msQuantile: Quantile of the multiscale statistics
In essHist: The Essential Histogram

Description Usage Arguments Details Value References See Also Examples

View source: R/main.R View source: R/RcppExports.R

Simulate quantiles of the multiscale statistics under the null hypothesis.

1	msQuantile(n, alpha = c(0.1), nsim = 5000, verbose = TRUE, is.sim = (n < 1e4), ...)

`n`	number of observations
`alpha`	significance level; the (1-`alpha`)-quantile of the null distribution of the multiscale statistic via Monte Carlo simulation
`nsim`	numer of Monte Carlo simulations
`is.sim`	logical. If `TRUE` (default if `n` < 10,000) the quantile is determined via Monte Carlo simulations, which might take a long time; otherwise (default if `n` >= 10,000) it uses the quantile with `n` = 10,000, which has been precomputed and stored.
`verbose`	logical. If `TRUE` (default) it prints some details about the computation; otherwise nothing is printed.
`...`	further arguments passed to function `quantile`.

Empirically, it turns out that the (1-alpha)-quantile of the multiscale statistic converges fast to that of the limit distribution as the number of samples n increases. Thus, for the sake of computational efficiency, the quantile with n = 10,000 are used by default for that with n > 10,000, which has already been precomputed and stored. Of course, for arbitrary sample size n, one can always simulate the quantile by setting is.sim = TRUE, and use the precomputed value by setting is.sim = FALSE. For a given sample size n, simulations are once computed, and then automatically recorded in main memory for later usage.

A vector of length length(alpha) is returned, the same structure as returned by funtion quantile. See Li et al. (2016) for further details.

Li, H., Munk, A., Sieling, H., and Walther, G. (2016). The essential histogram. arXiv:1612.07216.

essHistogram

n    = 100 # number of observations
nsim = 100 # number of simulations

alpha = c(0.1, 0.9) # significance level
q     = msQuantile(n, alpha, nsim)

print(q)