gdsidr {assist}R Documentation

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~", 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 \#(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 chunlei\_ke@pstat.ucsb.edu and Yuedong Wang yuedong@pstat.ucsb.edu

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


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