Nonparametric Kernel Smoothing Methods. The sm library in Xlisp-Stat

Luca Scrucca

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In this paper we describe the Xlisp-Stat version of the sm library, a software for applying nonparametric kernel smoothing methods. The original version of the sm library was written by Bowman and Azzalini in S-Plus, and it is documented in their book Applied Smoothing Techniques for Data Analysis (1997). This is also the main reference for a complete description of the statistical methods implemented.

The sm library provides kernel smoothing methods for obtaining nonparametric estimates of density functions and regression curves for different data structures. Smoothing techniques may be employed as a descriptive graphical tool for exploratory data analysis. Furthermore, they can also serve for inferential purposes as, for instance, when a nonparametric estimate is used for checking a proposed parametric model. The Xlisp-Stat version includes some extensions to the original sm library, mainly in the area of local likelihood estimation for generalized linear models.

The Xlisp-Stat version of the sm library has been written following an object-oriented approach. This should allow experienced Xlisp-Stat users to implement easily their own methods and new research ideas into the built-in prototypes.

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