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assist (version 2.0)

dmudr: Interface of dmudr subroutine in RKPACK

Description

To calculate a spline estimate with multiple smoothing parameters

Usage

dmudr(y, q, s, weight = NULL, vmu = "v", theta = NULL, varht = NULL, 
    tol = 0, init = 0, prec = 1e-06, maxit = 30)

Arguments

y
a numerical vector representing the response.
q
a list, or an array, of square matrices of the same order as the length of y, which are the reproducing kernels 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.
weight
a weight matrix for penalized weighted least-square: $(y-f)'W(y-f)+n\lambda J(f)$. 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$\sim$", only used for non-Gaussian family, specifies UBR with estimated variance. Default is "v".
theta
If `init=1', theta includes intial values for smoothing parameters. Default is NULL.
varht
needed only when vmu="u", which gives the fixed variance in calculation of the UBR function. Default is NULL.
tol
the tolerance for truncation in the tridiagonalization. Default is 0.0.
init
an integer of 0 or 1 indicating if initial values are provided for theta. If init=1, initial values are provided using theta. Default is 0.
prec
precision requested for the minimum score value, where precision is the weaker of the absolute and relative precisions. Default is $1e-06$.
maxit
maximum number of iterations allowed. Default is 30.

Value

  • infoan integer that provides error message. info=-1 indicates dimension error, info=-2 indicates $F_{2}^{T} Q_{*}^{\theta} F_{2} !>= 0$, info=-3 indicates tuning parameters are out of scope, info=-4 indicates fails to converge within maxite steps, info=-5 indicates fails to find a reasonable descent direction, info>0 indicates the matrix S is rank deficient with $info=rank(S)+1$.
  • fitfitted values.
  • cestimates of c.
  • destimates of d.
  • resivector of residuals.
  • varhtestimate of variance.
  • thetaestimates of parameters $log10(\theta)$.
  • nlahtthe estimate of $log10(nobs*\lambda)$.
  • scorethe minimum GCV/GML/UBR score at the estimated smoothing parameters.
  • dfequavilent degree of freedom.
  • nobslength(y), number of observations.
  • nnulldim($H_0$), number of bases.
  • nqlength(rk), number of reproducing kernels.
  • s,q,ychanged from the inputs.

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

dsidr, gdsidr, gdmudr, ssr