Sankhya. Series B. [Methodological.]最新文献

Often linear regression is used to estimate mediation effects. In many instances the underlying relationships may not be linear. Although, the exact functional form of the relationship may be unknown, based on the underlying science, one may hypothesize the shape of the relationship. For these reasons, we develop a novel shape-restricted inference-based methodology for conducting mediation analysis. This work is motivated by an application in fetal endocrinology where researchers are interested in understanding the effects of pesticide application on birth weight, with human chorionic gonadotropin (hCG) as the mediator. Using the proposed methodology on a population-level prenatal screening program data, with hCG as the mediator, we discovered that while the natural direct effects suggest a positive association between pesticide application and birth weight, the natural indirect effects were negative.

The drastic improvement in data collection and acquisition technologies has enabled scientists to collect a great amount of data. With the growing dataset size, typically comes a growing complexity of data structures and of complex models to account for the data structures. How to estimate the parameters of complex models has put a great challenge on current statistical methods. This paper proposes a blockwise consistency approach as a potential solution to the problem, which works by iteratively finding consistent estimates for each block of parameters conditional on the current estimates of the parameters in other blocks. The blockwise consistency approach decomposes the high-dimensional parameter estimation problem into a series of lower-dimensional parameter estimation problems, which often have much simpler structures than the original problem and thus can be easily solved. Moreover, under the framework provided by the blockwise consistency approach, a variety of methods, such as Bayesian and frequentist methods, can be jointly used to achieve a consistent estimator for the original high-dimensional complex model. The blockwise consistency approach is illustrated using two high-dimensional problems, variable selection and multivariate regression. The results of both problems show that the blockwise consistency approach can provide drastic improvements over the existing methods. Extension of the blockwise consistency approach to many other complex models is straightforward.

We consider the finite sample performance of a new nonparametric method for bioassay and benchmark analysis in risk assessment, which averages isotonic MLEs based on disjoint subgroups of dosages, and whose asymptotic behavior is essentially optimal (Bhattacharya and Lin (2010)). It is compared with three other methods, including the leading kernel-based method, called DNP, due to Dette et al. (2005) and Dette and Scheder (2010). In simulation studies, the present method, termed NAM, outperforms the DNP in the majority of cases considered, although both methods generally do well. In small samples, NAM and DNP both outperform the MLE.

The number of scientific publications on semiparametric methods per year has been steadily increasing since the early 1980s. This increased interest has happened in spite of the fact that the novelty of semiparametrics for its own sake has run its course, and semiparametric methods are by now considered classical. The underlying reasons for this continued interest include the genuine scientific utility of semiparametric models combined with the breadth and depth of the many theoretical questions that remain to be answered. Empirical process techniques are an essential research tool for many of these questions. Moreover, both semiparametric methods and empirical processes are playing an increasingly valuable role in high dimensional data analysis and in other emerging areas in statistics. The topics are very fruitful and intriguing for new researchers to engage in. Graduate programs in statistics, biostatistics and econometrics can and should include more empirical processes and semiparametrics in their teaching in order to ensure a sufficient supply of suitably qualified researchers.

In this article we introduce a new procedure for estimating population parameters under inequality constraints (known as order restrictions) when the unrestricted maximum liklelihood estimator (UMLE) is multivariate normally distributed with a known covariance matrix. Furthermore, a Dunnett-type test procedure along with the corresponding simultaneous confidence intervals are proposed for drawing inferences on elementary contrasts of population parameters under order restrictions. The proposed methodology is motivated by estimation and testing problems encountered in the analysis of covariance models. It is well-known that the restricted maximum likelihood estimator (RMLE) may perform poorly under certain conditions in terms of quadratic loss. For example, when the UMLE is distributed according to multivariate normal distribution with means satisfying simple tree order restriction and the dimension of the population mean vector is large. We investigate the performance of the proposed estimator analytically as well as using computer simulations and discover that the proposed method does not fail in the situations where RMLE fails. We illustrate the proposed methodology by re-analyzing a recently published rat uterotrophic bioassay data.

"A class of analytical models to study the distribution of maternal age at different births from the data on age-specific fertility rates has been presented. Deriving the distributions and means of maternal age at birth of any specific order, final parity and at next-to-last birth, we have extended the approach to estimate parity progression ratios and the ultimate parity distribution of women in the population.... We illustrate computations of various components of the model expressions with the current fertility experiences of the United States for 1970."

"In this paper, a set of two probability models have been derived to describe the variation in the length of open birth interval of women having given birth to a child during the last 'T' years of their current reproductive age. The first model is derived by assuming the reproduction process as steady-state, the second is obtained by varying the fecundability parameter involved in the first model after the last birth. These models are applied to the three sets of data, one collected from [the Indian] Varanasi-survey, 1969-70 and the other two generated from the data on age-specific fertility rates using the life table technique. The biological parameters such as fecundability and secondary sterility have been estimated using some simple procedure of estimation."