Description Usage Arguments Value Author(s) References Examples
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.
1 2 3 4 5 6 7 8 9 10 11 12 | vhidetify(
x,
y,
xquant,
yquant,
inv_rob_sdx,
rob_sdy,
asymvec,
inf_set,
non_inf_set,
alpha
)
|
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. |
Vector of index values containing the influential observations id.
inf_setfinal |
The final set of influential observations. |
Amadou Barry barryhafia@gmail.com
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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 | ## 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)
|
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