View source: R/bootstrapBand.R
bootstrapBand  R Documentation 
The function bootstrapBand
computes a uniform symmetric confidence band around a function of the data X
, evaluated on a Grid
, using the bootstrap algorithm. See Details and References.
bootstrapBand( X, FUN, Grid, B = 30, alpha = 0.05, parallel = FALSE, printProgress = FALSE, weight = NULL, ...)
X 
an n by d matrix of coordinates of points used by the function 
FUN 
a function whose inputs are an n by d matrix of coordinates 
Grid 
an m by d matrix of coordinates, where m is the number of points in the grid, at which 
B 
the number of bootstrap iterations. 
alpha 

parallel 
logical: if 
printProgress 
if 
weight 
either NULL, a number, or a vector of length n. If it is NULL, weight is not used. If it is a number, then same weight is applied to each points of 
... 
additional parameters for the function 
First, the input function FUN
is evaluated on the Grid
using the original data X
. Then, for B
times, the bootstrap algorithm subsamples n
points of X
(with replacement), evaluates the function FUN
on the Grid
using the subsample, and computes the l_∞ distance between the original function and the bootstrapped one. The result is a sequence of B
values. The (1alpha
) confidence band is constructed by taking the (1alpha
) quantile of these values.
The function bootstrapBand
returns a list with the following elements:
width 
number: ( 
fun 
a numeric vector of length m, storing the values of the input function 
band 
an m by 2 matrix that stores the values of the lower limit of the confidence band (first column) and upper limit of the confidence band (second column), evaluated over the 
Jisu Kim and Fabrizio Lecci
Wasserman L (2004). "All of statistics: a concise course in statistical inference." Springer.
Fasy BT, Lecci F, Rinaldo A, Wasserman L, Balakrishnan S, Singh A (2013). "Statistical Inference For Persistent Homology: Confidence Sets for Persistence Diagrams." (arXiv:1303.7117). Annals of Statistics.
Chazal F, Fasy BT, Lecci F, Michel B, Rinaldo A, Wasserman L (2014). "Robust Topological Inference: DistanceToaMeasure and Kernel Distance." Technical Report.
kde
, dtm
# Generate data from mixture of 2 normals. n < 2000 X < c(rnorm(n / 2), rnorm(n / 2, mean = 3, sd = 1.2)) # Construct a grid of points over which we evaluate the function by < 0.02 Grid < seq(3, 6, by = by) ## bandwidth for kernel density estimator h < 0.3 ## Bootstrap confidence band band < bootstrapBand(X, kde, Grid, B = 80, parallel = FALSE, alpha = 0.05, h = h) plot(Grid, band[["fun"]], type = "l", lwd = 2, ylim = c(0, max(band[["band"]])), main = "kde with 0.95 confidence band") lines(Grid, pmax(band[["band"]][, 1], 0), col = 2, lwd = 2) lines(Grid, band[["band"]][, 2], col = 2, lwd = 2)
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