semihregScair: Fit the semiparametric harmonic regression with monotone...

In CliffordLai/harper: Harmonic Regression and Periodicity Test

Description

Fit the semiparametric harmonic regression with monotone generalzied additive index model by maximizing non-parametric likelihood. It utilizes the function scair in the R package scar.

Usage

semihregScair(y, t, lambda0, shape = c("l", "in", "de", "cvxin", "cvxde",
  "ccvin", "ccvde"), family = gaussian(), ...)

Arguments

y	A vector containg series as columns.
t	A vector of sampled time points.
lambda0	The frequency of the harmonic compoenent.
shape	The shape constraint for the function g. See scair in the R package scar.
family	a description of the error distribution and link function to be used in the model. Default is gaussian(). See scair.
...	Additional parameters passed to scair.

Details

Given frequency λ, fit a monotonic single index model with the likelihood method, i.e.,

E[y_t] = μ+g( A\cos(2πλ t)+B\sin(2π λ 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 [0,1], 0<f<0.5, A^2 + B^2 =1 and σ>0.

This is done by using the R package scar. For more details, see scair in the R package scar.

Value

Object of class "semihregScair" produced.

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

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

Author(s)

Yuanhao Lai

References

Chen, Y. and Samworth, R. J. (2014). Generalised additive and index models with shape constraints. arXiv:1404.2957.

See Also

scair.

Examples

# 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 <- semihregScair(y,t,lambda0=paraRankLS[2],shape="in",iter=100)
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 scair",
     xlab="t", ylab="g(u)",
     ylim=c(min(predy[,2])-1,max(predy[,2])+0.5) )
lines(newt,predy[,2],col="red",type="b")

CliffordLai/harper documentation built on May 8, 2019, 1:53 p.m.