Locally Efficient Estimation in Censored Data Models: Theory and Examples

In many applications the observed data can be viewed as a censored high dimensional full data random variable X. By the curve of dimensionality it is typically not possible to construct estimators that are asymptotically efficient at every probability distribution in a semiparametric censored data model of such a high dimensional censored data structure. We provide a general method for construction of one-step estimators that are efficient at a chosen submodel of the full-data model, are still well behaved off this submodel and can be chosen to always improve on a given initial estimator. These one-step estimators rely on good estimators of the censoring mechanism and thus will require a parametric or semiparametric model for the censoring mechanism. We present a general theorem that provides a template for proving the desired asymptotic results. We illustrate the general one-step estimation methods by constructing locally efficient one-step estimators of marginal distributions and regression parameters with right-censored data, current status data and bivariate right-censored data, in all models allowing the presence of time-dependent covariates. The conditions of the asymptotics theorem are rigorously verified in one of the examples and the key condition of the general theorem is verified for all examples.

Eastern Temperate Forests

Human activity in the last century has led to a substantial increase in nitrogen (N) emissions and deposition. This N deposition has reached a level that has caused or is likely to cause alterations to the structure and function of many ecosystems across the United States. One approach for quantifying the level of pollution that would be harmful to ecosystems is the critical loads approach. The critical load is dei ned as the level of a pollutant below which no detrimental ecological effect occurs over the long term according to present knowledge. The objective of this project was to synthesize current research relating atmospheric N deposition to effects on terrestrial and aquatic ecosystems in the United States and to identify empirical critical loads for atmospheric N deposition. The receptors that we evaluated included freshwater diatoms, mycorrhizal fungi and other soil microbes, lichens, herbaceous plants, shrubs, and trees. The main responses reported fell into two categories: (1) biogeochemical, and (2) individual species, population, and community responses. The range of critical loads for nutrient N reported for U.S. ecoregions, inland surface waters, and freshwater wetlands is 1 to 39 kg N ha-1 y-1. This broad range spans the range of N deposition observed over most of the country. The empirical critical loads for N tend to increase in the following sequence for different life forms: diatoms, lichens and bryophytes, mycorrhizal fungi, herbaceous plants and shrubs, trees. The critical loads approach is an ecosystem assessment tool with great potential to simplify complex scientii c information and effectively communicate with the policy community and the public. This synthesis represents the i rst comprehensive assessment of empirical critical loads of N for ecoregions across the United States.