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 Quantlet: regxest Description: computes the Nadaraya-Watson estimator for univariate regression.

Reference(s):
Haerdle, W. (1990). Applied Nonparametric Regression. Econometric Society Monographs, No. 19. Cambridge University Press.

 Usage: mh = regxest(x {,h {,K} {,v} }) Input: x n x 2 matrix, the data. The first column contains the independent and the second column the dependent variable. h optional scalar, bandwidth. If not given, 20% of the range of x[,1] is used as default. K optional string, kernel function on [-1,1] or Gaussian kernel "gau". If not given, the Quartic kernel "qua" is used as default. v optional m x 1 vector, values of the independent variable on which to compute the regression. If not given, the (sorted) x is used as default. Output: mh n x 2 or m x 2 matrix, the first column represents the sorted first column of x or the sorted v and the second column contains the regression estimate on the values of the first column.

Note:
This function does an exact computation, i.e., requires O(n^2) operations for estimating the regression function on all observations. For exploratory purposes, the quantlet "regest" is recommended, which uses the faster WARPing method.

Example:
```library("smoother")
library("plot")
;
x = 4.*pi.*(uniform(200)-0.5)   ; independent variable
m = cos(x)                      ; true function
e = uniform(200)-0.5            ; error term
x = x~(m+e)
;
mh = regxest(x,1)                ; estimate function
;
plot(x,mh,m)

```
Result:
```The Nadaraya-Watson regession estimate (blue line) using
Quartic kernel and bandwidth h = 1 and the true
regression function (thin black line) are pictured.
```
Example:
```library("smoother")
library("plot")
;
mhe = regxest(x,3,"epa")      ; estimate function
mhu = regxest(x,2,"uni")      ; estimate function
;
```The Nadaraya-Watson regession estimates using