Template:Non-parametric LDA introduction

Introduction

Nonparametric analysis allows the user to analyze data without assuming an underlying distribution. This can have certain advantages as well as disadvantages. The ability to analyze data without assuming an underlying life distribution avoids the potentially large errors brought about by making incorrect assumptions about the distribution. On the other hand, the confidence bounds associated with nonparametric analysis are usually much wider than those calculated via parametric analysis, and predictions outside the range of the observations are not possible. Some practitioners recommend that any set of life data should first be subjected to a nonparametric analysis before moving on to the assumption of an underlying distribution.

There are several methods for conducting a nonparametric analysis, including the Kaplan-Meier, simple actuarial, and standard actuarial methods. A method for attaching confidence bounds to the results of these nonparametric analysis techniques can also be developed. The basis of nonparametric life data analysis is the empirical [math]\displaystyle{ cdf }[/math] function, which is given by:

[math]\displaystyle{ \widehat{F}(t)=\frac{observations\le t}{n} }[/math]

Note that this is similar to the Bernard's approximation of the median ranks, as discussed in Chapter Parameter Estimation. The following nonparametric analysis methods are essentially variations of this concept.