semihregScam: Fit the semiparametric harmonic regression with monotone...
In CliffordLai/harper: Harmonic Regression and Periodicity Test

Description Usage Arguments Details Value Author(s) References See Also Examples

Fit the semiparametric harmonic regression with monotone generalzied additive model. It utilizes the R package scam. The estimation procedure iterates between the coefficient of the index term and the smooth monotone P-spline function.

1 2	semihregScam(y, t, lambda0, k = -1, m = 2, bs = c("mpi", "mpd"), family = gaussian())

`y`	A vector containg series as columns.
`t`	A vector of sampled time points.
`lambda0`	The frequency of the harmonic compoenent.
`k`	the dimension of the basis used to represent the smooth term. See `smooth.construct.mpi.smooth.spec` in the R package `scam`.
`m`	m+1 is the order of the B-spline basis. See `smooth.construct.mpi.smooth.spec` in the R package `scam`.
`bs`	specify the usage of monotone increasing/decreasing P-splines ("mpi"/"mpd") as the penalized smoothing basis. See `shape.constrained.smooth.terms` in the R package `scam`.
`family`	A family object specifying the distribution of `z` and link to use in fitting. See `glm` and `family` for more details.

Given frequency λ and phase φ, fit a monotonic smoothing term of sinuosoid with a monotone increasing/decreasing P-splines, i.e.,

E[y_t] = g(a_{1} cos(2πλ t)+a_{2} sin(2πλ t) ),\ t=1,...,n,

where y_{t} consists of independet random variables, a_{1}^2+a_{2}^2=1, g(\cdot) is an unknown strictly monotone function in the range [-1,1], 0<f<0.5, φ\in [0,2π] and σ>0. This can be done by using the R package scam in the R package scam. Since the frequency λ is prespecified in the semiparametric harmonic regression model but the phase φ is unknown, then the estimations of the function g(\cdot) and φ is conducted in a iterative way. The general optimizer optim is used to minimize the UBRE of the fitted with respect to φ.

Object of class "semihregScam" produced.

An object of class "semihregScam" is a list containing the following components:

`harScam`	An object of class `scam`. See `scam` in the R package `scam`.
`lambda0`	The frequency of the harmonic compoenent.
`phi0`	The estimated phase/2pi of the harmonic compoenent.
`esty`	estimated mean for the observations.

Yuanhao Lai

Pya, N., & Wood, S. N. (2015). Shape constrained additive models. Statistics and Computing, 25(3), 543-559.

scam.

# Simulate the series
set.seed(193)
g <- function(x){-2*exp(-x^3)}
n <- 50
t <- 1:n
lambda0 <- 0.123
phi0 <- 0.2*2*pi
u <- cos(2*pi*lambda0*t+phi0)
e <- rnorm(n)
y <- g(u)+e

# Plot ther series
par(mfrow=c(1,2))
plot(t,g(u),type="b")
plot(t,y,type="b")
par(mfrow=c(1,1))

# Pre-estimate the frequency and the phase
lambdaRange <- seq(1/n,0.5-1/n,length.out = 5*n)
paraRankLS <- GetFitRankLS(y,t=1:n,lambdaRange)
paraRankLS    

# Fit the semi-harmonic regression
fit1 <- semihregScam(y,t,lambda0=paraRankLS[2],bs="mpi",family=gaussian())
names(fit1)
fit1$esty

# Prediction for the continuous time.
newt <- seq(1,n,0.05) 
head( predy <- predict(fit1,newt)) 

plot(newt,g(cos(2*pi*lambda0*newt+phi0)),
     type="b",pch=19,main="Semiparametric with scam",
     ylim=c(min(predy[,2])-1,max(predy[,2])+0.5) )
lines(newt,predy[,2],col="red",type="l")