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 (1-alpha
) confidence band is constructed by taking the (1-alpha
) 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: Distance-To-a-Measure 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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