LebA_slice_est {ambit}

Nonparametric estimation of the trawl (sub-) sets Leb(A), Leb(A intersection A_h), Leb(A setdifference A_h)

Description

This function estimates Leb(A), Leb(A intersection A_h), Leb(A\ A_h).

Usage

LebA_slice_est(data, Delta, h, biascor = FALSE)

Arguments

data

Data to be used in the trawl function estimation.

Delta

Width of the grid on which we observe the data

h

Time point used in A intersection A_h and the setdifference A setdifference A_h

biascor

A binary variable determining whether a bias correction should be computed, the default is FALSE

Details

Estimation of the trawl function using the methodology proposed in Sauri and Veraart (2022).

Value

LebA

LebAintersection

LebAsetdifference

Examples

##Simulate a trawl process
##Determine the sampling grid
my_n <- 5000
my_delta <- 0.1
my_t <- my_n*my_delta

###Choose the model parameter
#Exponential trawl function:
my_lambda <- 2
#Poisson marginal distribution trawl
my_v <- 1

#Set the seed
set.seed(1726)
#Simulate the trawl process
Poi_data<-ambit::sim_weighted_trawl(my_n, my_delta, "Exp", my_lambda, "Poi", my_v)$path

#Estimate the trawl set and its two slices at time h=2 without bias correction
est1 <- LebA_slice_est(Poi_data, my_delta, h=2)
est1$LebA
est1$LebAintersection
est1$LebAsetdifference

#Estimate the trawl set and its two slices at time h=2 without bias correction
est2 <- LebA_slice_est(Poi_data, my_delta, h=2, biascor=TRUE)
est2$LebA
est2$LebAintersection
est2$LebAsetdifference

#Note that Leb(A)=1/my_lambda for an exponential trawl