nonparametric stats

[seth]

Hi,

I'm a grad student reading up on nonparametric stats. I have a basic question. Are techniques such as local regression and smoothing splines useful for prediction only (fitting a nice line you can use to interpolate other points later) or are they useful for explanation (seeing what variables explain the variance and to what degree)? For example, with local regression the coefficients for each regression of the many should be different. How could this tell us about the relationship among variables globally (anywhere other than that point)? The relationship among variables at any single point could be only noise anyway. I suppose some "averaging" of coefficients among local regressions could be done. If someone has a good explanation could you also send links or citations so I can do some further reading? I just want to know this answer without having to read a whole textbook! Thanks.

Seth

 

[JohnM]

Just my 2 cents:

Whenever I've used smoothing, whether it be a simple moving average or other more sophisticated method, it's always done in order for me to see the smooth pattern in a noisy data set.

- so it's more of a tool used in prediction - often it is more "accurate" to use the predicted value from a smoothed curve rather than the original noisy one, because it contains - you guessed it - noise.

Other contributors with differing experiences may have more input on this.

 

[quark]

If I remember correctly, smooth splines is an one-dimensional model, there is only one x. I think it's useful primarily for prediction. Ditto for local regression.