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

这一研究项目的目标是为卫星数据分析制定若干统计程序。这样的天文数据有许多独特的方面，需要开发新的统计方法。要解决的具体问题包括当自变量和因变量都受到左删失时的非参数回归，以及从左删失数据获得的比率之间的非参数回归。将开发无探测天文测量的最优设计。还将开发具有测量误差的回归的Bootstrap方法，并将分析变量受测量误差影响的回归问题，测量误差的方差已知，但随观测而变化。

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.