A local polynomial jump-detection algorithm in nonparametric regression

We suggest a one-dimensional jump-detection algorithm based on local polynomial fitting for jumps in regression functions (zero-order jumps) or jumps in derivatives (first-order or higher-order jumps), If jumps exist in the mth-order derivative of the underlying regression function, then an (m+1)-order polynomial is fitted in a neighborhood of each design point. We then characterize the jump information in the coefficients of the highest-order terms of the fitted polynomials and suggest an algorithm for jump detection. This method is introduced briefly for the general setup and then presented in detail for zero-order and first-order jumps. Several simulation examples are discussed. We apply this method to the Bombay (India) sea-level pressure data.