financial institution to keep extra capital to meet the requirement set by the regulators. We propose a new robust coherent risk measure called modified expected shortfall, which quantifies the authentic risk of a portfolio. In comparison with the expected shortfall, the magnitude of the suggested risk measure is found to be lower. We propose non-parametric estimators of the modified expected shortfall and establish their statistical properties such as consistency and asymptotic normality.