×

Least-squares estimation of a step function. (English) Zbl 0711.62031

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.

MSC:

62G05 Nonparametric estimation
62E20 Asymptotic distribution theory in statistics
60G50 Sums of independent random variables; random walks
PDFBibTeX XMLCite