Description Usage Arguments Details Value Note References See Also Examples

Compute the essential histogram via (pruned) dynamic programming.

1 2 3 | ```
essHistogram(x, alpha = 0.5, q = NULL, intv = NULL, plot = TRUE,
mode = ifelse(anyDuplicated(x),"Gen","Con"),
xname = deparse(substitute(x)), ...)
``` |

`x` |
a numeric vector containing the data. |

`alpha` |
significance level; default as 0.5. One should set |

`q` |
threshold value; by default, |

`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 also Li et al. (2016). |

`plot` |
logical. If |

`mode` |
By default, |

`xname` |
a character string with the actual |

`...` |
further arguments and |

The essential histogram is defined as the histogram with least blocks within the multiscale constraint. The one with highest likelihood is picked if there are more than one solutions. The essential histogram involves only one parameter `q`

, the threshold of the multiscale constraint. Such a parameter can be chosen by means of the significance level `alpha`

, which leads to nature statistical significance statements for the multiscale constraint. The computational complexity is often linear in terms of sample size, although the worst complexity bound is quadratic up to a log-factor in case of the sparse interval system. See Li et al. (2016) for further details.

An object of class "`histogram`

", which is of the same class as returned by function `hist`

.

The argument `intv`

is internally adjusted to ensure it contains no empty intervals, especially in case of tied observations. The first block of the returned histogram is a closed interval, and the rest blocks are left open right closed intervals. 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`

,
`genIntv`

,
`hist`

,
`msQuantile`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
# Simulate data
set.seed(123)
type = 'skewed_unimodal'
n = 500
y = rmixnorm(n, type = type)
# Compute the essential histogram
eh = essHistogram(y, plot = FALSE)
# Plot results
# compute oracle density
x = sort(y)
od = dmixnorm(x, type = type)
# compare with orcle density
plot(x, od, type = "l", xlab = NA, ylab = NA, col = "red", main = type)
lines(eh)
legend("topleft", c("Oracle density", "Essential histogram"),
lty = c(1,1), col = c("red", "black"))
``` |

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