density estimation

Hi,

I have been looking for a method of estimating a parametric model from 
the output (x, y) from the R function "density". Below is my thought and 
wonder if it looks OK. Suppose that we build a single gaussian model for 
each input data point x (x is the mean),  the overal model may be a sum 
of these gaussian models built on each x, i.e. P(y) = \sum_x P(y|x, 
\sigma), where y is any new data point. Is this right? Any normalization 
is applied?

Thanks in advance for any suggestion that you may offer me!

Best regards,
Hui