R: Fréchet Change Point Detection for Densities

DenCPD {frechet}

R Documentation

Fréchet Change Point Detection for Densities

Description

Fréchet change point detection for densities with respect to L^2-Wasserstein distance.

Usage

DenCPD(
  yin = NULL,
  hin = NULL,
  din = NULL,
  qin = NULL,
  supin = NULL,
  optns = list()
)

Arguments

`yin`	A matrix or data frame or list holding the sample of measurements for the observed distributions. If `yin` is a matrix or data frame, each row holds the measurements for one distribution.
`hin`	A list holding the histograms for the observed distributions.
`din`	A matrix or data frame or list holding the density functions. If `din` is a matrix or data frame, each row of `din` holds the density function for one distribution.
`qin`	A matrix or data frame or list holding the quantile functions. If `qin` is a matrix or data frame, each row of `qin` holds the quantile function for one distribution. Note that the input can be only one of the four `yin`, `hin`, `din`, and `qin`. If more than one of them are specified, `yin` overwrites `hin`, `hin` overwrites `din`, and `din` overwrites `qin`.
`supin`	A matrix or data frame or list holding the support grids of the density functions in `din` or the quantile functions in `qin`. If `supin` is a matrix or data frame, each row of `supin` holds the support grid of the corresponding density function or quantile function. Ignored if the input is `yin` or `hin`. It can also be a vector if all density functions in `din` or all quantile functions in `qin` have the same support grid.
`optns`	A list of control parameters specified by `list(name = value)`. See 'Details'.

Details

Available control options are

cutOff: A scalar between 0 and 1 indicating the interval, i.e., [cutOff, 1 - cutOff], in which candidate change points lie.
Q: A scalar representing the number of Monte Carlo simulations to run while approximating the critical value (stardized Brownian bridge). Default is 1000.
boot: Logical, also compute bootstrap p-value if TRUE. Default is FALSE.
R: The number of bootstrap replicates. Only used when boot is TRUE. Default is 1000.
nqSup: A scalar giving the number of the support points for quantile functions based on which the L^2 Wasserstein distance (i.e., the L^2 distance between the quantile functions) is computed. Default is 201.
qSup: A numeric vector holding the support grid on [0, 1] based on which the L^2 Wasserstein distance (i.e., the L^2 distance between the quantile functions) is computed. It overrides nqSup.
bwDen: The bandwidth value used in CreateDensity() for density estimation; positive numeric - default: determine automatically based on the data-driven bandwidth selector proposed by Sheather and Jones (1991).
ndSup: A scalar giving the number of support points the kernel density estimation used in CreateDensity(); numeric - default: 101.
dSup: User defined output grid for the support of kernel density estimation used in CreateDensity(), it overrides ndSup.
delta: A scalar giving the size of the bin to be used used in CreateDensity(); numeric - default: diff(range(y))/1000. It only works when the raw sample is available.
kernelDen: A character holding the type of kernel functions used in CreateDensity() for density estimation; "rect", "gauss", "epan", "gausvar", "quar" - default: "gauss".
infSupport: logical if we expect the distribution to have infinite support or not, used in CreateDensity() for density estimation; logical - default: FALSE
denLowerThreshold: FALSE or a positive value giving the lower threshold of the densities used in CreateDensity(); default: 0.001 * mean(qin[,ncol(qin)] - qin[,1]).

Value

A DenCPD object — a list containing the following fields:

`tau`	a scalar holding the estimated change point.
`pvalAsy`	a scalar holding the asymptotic `p`-value.
`pvalBoot`	a scalar holding the bootstrap `p`-value. Returned if `optns$boot` is TRUE.
`optns`	the control options used.

References

Dubey, P. and Müller, H.G., 2020. Fréchet change-point detection. The Annals of Statistics, 48(6), pp.3312-3335.

Examples


set.seed(1)
n1 <- 100
n2 <- 200
delta <- 0.75
qSup <- seq(0.01, 0.99, (0.99 - 0.01) / 50)
mu1 <- rnorm(n1, mean = delta, sd = 0.5)
mu2 <- rnorm(n2, mean = 0, sd = 0.5)
Y1 <- lapply(1:n1, function(i) {
  qnorm(qSup, mu1[i], sd = 1)
})
Y2 <- lapply(1:n2, function(i) {
  qnorm(qSup, mu2[i], sd = 1)
})
Ly <- c(Y1, Y2)
Lx <- qSup
res <- DenCPD(qin = Ly, supin = Lx, optns = list(boot = TRUE))
res$tau # returns the estimated change point
res$pvalAsy # returns asymptotic pvalue
res$pvalBoot # returns bootstrap pvalue

[Package frechet version 0.3.0 Index]