文章基本信息

标题：Further statistical analysis of circle fitting
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作者：Ali Al-Sharadqah
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2014
卷号：8
期号：2
页码：2741-2778
DOI：10.1214/14-EJS971
语种：English
出版社：Institute of Mathematical Statistics
摘要：This study is devoted to comparing the most popular circle fits (the geometric fit, Pratt’s, Taubin’s, Kåsa’s) and the most recently developed algebraic circle fits: hyperaccurate fit and HyperLS fit. Even though hyperaccurate fit has zero essential bias and HyperLS fit is unbiased up to order $\sigma^{4}$, the geometric fit still outperforms them in some circumstances. Since the first-order leading term of the MSE for all fits are equal, we go one step further and derive all terms of order $\sigma^{4}$, which come from essential bias, as well as all terms of order $\sigma^{4}/n$, which come from two sources: the variance and the outer product of the essential bias and the nonessential bias.