# Fast and Fair Simultaneous Confidence Bands for Functional Parameters.

@article{Liebl2019FastAF, title={Fast and Fair Simultaneous Confidence Bands for Functional Parameters.}, author={Dominik Liebl and Matthew L. Reimherr}, journal={arXiv: Methodology}, year={2019} }

Quantifying uncertainty using confidence regions is a central goal of statistical inference. Despite this, methodologies for confidence bands in Functional Data Analysis are underdeveloped compared to estimation and hypothesis testing. This work represents a major leap forward in this area by presenting a new methodology for constructing simultaneous confidence bands for functional parameter estimates. These bands possess a number of striking qualities: (1) they have a nearly closed-form…

## Figures and Tables from this paper

## 12 Citations

Functional delta residuals and applications to simultaneous confidence bands of moment based statistics

- MathematicsJournal of Multivariate Analysis
- 2022

Confidence surfaces for the mean of locally stationary functional time series

- Mathematics
- 2021

The problem of constructing a simultaneous confidence surface for the 2-dimensional mean function of a non-stationary functional time series is challenging as these bands can not be built on…

Estimating the conditional distribution in functional regression problems

- Mathematics
- 2021

We consider the problem of consistently estimating the conditional distribution P (Y ∈ A|X) of a functional data object Y = (Y (t) : t ∈ [0, 1]) given covariates X in a general space, assuming that Y…

Confidence regions for the location of peaks of a smooth random field

- Mathematics
- 2022

Local maxima of random processes are useful for ﬁnding important regions and are routinely used, for summarising features of interest (e.g. in neuroimaging). In this work we provide conﬁdence regions…

Letter to the Editor on: “Comparing Groups of Time Dependent Data Using Locally Weighted Scatterplot Smoothing Alpha-Adjusted Serial T-tests” by

- MathematicsGait & Posture
- 2021

Multivariate functional additive mixed models

- MathematicsStatistical Modelling
- 2021

Multivariate functional data can be intrinsically multivariate like movement trajectories in 2D or complementary such as precipitation, temperature and wind speeds over time at a given weather…

Bio-equivalence tests in functional data by maximum deviation

- Mathematics
- 2020

We study the problem of testing equivalence of functional parameters, such as the mean or the variance function, in the two-sample functional data setting. In contrast to previous work where the…

Estimation of Expected Euler Characteristic Curves of Nonstationary Smooth Gaussian Fields

- Mathematics
- 2020

The expected Euler characteristic (EEC) of excursion sets of a Gaussian random field over a compact manifold approximates the distribution of its supremum for high thresholds. Viewed as a function of…

Detecting relevant differences in the covariance operators of functional time series: a sup-norm approach

- MathematicsAnnals of the Institute of Statistical Mathematics
- 2020

In this paper we propose statistical inference tools for the covariance operators of functional time series in the two sample and change point problem. In contrast to most of the literature the focus…

Maximum likelihood estimation and uncertainty quantification for Gaussian process approximation of deterministic functions

- Computer Science, MathematicsSIAM/ASA J. Uncertain. Quantification
- 2020

It is shown that the maximum likelihood estimation of the scale parameter alone provides significant adaptation against misspecification of the Gaussian process model in the sense that the model can become "slowly" overconfident at worst, regardless of the difference between the smoothness of the data-generating function and that expected by the model.

## References

SHOWING 1-10 OF 87 REFERENCES

Bone mineral acquisition in healthy Asian, Hispanic, black, and Caucasian youth: a longitudinal study.

- MedicineThe Journal of clinical endocrinology and metabolism
- 1999

Ethnic and gender differences in bone mineral acquisition were examined in a longitudinal study of 423 healthy Asian, black, Hispanic, and white males and females and the use of gender- and ethnic-specific standards is recommended when interpreting pediatric bone densitometry data.

Random Fields and Geometry

- Mathematics
- 2007

* Recasts topics in random fields by following a completely new way of handling both geometry and probability
* Significant exposition of the work of others in the field
* Presentation is clear and…

Simultaneous Confidence Bands for Functional Data Using the Gaussian Kinematic Formula.

- Mathematics
- 2019

Variable selection in function‐on‐scalar regression

- Computer ScienceStat
- 2016

This work adapts techniques from generalized least squares to account for residual covariance by “pre‐whitening” using an estimate of the covariance matrix and develops an iterative algorithm that alternately updates the spline coefficients and covariance.

Simultaneous inference for the mean function based on dense functional data

- MathematicsJournal of nonparametric statistics
- 2012

A polynomial spline estimator is proposed for the mean function of dense functional data together with a simultaneous confidence band which is asymptotically correct, and the confidence band is extended to the difference of mean functions of two populations of functional data.

CLT in functional linear regression models

- Mathematics
- 2005

We propose in this work to derive a CLT in the functional linear regression model. The main difficulty is due to the fact that estimation of the functional parameter leads to a kind of ill-posed…

ffscb: Fast and fair simultanouse confidence for functional parameters

- R package version 0.0.9.
- 2019

Nonparametric testing for differences in electricity prices: The case of the Fukushima nuclear accident

- MathematicsThe Annals of Applied Statistics
- 2019

This work is motivated by the problem of testing for differences in the mean electricity prices before and after Germany's abrupt nuclear phaseout after the nuclear disaster in Fukushima Daiichi,…

A geometric approach to confidence regions and bands for functional parameters

- Mathematics
- 2016

Functional data analysis is now a well‐established discipline of statistics, with its core concepts and perspectives in place. Despite this, there are still fundamental statistical questions which…

Fairness in Prediction and Allocation∗

- Computer Science
- 2021

Many high stakes decisions that are now aided by machine learning can be viewed as allocation problems. We will often have some good (such as a job or a loan) or bad (such as incarceration) to…