gdsidr: Interface of dbsdr, dbisdr, dgsdr, dpsdr in GRKPACK.

In assist: A Suite of R Functions Implementing Spline Smoothing Techniques

Interface of dbsdr, dbisdr, dgsdr, dpsdr in GRKPACK.

Description

To calculate a spline estimate with single smoothing parameter for non-Gaussian data.

Usage

gdsidr(y, q, s, family, vmu="v", varht=NULL, limnla=c(-10, 3), 
maxit=30, job=-1, tol1=0, tol2=0, prec=1e-06)

Arguments

y	a numerical vector representing the response, or a matrix of two columns for binomial data with the first column as the largest possible counts and the second column as the counts actually obsered.
q	a square matrix of the same order as the length of y, with elements equal to the reproducing kernel evaluated at the design points.
s	the design matrix of the null space H_0 of size (length-of-y,dim(H_0)), with elements equal to the bases of H_0 evaluated at design points.
family	a string specifying the family of distribution. Families supported are "binary", "binomial", "poisson" and "gamma" for Bernoulli, binomial, poisson, and gamma distributions respectively. Canonical links are used except for Gamma family where a log link is used.
vmu	a character string specifying a method for choosing the smoothing parameter. "v", "m" and "u" represent GCV, GML and UBR respectively. "u\sim", only used for non-Gaussian family, specifies UBR with estimated variance. Default is "v".
varht	needed only when vmu="u", which gives the fixed variance in calculation of the UBR function. Default is 1.0.
limnla	a vector of length 2, specifying a search range for the n times smoothing parameter on log10 scale. Default is (-10, 3).
maxit	maximum number of iterations allowed for the iteration in GRKPACK.
job	an integer representing the optimization method used to find the smoothing parameter. The options are job=-1: golden-section search on (limnla(1), limnla(2)); job=0: golden-section search with interval specified automatically; job >0: regular grid search on [limnla(1), limnla(2)] with the number of grids = job + 1. Default is -1.
tol1	the tolerance for elements of w's. Default is 0.0 which sets to square of machine precision.
tol2	tolerance for truncation used in ‘dsidr’. Default is 0.0 which sets to square of machine precision.
prec	precision requested for stopping the iteration. Default is 1e-06.

Value

info	an integer that provides error message. info=0 indicates normal termination, info=-1 indicates dimension error, info=-2 indicates F_{2}^{T} Q F_{2} !>= 0, info=-3 indicates vmu is out of scope, info=-4 indicates the algorithm fails to converge at the maxiter steps, info=-5 indicates there are some w's equals to zero, and info>0 indicates the matrix S is rank deficient with info=rank(S)+1.
fit	estimate of the function at design points.
c	estimates of c.
d	estimates of d.
resi	vector of working residuals.
varht	estimate of dispersion parameter.
nlaht	the estimate of log10(nobs*lambda).
limnla	searching range for nlaht.
score	the minimum GCV/GML/UBR score at the estimated smoothing parameter. When job>0, it gives a vector of GCV/GML/UBR functions evaluated at regular grid points.
df	equavilent degree of freedom.
nobs	length-of-y, number of observations.
nnull	dim(H_0), number of bases.
s,qraux,jpvt	QR decomposition of S=FR, as from Linpack ‘dqrdc’.
q	first dim(H_0) columns gives F^{T} Q F_{1}, and its bottom-right corner gives tridiagonalization of F_{2}^{T} Q F_{2}.

Author(s)

Chunlei Ke [e-mail] and Yuedong Wang [e-mail]

References

Wahba, G. (1990). Spline Models for Observational Data. SIAM, Vol. 59.

Wang, Y. (1997). GRKPACK: Fitting Smoothing Spline ANOVA Models for Exponential Families. Communications in Statistics: Simulation and Computation, 24: 1037-1059.

See Also

dsidr, dmudr, gdmudr, ssr

assist documentation built on Aug. 22, 2023, 9:12 a.m.