help mata mm_kern()
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Title

    mm_kern() -- Kernel functions


Syntax

        real matrix mm_kern(k, real matrix z)

        real matrix mm_kint(k, real scalar l [, real matrix z])

        real scalar mm_kdel0(k)

    where       k:  string scalar containing "epanechnikov", "epan2"
                    (default), "biweight", "triweight", "cosine", "gaussian",
                    "parzen", "rectangle" or "triangle"


        real matrix mm_kern_name(real matrix z)

        real matrix mm_kint_name(real scalar l [, real matrix z])

        real scalar mm_kdel0_name()

    where name is   epanechnikov, epan2, biweight, triweight, cosine,
                    gaussian, parzen, rectangle, or triangle


Description

    mm_kern(k, z) returns the value of kernel function k for the input value
    z. k is the kernel's name and may be abbreviated as indicated above.

    mm_kint(k, l, z) returns kernel integrals from minus infinity to z or, if
    z is omitted, from minus infinity to plus infinity. l determines the type
    of integral. Let K(x) denote the kernel function. Then the integrals
    returned for different choices of l are:

        l   integrated function
       -------------------------
        1           K(x)
        2          K(x)^2
        3         x * K(x)
        4        x^2 * K(x)

    Note that mm_kint(k, 2) returns the so-called "roughness" of kernel
    function. mm_kint(k, 4) returns the variance of the kernel function.

    mm_kdel0(k) returns the canonical bandwidth of kernel function k.

    Instead of using the wrappers mm_kern(), mm_kint(), and mm_kdel0() you
    may prefer to apply mm_kern_name(), mm_kint_name(), and mm_kdel0_name()
    directly, where name stands for epanechnikov, epan2, biweight, triweight,
    cosine, gaussian, parzen, rectangle, or triangle.


Remarks

    The formulas for the kernels and their properties can be found in 
    http://fmwww.bc.edu/RePEc/bocode/k/kdens.pdf.


Conformability

    mm_kern(k, z):
             k:  1 x 1
             z:  r x c
        result:  r x c.

    mm_kint(k, l, z):
             k:  1 x 1
             l:  1 x 1
             z:  r x c
        result:  r x c (or 1 x 1 if z is omitted).

    mm_kdel0(k):
             k:  1 x 1
        result:  1 x 1.

    mm_kern_name(z):
             z:  r x c
        result:  r x c.

    mm_kint_name(l, z):
             l:  1 x 1
             z:  r x c
        result:  r x c (or 1 x 1 if z is omitted).

    mm_kdel0_name():
        result:  1 x 1.


Diagnostics

    If argument k in mm_kern(), mm_kint(), and mm_kdel0() is empty (i.e.
    k==""), the epan2 kernel is used.


Source code

    mm_kern.mata


Author

    Ben Jann, ETH Zurich, jann@soz.gess.ethz.ch


Aknowledgements

    Shouts to Matthias Naef for helping me with the math.


Also see

    Online:  help for kdens (if installed), moremata