-混合误差下非参数回归权函数估计的渐近正态性

本文在一定条件下讨论了－混合误差下非参数回归权函数估计的渐近正态性,并且减弱了文献［３］的条件,证明方法大大简化了。     

Stabilization Coefficient of Random Variable

Coefficient of variation, standard deviation divided by mean, has some essential defects. Its density, expectation and variance are too complex to make the statistical inference for such a coefficient. The definition of stabilization coefficient is just the reciprocal of variation coefficient, mean divided by standard deviation. Such a coefficient has a simple expectation and a simple variance, and is an asymptotically unbiased estimator and a consistent estimator of its true value. Furthermore, coefficient of stabilization has an asymptotic normality. Due to its statistical advantages, coefficient of stabilization is easy to be tested statistically. In some applied fields, usually, there is an increasing standard deviation accompanying an increasing mean. Coefficient of stabilization can be practically used for some comparison studies in such fields. Illustrations about comparing microorganism strains are given in this paper. The robustness of stabilization coefficient is satisfactory.     

Estimation of a Joint Distribution Function with Multivariate Interval‐Censored Data when the Nonparametric MLE is not Unique

A nonparametric estimator of a joint distribution function F₀ of a d‐dimensional random vector with interval‐censored (IC) data is the generalized maximum likelihood estimator (GMLE), where d ≥ 2. The GMLE of F₀ with univariate IC data is uniquely defined at each follow‐up time. However, this is no longer true in general with multivariate IC data as demonstrated by a data set from an eye study. How to estimate the survival function and the covariance matrix of the estimator in such a case is a new practical issue in analyzing IC data. We propose a procedure in such a situation and apply it to the data set from the eye study. Our method always results in a GMLE with a nonsingular sample information matrix. We also give a theoretical justification for such a procedure. Extension of our procedure to Cox's regression model is also mentioned.     

Estimating functions for inhomogeneous spatial point processes with incomplete covariate data

The R package spatstat provides a very flexible and useful frameworkfor analysing spatial point patterns. A fundamental featureis a procedure for fitting spatial point process models dependingon covariates. However, in practice one often faces incompleteobservation of the covariates and this leads to parameter estimationerror which is difficult to quantify. In this paper, we introducea Monte Carlo version of the estimating function used in spatstatfor fitting inhomogeneous Poisson processes and certain inhomogeneouscluster processes. For this modified estimating function, itis feasible to obtain the asymptotic distribution of the parameterestimators in the case of incomplete covariate information.This allows a study of the loss of efficiency due to the missingcovariate data.