SplineEst {CollocInfer}

Spline Estimation Functions

Description

Model-based smoothing; estimation, objective criterion and derivatives.

Usage

SplineEst.NewtRaph(coefs,times,data,lik,proc,pars,
      control=list(reltol=1e-12,maxit=1000,maxtry=10,trace=0))
      
SplineCoefsList(coefs,times,data,lik,proc,pars,sgn=1)

SplineCoefsErr(coefs,times,data,lik,proc,pars,sgn=1)

SplineCoefsDC(coefs,times,data,lik,proc,pars,sgn=1)

SplineCoefsDP(coefs,times,data,lik,proc,pars,sgn=1)

SplineCoefsDC2(coefs,times,data,lik,proc,pars,sgn=1)

SplineCoefsDCDP(coefs,times,data,lik,proc,pars,sgn=1)

Arguments

coefs

Vector giving the current estimate of the coefficients in the spline.

times

Vector observation times for the data.

data

Matrix of observed data values.

lik

lik object defining the observation process.

proc

proc object defining the state process.

pars

Parameters to be used for the processes.

sgn

Is the minimizing (1) or maximizing (0)?

control

A list giving control parameters for Newton-Raphson optimization. It should contain

• reltol Relative tollerance criterion for the gradient and improvement before termination.

• maxit Maximum number of iterations.

• maxtry Maximum number of halving-steps to try before declaring no improvement is possible.

• trace How much iteration history to output; 0 surpresses all output, a positive value outputs parameters and improvement at each iteration.

Details

SplineEst.NewtRaph performs a simple Newton-Raphson estimate for the optimal value of the coefficients. This estimate lacks the convergence checks of other estimation packages, but may yeild a fast solution when needed.

Value

SplineEst.NewtRaph

Returns a list that is the result of the optimization with elements

• value The final objective criterion.

• coefs The optimizing value of the coefficients.

• g The gradient at the optimizing value.

• H The Hessian at the optimizing value.

SplineCoefsList

Collates the gradient calculations and returns a list with elements

• value Output of SplineCoefsErr

• gradient Output of SplineCoefsDC

• Hessian Output of SplineCoefsDC2

SplineCoefsErr

The complete data log likelihood for the smooth; the inner optimization objective.

SplineCoefsDC

The derivative of SplineCoefsErr with respect to coefs.

SplineCoefsDP

The derivative of SplineCoefsErr with respect to pars.

SplineCoefsDC2

The second derivative of SplineCoefsErr with respect to coefs.

SplineCoefsDCDP

The second derivative of SplineCoefsErr with respect to coefs and pars.

The output of gradients is in terms of an array with dimensions corresponding to derivatives. Derivatives with with respect to coefficients are given in dimensions before those that give derivatives with respect to parameters.

See Also

inneropt, Smooth.LS