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help scdensity
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Univariate self-consistent density estimation

Syntax

        scdensity varname [if] [in] [ , generate(newvar1 [newvar2]) n(#)
                 range(# #) nograph name(name[, replace]) ]


Description

    scdensity is an implementation of the self-consistent density estimator
    as described in Bernacchia & Pigolotti (2011).  The self-consistent
    method is a non-parametric way to estimate a density from a number of
    data points without relying on any a-priori fixation of parameters like
    smoothing parameters in kernel density estimation, for example.

Options 

    generate() generates new variable(s). One or two (new) variable names can
        be specified. If one name is specified, scdensity saves the density
        estimate in a new variable. If two variables are requested, scdensity
        saves the density estimate and the grid points, at which the density
        is evaluated.

    n() Number of grid points to be used at which the density is evaluated.
        If the number of data points is greater than N=1000, the number of
        grid points defaults to n=1000. If the number of data points is lower
        than N=1000, the number of grid points defaults to n=N.  If a number
        larger than the actual sample size is requested, n is set to N.

    range() Defines the grid range at which the density is to be evaluated.
        Per default, the endpoints of the evaluation grid are determined by
        the minimum and maximum value of the actual data points and the
        range() option can be used to change this default behavior.  The
        input of two numbers is required with the first one being the minimum
        and the second one being the maximum of the range.

    nograph Suppresses the graph. This can be useful in combination with the
        generate() option.

    name() Name of the graph.

Saved results 

    scdensity saves the following in r():

    Scalars   
      r(n_points)    Number of evaluation points
      r(range_min)   Minimum grid point
      r(range_max)   Maximum grid point

Dependencies

    scdensity requires moremata (Jann 2005), available from SSC.  Type -ssc
        install moremata- in Stata to obtain it. Also, scdensity requires
        Stata version 9.2 or higher.

Example

    . webuse nhanes2

    . scdensity height

References 

    Bernacchia, A. & Pigolotti, S. (2011). Self-Consistent Method For Density
    Estimation Journal of the Royal Statistical Society B, 73(3), 407-422.

    Jann, B. (2005). "MOREMATA: Stata module (Mata) to provide various
    functions," Statistical Software Components S455001, Boston College
    Department of Economics, revised 19 Feb 2009.

Acknowledgment 

    I am thankful to Alberto Bernacchia (Yale University) for helpful
    discussions and sharing his R code.

Author

    Joerg Luedicke
    Yale University and University of Florida
    United States
    email: joerg.luedicke@ufl.edu


Also see