lasso function

Adaptive LASSO Estimation for Stochastic Differential Equations

Adaptive LASSO estimation for stochastic differential equations.

lasso(yuima, lambda0, start, delta=1, ...)

Arguments

• yuima: a yuima object.
• lambda0: a named list with penalty for each parameter.
• start: initial values to be passed to the optimizer.
• delta: controls the amount of shrinking in the adaptive sequences.
• ...: passed to optim method. See Examples.

Details

lasso behaves more likely the standard qmle function in and argument method is one of the methods available in optim.

From initial guess of QML estimates, performs adaptive LASSO estimation using the Least Squares Approximation (LSA) as in Wang and Leng (2007, JASA).

Returns

• ans: a list with both QMLE and LASSO estimates.

Author(s)

The YUIMA Project Team

Examples

## Not run:

##multidimension case
diff.matrix <- matrix(c("theta1.1","theta1.2", "1", "1"), 2, 2)

drift.c <- c("-theta2.1*x1", "-theta2.2*x2", "-theta2.2", "-theta2.1")
drift.matrix <- matrix(drift.c, 2, 2)

ymodel <- setModel(drift=drift.matrix, diffusion=diff.matrix, time.variable="t",
                   state.variable=c("x1", "x2"), solve.variable=c("x1", "x2"))
n <- 100
ysamp <- setSampling(Terminal=(n)^(1/3), n=n)
yuima <- setYuima(model=ymodel, sampling=ysamp)
set.seed(123)

truep <- list(theta1.1=0.6, theta1.2=0,theta2.1=0.5, theta2.2=0)
yuima <- simulate(yuima, xinit=c(1, 1), 
 true.parameter=truep)

est <- lasso(yuima, start=list(theta2.1=0.8, theta2.2=0.2, theta1.1=0.7, theta1.2=0.1),
 lower=list(theta1.1=1e-10,theta1.2=1e-10,theta2.1=.1,theta2.2=1e-10),
 upper=list(theta1.1=4,theta1.2=4,theta2.1=4,theta2.2=4), method="L-BFGS-B")

# TRUE
unlist(truep)

# QMLE
round(est$mle,3)

# LASSO
round(est$lasso,3) 
## End(Not run)