# NxKREG - Kernel Regression

## Syntax

NxKREG(X, Y, P, Kernel, H, Optimize, Target, Return)

X
is the x-component of the input data table (a one-dimensional array of cells (e.g. rows or columns)).
Y
is the y-component (i.e. function) of the input data table (a one-dimensional array of cells (e.g. rows or columns)).
P
is the polynomial order (0 = constant, 1 = linear, 2 = Quadratic, 3 = Cubic, etc.), etc.). If missing, P = 0.
Kernel
is the weighting kernel function used with KNN-Regression method : 0(or missing) = Uniform, 1 = Triangular, 2 = Epanechnikov, 3 = Quartic, 4 = Triweight, 5 = Tricube, 6 = Gaussian, 7 = Cosine, 8 = Logistic, 9 = Sigmoid, 10 = Silverman.
Value Kernel
0 Uniform Kernel (default).
1 Triangular Kernel.
2 Epanechnikov Kernel.
3 Quartic Kernel.
4 Triweight Kernel.
5 Tricube Kernel.
6 Gaussian Kernel.
7 Cosine Kernel.
8 Logistic Kernel.
9 Sigmoid Kernel.
10 Silverman Kernel.
H
is the smoothing parameter (bandwidth) of the kernel density estimator. If missing, a default value of one(1) is assumed.
Optimize
is a flag (True/False) for searching and using optimal integer value K (i.e. number of data points). If missing or omitted, optimize is assumed False.
target
is the desired x-value(s) to interpolate for (a single value or a one-dimensional array of cells (e.g. rows or columns)).
Return
is a number that determines the type of return value: 0 = Forecast (default), 1 = errors, 2 = Smoothing parameter (bandwidth), 3 = RMSE (CV). If missing or omitted, NxREG returns forecast/regression value(s).
Return Description
0 Forecast/Regression value(s) (default).
1 Forecast/Regression error(s).
2 Kernel Smoothing parameter (bandwidth).
3 RMSE (cross-validation).

## Remarks

1. The number of rows of the response variable (Y) must be equal to the number of rows of the explanatory variable (X).
2. Observations (i.e. rows) with missing values in X or Y are removed.
3. The NxKREG() function is available starting with version 1.66 PARSON.

## References

• Pagan, A.; Ullah, A. (1999). Nonparametric Econometrics. Cambridge University Press. ISBN 0-521-35564-8.
• Simonoff, Jeffrey S. (1996). Smoothing Methods in Statistics. Springer. ISBN 0-387-94716-7.
• Li, Qi; Racine, Jeffrey S. (2007). Nonparametric Econometrics: Theory and Practice. Princeton University Press. ISBN 0-691-12161-3.
• Henderson, Daniel J.; Parmeter, Christopher F. (2015). Applied Nonparametric Econometrics. Cambridge University Press. ISBN 978-1-107-01025-3.