dsidr {assist}R Documentation

Interface of dsidr subroutines in RKPACK

Description

To calculate a spline estimate with a single smoothing parameter

Usage

dsidr(y, q, s=NULL, weight=NULL, vmu="v", varht=NULL, 
limnla=c(-10, 3), job=-1, tol=0)

Arguments

y

a numerical vector representing the response.

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(y),dim(H_0)), with elements equal to the bases of H_0 evaluated at design points. Default is NULL, representing an empty NULL space.

weight

A weight matrix for penalized weighted least-square: (y-f)'W(y-f)+nλ J(f). Default is NULL for iid random errors.

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 NULL.

limnla

a vector of length 2, specifying a search range for the n times smoothing parameter on log10 scale. Default is (-10, 3).

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.

tol

tolerance for truncation used in ‘dsidr’. Default is 0.0, which sets to square of machine precision.

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, and info>0 indicates the matrix S is rank deficient with info=rank(S)+1.

fit

fitted values.

c

estimates of c.

d

estimates of d.

resi

vector of residuals.

varht

estimate of variance.

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(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

Gu, C. (1989). RKPACK and its applications: Fitting smoothing spline models. Proceedings of the Statistical Computing Section, ASA, 42-51.

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

See Also

dmudr, gdsidr, gdmudr, ssr


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