RandomCoefficients (version 0.0.2)

rc_estim: Adaptive estimation of the joint density of random coefficients model in a linear random coefficient model

Description

This function implements the adaptive estimation of the joint density of random coefficients model as in Gaillac and Gautier (2019). It takes as inputs data (Y,X) then estimates the density and return its evaluation on a grid b_grid times a_grid. By setting nbCores greater than 1 computations are done in parallel.

Usage

rc_estim(X, Y, b_grid, a_grid = b_grid, nbCores = 1, M_T = 60,
  N_u = 10, epsilon = (log(N)/log(log(N)))^(-2), n_0 = 0,
  trunc = 0, center = 0)

Arguments

X

Vector of size $N$, $N$ being the number of observation and the number of regressors limited to 1 in this version of the package.

Y

Outcome vector of size $N $.

b_grid

vector grid on which the estimator of the density of the random slope will we evaluated.

a_grid

Vector grid on which the estimator of the density of the random intercept will we evaluated.

nbCores

number of cores for the parallel implementation. Default is 1, no parallel computation.

M_T

number of discretisation points for the estimated partial Fourier transform. Default is 60.

N_u

aximal number of singular functions used in the estimation. Default is the maximum of 10 and $N_max$.

epsilon

parameter for the interpolation. Default is (log(N)/log(log(N)))^(-4) as is (T5.1) in Gaillac and Gautier (2019).

n_0

Parameter for the sample splitting. If n_0 = 0 then no sample splitting is done and we use the same sample of size $N$ to perform the estimation of the truncated density. If n_0 >0 , then this is the size of the sample used to perform the estimation of the truncated density. Default is $n_0 =0$.\

trunc

Dummy for the truncation of the density of the regressors to an hypercube [x_0,x_0]^p. If trunc=1, then truncation is performed and [x_0,x_0]^p is defined using the argmin of the ratio of the estimated constant c_X over the percentage of observation in [x_0,x_0]^p. Default is 0, no truncation.

center

Dummy to trigger the use of X -x_bar instead of $X$ as regressor. If center=1, then use X - x_bar where x_bar is the vector of the medians coordinates by coordinates for $X$. Default is center=0, where regressors are left unchanged.

Value

a list containing, in order:

- outcome : the matrix of size length(b_grid)x length(a_grid) which contains the evaluation of the estimator of the density on the grid b_grid times a_grid

- b_grid : vector grid on which the estimator of the density is evaluated for the random slope

- a_grid : vector grid on which the estimator of the density is evaluated for the random intercept

- x_bar : vector used to center the regressors, if center=1

- n_f_X : estimated supnorm of the inverse of the density of the regressors

- und_X : parameter x_0 used for the truncation (truncate =1) of the density of the regressors.

Examples

# NOT RUN {
library(orthopolynom)
library(polynom)
library(tmvtnorm)
library(ks)
library(sfsmisc)
library(snowfall)
library(fourierin)
library(rdetools)
library(statmod)
library(RCEIM)
library(robustbase)
library(VGAM)
library(RandomCoefficients)

# beta (output) Grid
M=100
limit =7.5
b_grid  <- seq(-limit ,limit ,length.out=M)
a = limit

up =1.5
down = -up
und_beta <- a
x2 <- b_grid
x.grid <- as.matrix(expand.grid(b_grid ,b_grid ))
# DATA generating process
d = 1
Mean_mu1 = c(-2,- 3)
Mean_mu2= c(3,  0)
Sigma= diag(2, 2)
Sigma[1,2] = 1
Sigma[2,1] = 1
limit2 = 6

# }
# NOT RUN {
N <- 1000
xi1 <- rtmvnorm(N, mean = Mean_mu1, sigma=Sigma, lower=c( -limit2,-limit2), upper=c(limit2,limit2))
xi2 <- rtmvnorm(N, mean = Mean_mu2, sigma=Sigma, lower=c( -limit2,-limit2), upper=c(limit2,limit2))
theta = runif(N, -1 , 1)
beta <- 1*(theta >=0) * xi1  + 1*(theta <0) * xi2
X <- rtmvnorm(N, mean = c(0), sigma=2.5, lower=c( down), upper=c(up))
X_t <- cbind(matrix(1, N,1),X)
Y <-rowSums(beta*X_t)
out <- rc_estim( X,Y,b_grid,b_grid,nbCores = 1, M_T = 60)
# }
# NOT RUN {

# }