We propose new median type estimators of the quadratic trend parameter of location based on the second order differences of observations. Asymptotic normality and strong consistency of the estimators are proved. The estimators have a high breakdown point and high asymptotic efficiency in the Gaussian case, and do not depend on the slope and intercept parameters or their estimates. The simulation results confirm the theoretical ones starting with 20–30 observations. We suppose that the estimators could be used for robust filtering of time series.
['Anna V. Kitaeva', 'Alexandra O. Zhukovskaya']
Robust estimating of a quadratic trend's parameter