FitMatch {CollocInfer}

Estimating Hidden States

Description

Estimating hidden states to maximize agreement with the process.

Usage

FitMatchOpt(coefs,which,pars,proc,meth='nlminb',control=list())

FitMatchErr(coefs,allcoefs,which,pars,proc,sgn=1)

FitMatchDC(coefs,allcoefs,which,pars,proc,sgn=1)

FitMatchDC2(coefs,allcoefs,which,pars,proc,sgn=1)

FitMatchList(coefs,allcoefs,which,pars,proc,sgn=1)

Arguments

coefs

Vector giving the current estimate of the coefficients for the hidden states.

allcoefs

Matrix giving the coefficients of all the states including initial values for coefs.

which

Vector of indices of states to be estimated.

pars

Parameters to be used for the processes.

proc

proc object defining the state process.

sgn

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

meth

Optimization function currently one of 'nlminb', 'MaxNR', 'optim' or 'trust'.

control

Control object for optimization function.

Details

These routines allow the values of coefficients for some states to be optimized relative to the others. That is, the objective defined by proc is minimized over those states specified in which leaving the others constant. This would be typically done, for example, a smooth is taken to estimate some states non-parametrically, but data is not available on all of them.

A number of optimization routines have been implemented in FitMatchOpt, some experimentation is advised.

Value

FitMatchOpt

A list containing

• coefs The optimized coefficients for all states.

• res The output of the optimization routine.

FitMatchErr

The value of the process likelihood at the current estimated states.

FitMatchDC

The derivative of FitMatchErr with respect to the elements coefs for the states being estimated.

FitMatchDC2

The second derivative of FitMatchErr with respect to the elements coefs for the states being estimated.

FitMatchList

Returns a list with elements value, gradient and hessian given by the output of FitMatchErr, FitMatchDC and FitMatchDC2.

See Also

ParsMatchErr, SplineCoefsErr, inneropt

Examples

###############################
#### Some Data            #####
###############################

data(FhNdata)


###############################
####  Basis Object      #######
###############################

knots = seq(0,20,0.2)
norder = 3
nbasis = length(knots) + norder - 2
range = c(0,20)

bbasis = create.bspline.basis(range=range(FhNtimes),nbasis=nbasis,
	norder=norder,breaks=knots)


# Initial values for coefficients will be obtained by smoothing

fd.data = FhNdata[,1]

DEfd = smooth.basis(FhNtimes,fd.data,fdPar(bbasis,1,0.5))   

coefs = cbind(DEfd$fd$coefs,rep(0,nbasis))
colnames(coefs) = FhNvarnames

#############################################################
### If We Only Observe One State, We Can Re-Smooth Others ### 
#############################################################

profile.obj = LS.setup(pars=FhNpars,coefs=coefs,fn=make.fhn(),
                      basisvals=bbasis,lambda=1000,times=FhNtimes)
lik = profile.obj$lik
proc= profile.obj$proc

#  DD = Matrix(diag(1,200),sparse=TRUE)
#  tDD = t(DD)

fres = FitMatchOpt(coefs=coefs,which=2,pars=FhNpars,proc)

plot(fd(fres$coefs,bbasis))