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handout_LOWESS - Statistics 416X Statistical Design and...

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Statistics 416X : Statistical Design and Analysis of Microarray Experiments Handout, Spring 2008 Lowess and Loess: Local Regression Smoothing The names "lowess" and "loess" are derived from the term "locally weighted scatter plot smooth," as both methods use locally weighted linear regression to smooth data. The smoothing process is considered local because each smoothed value is determined by neighboring data points defined within the span. The process is weighted because a regression weight function is defined for the data points contained within the span. In addition to the regression weight function, you can use a robust weight function, which makes the process resistant to outliers. Finally, the methods are differentiated by the model used in the regression: lowess uses a linear polynomial, while loess uses a quadratic polynomial. The regression smoothing and robust smoothing procedures are described in detail below. Local Regression Smoothing Procedure The local regression smoothing process follows these steps for each data point: 1. Compute the regression weights for each data point in the span. The weights are given by the tricube function shown below. x is the predictor value associated with the response value to be smoothed, x i are the nearest neighbors of x as defined by the span, and d ( x
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