Yao, Yi-Ching; Au, S. T. Least-squares estimation of a step function. (English) Zbl 0711.62031 Sankhyā, Ser. A 51, No. 3, 370-381 (1989). Summary: Consider the problem of estimating step functions in the presence of additive measurement noise. In the case that the number of jumps is known, the least-squares estimators for the locations of the jumps and the levels of the step function are studied and their limiting distributions are derived. When the number of jumps is unknown, an estimator is proposed which is consistent under the condition that the number of jumps is not greater than a given upper bound. Cited in 57 Documents MSC: 62G05 Nonparametric estimation 62E20 Asymptotic distribution theory in statistics 60G50 Sums of independent random variables; random walks Keywords:seismology; change-point; estimating step functions; additive measurement noise; number of jumps; least-squares estimators; limiting distributions PDFBibTeX XMLCite \textit{Y.-C. Yao} and \textit{S. T. Au}, Sankhyā, Ser. A 51, No. 3, 370--381 (1989; Zbl 0711.62031)