hidetify (version 0.0.1)

mhidetify: Multiple detection asymmetric influential measure for high dimensional linear regression.

Description

The function computes the asymmetric influential measure to identify influential observations in high dimensional linear regression using the multiple detection approach.

Usage

mhidetify(
  x, 
  y, 
  number_subset, 
  size_subset, 
  asymvec, 
  ep=0.1, 
  alpha_swamp, 
  alpha_mask, 
  alpha_validate
  )

Arguments

x

Matrix of the predictors.

y

Numeric vector of the response variable.

number_subset

Number of random subsets, default is 5.

size_subset

Size of the random subsets. The default is half of the initial sample size.

asymvec

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

ep

Threshold value to ensure that the estimated clean set is not empty. The default value is 0.1.

alpha_swamp

Significance level for the swamping stage.

alpha_mask

Significance level for the masking stage.

alpha_validate

Significance level for the validation stage.

Value

A dataframe with two variables.

ind

Index of the subjects of the sample

outlier_ind

Influential observations indicator: 1 is influential and 0 otherwise

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)


# number of random subsets
number_subset <- 5

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

# the significance level for the swamping stage
alpha_swamp <- 0.1

# the significance level for the masking stage
alpha_mask <- 0.01

# the significance level for the validation stage
alpha_validate <- 0.01

# Threshold value to ensure that the estimated clean set is not empty. 
ep <- 0.1

out <- 
  mhidetify(
    x, 
    youtlier, 
    number_subset, 
    size_subset, 
    asymvec, 
    ep, 
    alpha_swamp, 
    alpha_mask,
    alpha_validate)

# }