logspline             package:polspline             R Documentation

_L_o_g_s_p_l_i_n_e _D_e_n_s_i_t_y _E_s_t_i_m_a_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     Fits a 'logspline' density using splines to approximate the
     log-density using  the 1997 knot addition and deletion algorithm
     ('logspline').  The 1992 algorithm is available using the
     'oldlogspline' function.

_U_s_a_g_e:

     logspline(x, lbound, ubound, maxknots = 0, knots, nknots = 0, penalty,
     silent = TRUE, mind = -1) 

_A_r_g_u_m_e_n_t_s:

       x: data vector. The data needs to be uncensored. 'oldlogspline'
          can deal with right- left- and interval-censored data.  

lbound,ubound: lower/upper bound for the support of the density. For
          example, if there  is a priori knowledge that the density
          equals zero to the left of 0,  and has a discontinuity at 0, 
          the user could specify 'lbound = 0'. However, if the density
          is   essentially zero near 0, one does not need to specify
          'lbound'.  

maxknots: the maximum number of knots. The routine stops adding knots 
          when this number of knots is reached.  The method has an
          automatic rule  for selecting maxknots if this parameter is
          not specified.  

   knots: ordered vector of values (that should cover the complete
          range of the  observations), which forces the method to start
          with these knots.  Overrules knots.          If 'knots' is
          not specified, a default knot-placement rule is employed.  

  nknots: forces the method to start with 'nknots' knots.  The method
          has an automatic rule  for selecting 'nknots' if this
          parameter is not specified.  

 penalty: the parameter to be used in the AIC criterion. The method
          chooses  the number of knots that minimizes '-2 *
          loglikelihood + penalty * (number of knots - 1)'.  The
          default  is to use a penalty parameter of 'penalty =
          log(samplesize)' as in BIC. The effect of  this parameter is
          summarized in 'summary.logspline'.  

  silent: should diagnostic output be printed?  

    mind: minimum distance, in order statistics, between knots.  

_V_a_l_u_e:

     Object of the class 'logspline', that is intended as input for
     'plot.logspline' (summary plots),  'summary.logspline' (fitting
     summary),  'dlogspline' (densities),  'plogspline'
     (probabilities), 'qlogspline' (quantiles), 'rlogspline' (random
     numbers from the fitted distribution).

     The object has the following members: 

    call: the command that was executed.

  nknots: the number of knots in the model that was selected.

coef.pol: coefficients of the polynomial part of the spline. The first
          coefficient is the constant term and the second is the linear
          term.

coef.kts: coefficients of the knots  part of the spline. The 'k'-th
          element is the coefficient  of (x-t(k))^3_+ (where x^3_+
          means the positive part of the third power of x,  and t(k)
          means knot 'k').

   knots: vector of the locations of the knots in the 'logspline'
          model.

maxknots: the largest number of knots minus one considered during
          fitting (i.e. with 'maxknots = 6' the maximum number of knots
          is 5).

 penalty: the penalty that was used.  

   bound: first element: 0 - 'lbound' was -infinity, 1 it was something
          else; second  element: 'lbound', if specified; third element:
          0 - 'ubound' was infinity,  1 it was something else; fourth
          element: 'ubound', if specified.  

 samples: the sample size.

    logl: 

   range: range of the input data.

    mind: minimum distance in order statistics between knots required
          during fitting (the actual minimum distance may be much
          larger).

_A_u_t_h_o_r(_s):

     Charles Kooperberg clk@fhcrc.org.

_R_e_f_e_r_e_n_c_e_s:

     Charles Kooperberg and Charles J. Stone.  Logspline density
     estimation for censored data (1992). _Journal of Computational and
     Graphical Statistics_, *1*, 301-328.

     Charles J. Stone, Mark Hansen, Charles Kooperberg, and Young K.
     Truong. The use of polynomial splines and their tensor products in
     extended linear modeling (with discussion) (1997).  _Annals of
     Statistics_, *25*, 1371-1470.

_S_e_e _A_l_s_o:

     'plot.logspline',  'summary.logspline', 'dlogspline', 
     'plogspline', 'qlogspline', 
      'rlogspline', 'oldlogspline'.

_E_x_a_m_p_l_e_s:

     y <- rnorm(100)
     fit <- logspline(y)       
     plot(fit)
     # as (4 == length(-2, -1, 0, 1, 2) -1), this forces these initial knots,
     # and does no knot selection
     fit <- logspline(y, knots = c(-2, -1, 0, 1, 2), maxknots = 4, penalty = 0)  

