Description Usage Arguments Details Value Author(s) References See Also Examples

Construction of CD-plot and adjusted deviance test. The confidence bands are also adjusted for post-selection inference.

1 2 3 |

`data` |
A vector of data. See details. |

`g` |
The postulated model from which we want to assess if deviations occur. |

`M` |
The desired size of the polynomial basis to be used. |

`Mmax` |
The maximum size of the polynomial basis from which |

`smooth` |
A logical argument indicating if a denoised solution should be implemented. The default is |

`criterion` |
If |

`hist.u` |
A logical argument indicating if the CD-plot should be displayed or not. The default is |

`breaks` |
If |

`ylim` |
If |

`range` |
Range of the data/search region considered. |

`sigma` |
The significance level (in sigmas) with respect to which the confidence bands should be constructed. See details. |

The argument `data`

collects the data for which we want to test if its distribution deviates from the one of the postulated model specified in the argument `g`

. In Algeri, 2019, the sample specified under `data`

corresponds to the source-free sample in the background calibration phase and to the physics sample in the signal search phase.
The value `M`

selected determines the smoothness of the estimated comparison density, with smaller values of `M`

leading to smoother estimates. The deviance test is used to select the value `M`

which leads to the most significant deviation from the postulated model. The default value for `Mmax`

is set to `20`

. Notice that numerical issues may
arise for larger values of `Mmax`

.
If `smooth=TRUE`

the largest coefficient estimates are selected according to either the AIC or BIC criterion as described in Algeri, 2019 and Mukhopadhyay, 2017.
If `Mmax>1`

and/or `smooth=TRUE`

, post-selection Bonferroni's correction is automatically implemented to both the deviance test p-value and the confidence bands. The desired level of significance can be expressed as one minus the cdf of a standard normal evaluated at `sigma`

(see Algeri, 2019).

`Deviance` |
Value of the deviance test statistic. |

`Dev_pvalue` |
Unadjusted p-value of the deviance test. |

`Dev_adj_pvalue` |
Post-selection Bonferroni adjusted p-value of the deviance test. |

`kstar` |
Number of coefficients selected by the denoising process. If |

`dhat` |
Function corresponding to the estimated comparison density in the u domain. |

`dhat.x` |
Function corresponding to the estimated comparison density in the x domain. |

`SE` |
Function corresponding to the estimated standard errors of the comparison density in the u domain. |

`LBf1` |
Function corresponding to the lower bound of the confidence bands under in u domain. |

`UBf1` |
Function corresponding to the upper bound of the confidence bands in u domain. |

`f` |
Function corresponding to the estimated density of the data. |

`u` |
Vector of values corresponding to the cdf of the model specified in |

`LP` |
Estimates of the coefficients. |

`G` |
Cumulative density function of the postulated model specified in the argument |

Sara Algeri

S. Algeri, 2019. Detecting new signals under background mismodelling. <arXiv:1906.06615>.

S. Mukhopadhyay, 2017. Large-scale mode identification and data-driven sciences. Electronic Journal of Statistics 11 (2017), no. 1, 215–240.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ```
#generaing data
x<-rnorm(1000,10,7)
xx<-x[x>=10 & x<=20]
#create suitable postulated quantile function of data
G<-pnorm(20,5,15)-pnorm(10,5,15)
g<-function(x){dnorm(x,5,15)/G}
#Choose best M
Mmax=20
range=c(10,20)
m<-BestM(data=xx,g, Mmax,range)
# vectorize postulated quantile function
g<-Vectorize(g)
u<-g(xx)
#M has to be sufficient big, otherwise dhatL2 function will crush.
#So,here we set m eqaul 6 as an example
m<-6
comp.density<-dhatL2(data=xx,g, M=m, Mmax=Mmax,smooth=FALSE,criterion="AIC",hist.u=TRUE,breaks=20,
ylim=c(0,2.5),range=range,sigma=2)
``` |

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.