locpoly              package:KernSmooth              R Documentation

Estimate Functions Using Local Polynomials

Description:

     Estimates a probability density function,   regression function or
     their derivatives using local polynomials. A fast binned
     implementation over an equally-spaced grid is used.

Usage:

     locpoly(x, y, drv = 0, degree =, kernel = "normal", 
             bandwidth, gridsize = 401, bwdisc = 25, 
             range.x, binned = FALSE, truncate = TRUE)

Arguments:

       x: vector of x data. Missing values are not accepted. 

bandwidth: the kernel bandwidth smoothing parameter. It may be a single
          number or an array having length 'gridsize', representing a
          bandwidth that varies according to the location of
          estimation. 

       y: vector of y data. This must be same length as 'x', and
          missing values are not accepted. 

     drv: order of derivative to be estimated. 

  degree: degree of local polynomial used. Its value must be greater
          than or equal to the value of 'drv'. The default value is of
          'degree' is 'drv' + 1. 

  kernel: '"normal"' - the Gaussian density function. 

gridsize: number of equally-spaced grid points over which the  function
          is to be estimated. 

  bwdisc: number of logarithmically-equally-spaced bandwidths on which
          'bandwidth' is discretised, to speed up computation. 

 range.x: vector containing the minimum and maximum values of 'x' at
          which to compute the estimate. 

  binned: logical flag: if 'TRUE', then 'x' and 'y' are taken to be
          grid counts rather than raw data.  

truncate: logical flag: if 'TRUE', data with 'x' values outside the
          range specified by 'range.x' are ignored. 

Value:

     if 'y' is specified, a local polynomial regression estimate of 
     E[Y|X] (or its derivative) is computed. If 'y' is missing, a local
     polynomial estimate of the density of 'x' (or its derivative) is
     computed.

     a list containing the following components:

       x: vector of sorted x values at which the estimate was computed. 

       y: vector of smoothed estimates for either the density or the
          regression at the corresponding 'x'. 

Details:

     Local polynomial fitting with a kernel weight is used to estimate
     either a density, regression function or their derivatives. In the
     case of density estimation, the  data are binned and the local
     fitting procedure is applied to  the bin counts. In either case,
     binned approximations over an equally-spaced grid is used for fast
     computation. The bandwidth may be either scalar or a vector of
     length 'gridsize'.

References:

     Wand, M. P. and Jones, M. C. (1995). _Kernel Smoothing._ Chapman
     and Hall, London.

See Also:

     'bkde', 'density', 'dpill', 'ksmooth', 'loess', 'smooth',
     'supsmu'.

Examples:

     data(geyser, package = "MASS")
     x <- geyser$duration
     est <- locpoly(x, bandwidth = 0.25)
     plot(est, type = "l")
     # local linear density estimate
     y <- geyser$waiting
     plot(x, y)
     fit <- locpoly(x, y, bandwidth = 0.25)
     lines(fit)
     # local linear regression estimate

