Mathematical Sciences: Advanced Statistical Methods for Analyzing Data from Astronomical Surveys

这个研究项目的目标是为卫星数据分析制订若干统计程序。这样的天文数据有许多独特的方面，需要发展新的统计方法。将解决的具体问题涉及当自变量和因变量都受到左审查时的非参数回归以及从左审查数据获得的比率之间的非参数回归。将开发无探测天文调查的最佳设计。带测量误差的回归的自举方法也将被开发，回归问题将被分析，其中变量受测量误差的影响，其方差是已知的，但在观察中是不同的。

The objective of this research project is to develop a number of statistical procedures for satellite data analysis. Such astronomical data have a number of singular aspects that necessitate the development of new statistical methods. Specific problems that will be addressed involve nonparametric regression when both the independent and dependent variables are subject to left censoring and nonparametric regression between ratios obtained from left-censored data. Optimal designs for astronomical surveys with nondetections will be developed. Bootstrap methods for regression with measurement errors will also be developed and regression problems will be analyzed where the variables are subject to measurement error whose variance is known but varies across the observations.