Description Usage Arguments Details Value Note References See Also Examples

Simulate quantiles of the multiscale statistics under any continuous distribution function.

1 2 |

`n` |
number of observations. |

`alpha` |
significance level; default as 0.5, see also |

`nsim` |
numer of Monte Carlo simulations. |

`is.sim` |
logical. If |

`intv` |
a data frame provides the system of intervals on which the multiscale statistic is defined. The data frame constains the following two columns
By default, it is set to the sparse interval system proposed by Rivera and Walther (2013), see |

`mode` |
See Li et al. (2016) for further details. |

`...` |
further arguments passed to function |

Empirically, it turns out that the quantile of the multiscale statistic converges fast to that of the limit distribution as the number of observations `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 the R memory for later usage. For memory efficiency, only the last simulation is stored.

A vector of length `length(alpha)`

is returned, the same structure as returned by funtion `quantile`

with option `names = FALSE`

; The values are the (1-`alpha`

)-quantile(s) of the null distribution of the multiscale statistic via Monte Carlo simulation, corresponding to (1-`alpha`

)-confidence level(s). See Li et al. (2016) for further details.

All the printing messages can be disabled by calling `suppressMessages`

.

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

Rivera, C., & Walther, G. (2013). Optimal detection of a jump in the intensity of a Poisson process or in a density with likelihood ratio statistics. Scand. J. Stat. 40, 752–769.

`checkHistogram`

,
`essHistogram`

,
`genIntv`

1 2 3 4 5 6 7 | ```
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)
``` |

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