oldlogspline            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 - _1_9_9_2 _v_e_r_s_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 1992 knot deletion algorithm
     ('oldlogspline').  The 1997 algorithm using knot deletion and
     addition is available using the 'logspline' function.

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

     oldlogspline(uncensored, right, left, interval, lbound,
     ubound, nknots, knots, penalty, delete = TRUE) 

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

uncensored: vector of uncensored observations from the distribution
          whose density is  to be estimated. If there are no uncensored
          observations, this argument can  be omitted. However, either
          'uncensored' or 'interval' must be specified.  

   right: vector of right censored observations from the distribution 
          whose density is to be estimated. If there are no right
          censored  observations, this argument can be omitted.  

    left: vector of left censored observations from the distribution 
          whose density is to be estimated. If there are no left
          censored  observations, this argument can be omitted.  

interval: two column matrix of lower and upper bounds of observations 
          that are interval censored from the distribution whose
          density is  to be estimated. If there are no interval
          censored observations, this  argument can be omitted.  

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'. The default for 'lbound' is '-inf' and the default
          for 'ubound' is 'inf'. 

  nknots: forces the method to start with nknots knots ('delete =
          TRUE') or to fit a  density with nknots knots ('delete =
          FALSE'). The method has an automatic rule  for selecting
          nknots 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 ('delete = TRUE') or to fit a density with
          these knots 'delete = FALSE'). Overrules 'nknots'.  If
          'knots' is not specified, a default knot-placement rule is
          employed.  

 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.oldlogspline'.  

  delete: should stepwise knot deletion be employed?  

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

     Object of the class 'oldlogspline', that is intended as input for
     'plot.oldlogspline',  'summary.oldlogspline',  'doldlogspline'
     (densities),  'poldlogspline' (probabilities),
      'qoldlogspline' (quantiles), 'roldlogspline' (random numbers from
     the fitted distribution). The function 'oldlogspline.to.logspline'
     can translate an object of the class 'oldlogspline' to an object
     of the class 'logspline'.

     The object has the following members: 

    call: the command that was executed.  

  knots : vector of the locations of the knots in the 'oldlogspline'
          model.  old 

    coef: coefficients of the spline. The first coefficient is the
          constant term,  the second is the linear term and the k-th
          (k>2) is the coefficient  of (x-t(k-2))^3_+ (where x^3_+
          means the positive part of the third power of x,  and t(k-2)
          means knot k-2). If a coefficient is zero the corresponding 
          knot was deleted from the model.  

   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.  

    logl: the 'k'-th element is the log-likelihood of the fit with
          'k+2' knots.  

 penalty: the penalty that was used.  

  sample: the sample size that was used.  

  delete: was stepwise knot deletion employed?  

_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:

     'logspline',       'oldlogspline', 'plot.oldlogspline',
     'summary.oldlogspline',
      'doldlogspline', 'poldlogspline', 'qoldlogspline',
     'roldlogspline', 'oldlogspline.to.logspline'.

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

     # A simple example
     y <- rnorm(100)
     fit <- oldlogspline(y)       
     plot(fit)
     # An example involving censoring and a lower bound
     y <- rlnorm(1000)
     censoring <- rexp(1000) * 4
     delta <- 1 * (y <= censoring)
     y[delta == 0] <- censoring[delta == 0]
     fit <- oldlogspline(y[delta == 1], y[delta == 0], lbound = 0)

