hidetify (version 0.0.1)

vhidetify: Compute the single influence measure to validate the estimated influential set.

Description

This function is part of the algorithm which identify multiple influential observations in high dimension. It applies a single detection technique to validate the estimated influential set.

Usage

vhidetify(
    x, 
    y, 
    xquant, 
    yquant, 
    inv_rob_sdx, 
    rob_sdy, 
    asymvec, 
    inf_set, 
    non_inf_set, 
    alpha
    )

Arguments

x

Matrix of the predictors.

y

Numeric vector of the response variable.

xquant

Matrix of the quantiles of the predictors.

yquant

Numeric vector of the quantiles of the response variable.

inv_rob_sdx

Numeric vector of the inverse of the median absolute deviation of the predictors.

rob_sdy

Median absolute deviation of the response variable.

asymvec

Numeric vector of the asymmetric values or percentiles. It is suggested to choose 3 asymmetric points within the quartile.

inf_set

Estimated set of influential observations

non_inf_set

Estimated set of non-influential observations

alpha

Significance level.

Value

Vector of index values containing the influential observations id.

inf_setfinal

The final set of influential observations.

References

Barry, A., Bhagwat, N., Misic, B., Poline, J.-B., and Greenwood, C. M. T. (2020). Asymmetric influence measure for high dimensional regression. Communications in Statistics - Theory and Methods.

Barry, A., Bhagwat, N., Misic, B., Poline, J.-B., and Greenwood, C. M. T. (2021). An algorithm-based multiple detection influence measure for high dimensional regression using expectile. arXiv: 2105.12286 [stat]. arXiv: 2105.12286.

Examples

# NOT RUN {
## Simulate a dataset where the first 10 observations are influentials
require("MASS")
# the vector of asymmetric point
asymvec  <- c(0.25,0.5,0.75)

# the parameter of interest
beta_param <- c(3,1.5,0,0,2,rep(0,1000-5))

# the contamination parameter 
gama_param <- c(0,0,1,1,0,rep(1,1000-5))

# Covariance matrice for the predictors distribution 
sigmain <- diag(rep(1,1000))
for (i in 1:1000)
{
  for (j in i:1000) 
  {
    sigmain[i,j] <- 0.5^(abs(j-i))
    sigmain[j,i] <- sigmain[i,j]
  }
}

# set the seed
set.seed(13)

# the predictor matrix
x  <- mvrnorm(100, rep(0, 1000), sigmain)

# the error variable
error_var <- rnorm(100)

# the response variable
y  <- x %*% beta_param + error_var
y <- as.numeric(y)

### Generate influential observations

# the contaminated response variable
youtlier <- y
youtlier[1:10] <- x[1:10,] %*% (beta_param +  1.2*gama_param)  + error_var[1:10]
youtlier <- as.numeric(youtlier)

# the quantile of the predictors
xquant <- apply(x,2,quantile,asymvec)

# the quantile of contaminated response variable
yquant <- quantile(youtlier,asymvec)

# the inverse of the mad predictors
inv_rob_sdx <- 1/apply(x,2,mad)

# the mad contaminated response variable
rob_sdy <- mad(youtlier)

# the number of random subsets
number_subset <- 5

# the size of random subsets
size_subset <- 100/2

# the initial clean set
est_clean_set <- 1:100

# influential set
inf_set <- 1:20

# non-influential set
non_inf_set <- 21:100

# the significance level
alpha <- 0.05

final_inf_set <-
  vhidetify(
    x, 
    youtlier, 
    xquant, 
    yquant, 
    inv_rob_sdx, 
    rob_sdy, 
    asymvec, 
    inf_set, 
    non_inf_set, 
    alpha)
    
# }