Double robust estimator in general treatment regimes based on Covariate-balancing

Double robust estimators have double the chance of being a consistent estimator of a causal effect in binary treatments cases. In this paper, we proposed an estimator of a causal effect for general treatment regimes based on covariate-balancing. Under parametrical situation, our estimator has double robustness.     

On f-tests and linear hypothesis in a general linear model

A simple method of setting linear hypotheses testable by F-tests in a general linear model when the covariance matrix has a general form and is completely unknown, is provided. With some additional conditions imposed on the covariance matrix, there exist the UMP invariant tests of certain linear hypotheses. We derive them to compare the powers with those of F-tests obtained under no restrictions on the covariance matrix. The results are illustrated in a multiple regression model with some examples.     

On the consistency and the robustness in model selection criteria

Abstract

In the model selection problem, the consistency of the selection criterion has been often discussed. This paper derives a family of criteria based on a robust statistical divergence family by using a generalized Bayesian procedure. The proposed family can achieve both consistency and robustness at the same time since it has good performance with respect to contamination by outliers under appropriate circumstances. We show the selection accuracy of the proposed criterion family compared with the conventional methods through numerical experiments.     

On Efron's Parameterization

This paper discusses a curved exponential family of distributions which is defined by a differential equation with respect to the expectation parameters in the two–dimensional exponential family. The differential equation considered here is the same as the one given by Efron (1975) for the trinomial distribution. This equation is extended here to a general exponential family, and called Efron's parameterization in the two–dimensional exponential family. The solution of Efron's parameterization is obtained explicitly in an exponential family, although Kumagai & Inagaki (1996) showed that there exists no proper solution of Efron's equation for the trinomial distribution, in line with the counterexample given by Efron (1975 p. 1206). The paper gives some characterizations of Efron's parameterization with special reference to Fisher's circle model. The implications of these characterizations are the two–dimensional normal distribution and a spiral curve in the plane.     

A Bayesian inference of P(λ1<λ2) for two Poisson parameters

The statistical inference drawn from the difference between two independent Poisson parameters is often discussed in the medical literature. However, such discussions are usually based on the frequentist viewpoint rather than the Bayesian viewpoint. Here, we propose an index θ=P(λ_{1, post}<λ_{2, post}), where λ_{1, post} and λ_{2, post} denote Poisson parameters following posterior density. We provide an exact and an approximate expression for calculating θ using the conjugate gamma prior and compare the probabilities obtained using the approximate and the exact expressions. Moreover, we also show a relation between θ and the p-value. We also highlight the significance of θ by applying it to the result of actual clinical trials. Our findings suggest that θ may provide useful information in a clinical trial.     

A discrete probabilistic model for analyzing pairwise comparison matrices

The pairwise comparison matrix is often used for the estimation of the priorities in the analytic hierarchy process. In this paper, we propose an estimation method based on the discrete probabilistic expression of each choice. Moreover, we show numerical examples to compare our method with commonly used ones. As a result, it is shown that, using a robust divergence measure for the estimation, the proposed method can extract the priorities more stably even if some outlying observations are included.     

A Bayesian non‐inferiority test for two independent binomial proportions

In drug development, non‐inferiority tests are often employed to determine the difference between two independent binomial proportions. Many test statistics for non‐inferiority are based on the frequentist framework. However, research on non‐inferiority in the Bayesian framework is limited. In this paper, we suggest a new Bayesian index τ = P(π₁ > π₂ ? Δ₀ | X₁,X₂), where X₁ and X₂ denote binomial random variables for trials n₁ and n₂, and parameters π₁ and π₂, respectively, and the non‐inferiority margin is Δ₀ > 0. We show two calculation methods for τ, an approximate method that uses normal approximation and an exact method that uses an exact posterior PDF. We compare the approximate probability with the exact probability for τ. Finally, we present the results of actual clinical trials to show the utility of index τ. Copyright © 2013 John Wiley & Sons, Ltd.     

A robust generalization and asymptotic properties of the model selection criterion family

When selecting a model, robustness is a desirable property. However, most model selection criteria that are based on the Kullback–Leibler divergence tend to have reduced performance when the data are contaminated by outliers. In this paper, we derive and investigate a family of criteria that generalize the Akaike information criterion (AIC). When applied to a polynomial regression model, in the non contaminated case, the performance of this family of criteria is asymptotically equal to that of the AIC. Moreover, the proposed criteria tend to maintain sufficient levels of performance even in the presence of outliers.     

Empowering rural women through a community development approach in Nepal

This paper explores a community development strategy to empowerrural women through educational and small-scale household economicactivities. Qualitative and quantitative data analysis methodswere used to assess the impact of a community development projectlaunched in a remote hill district of Nepal. Focusing on twoproject components, the paper concludes that a functional literacyprogramme is a good start, which has revealed its dynamism withpractical extensions in a post-literacy period. On the otherhand, group savings and credit programmes provide the drivingforce to help illiterate rural women start small-scale economicactivities that are effective in absorbing the female workforcein these communities. Community development programmes shouldbe ready to meet changing needs of the target population tomake them truly self-reliant after the completion of the project.