We consider the problem of locating the jumps in regression surfaces. A least squares plane is fitted in a neighborhood of a design point in question. The gradient vector of this plane contains both the continuous and jump information of the regression surface at this design point. We try to remove the continuous information by using two neighboring least squares planes along the direction of that gradient vector. In such a way, the jump information is extracted, suggesting a jump detection algorithm. This method requires $O(Nk)$ computations, where $N$ is the sample size and $k$ is the window width of the neighborhood. This property makes it possible to handle large data sets. The conditions imposed on the jump location curves, the jump surfaces and the noise are mild enough. We demonstrate this method in detail with a simulation example.
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