A Local Polynomial Jump Detection Algorithm in Nonparametric Regression

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