# Testing One Hypothesis Multiple Times: The Multidimensional Case

@article{Algeri2018TestingOH, title={Testing One Hypothesis Multiple Times: The Multidimensional Case}, author={Sara Algeri and David A. van Dyk}, journal={Journal of Computational and Graphical Statistics}, year={2018}, volume={29}, pages={358 - 371} }

Abstract The identification of new rare signals in data, the detection of a sudden change in a trend, and the selection of competing models are among the most challenging problems in statistical practice. These challenges can be tackled using a test of hypothesis where a nuisance parameter is present only under the alternative, and a computationally efficient solution can be obtained by the “testing one hypothesis multiple times” (TOHM) method. In the one-dimensional setting, a fine…

## 10 Citations

### Testing One Hypothesis Multiple Times

- Mathematics, Computer ScienceStatistica Sinica
- 2021

A simple and computationally efficient inferential tool to perform TOHM under stringent significance requirements, such as those typically required in the physical sciences, and exploit the underlying discrete nature of the solution to clarify the connection between TOHM and multiple hypothesis testing.

### Likelihood Asymptotics in Nonregular Settings. A Review with Emphasis on the Likelihood Ratio

- Mathematics
- 2018

The review is focused on the large- and small-sample properties of the likelihood ratio, though other approaches to hypothesis testing and connections to estimation are mentioned in passing.

### Informative goodness-of-fit for multivariate distributions

- MathematicsElectronic Journal of Statistics
- 2021

This article introduces an informative goodness-of-fit (iGOF) approach to study multivariate distributions. Conversely from standard goodness-of-fit tests, when the null model is rejected, iGOF…

### Searching for new phenomena with profile likelihood ratio tests

- Mathematics
- 2020

This Expert Recommendation provides a guide to identifying practical situations where the likelihood ratio test statistic cannot be approximated by a χ 2 distribution and proposes adequate solutions.

### Sequential hypothesis testing for Axion Haloscopes

- Computer Science
- 2022

A novel likelihood-based inferential framework for axion haloscopes which is valid under the commonly applied “rescanning” protocol is introduced and compared with that of a simple method which exploits the geometric probability of rescan.

### Searching for new physics with profile likelihoods: Wilks and beyond

- Mathematics
- 2019

Particle physics experiments use likelihood ratio tests extensively to compare hypotheses and to construct confidence intervals. Often, the null distribution of the likelihood ratio test statistic is…

### Statistical challenges in the search for dark matter

- Physics
- 2018

The search for the particle nature of dark matter has given rise to a number of experimental, theoretical and statistical challenges. Here, we report on a number of these statistical challenges and…

### Comment on “Accumulating evidence for the associate production of a neutral scalar with mass around 151 GeV”

- PhysicsPhysics Letters B
- 2022

### Combined collider constraints on neutralinos and charginos

- PhysicsThe European Physical Journal C
- 2019

Searches for supersymmetric electroweakinos have entered a crucial phase, as the integrated luminosity of the Large Hadron Collider is now high enough to compensate for their weak production…

### Measuring the dark matter environments of black hole binaries with gravitational waves

- PhysicsPhysical Review D
- 2022

Large dark matter overdensities can form around black holes of astrophysical and primordial origin as they form and grow. This “dark dress” inevitably aﬀects the dynamical evolution of binary…

## References

SHOWING 1-10 OF 60 REFERENCES

### Testing One Hypothesis Multiple Times

- Mathematics, Computer ScienceStatistica Sinica
- 2021

A simple and computationally efficient inferential tool to perform TOHM under stringent significance requirements, such as those typically required in the physical sciences, and exploit the underlying discrete nature of the solution to clarify the connection between TOHM and multiple hypothesis testing.

### Inference in Perturbation Models, Finite Mixtures and Scan Statistics: The Volume-of-Tube Formula

- Mathematics
- 2005

This research creates a general class of "perturbation models" which are described by an underlying "null" model that accounts for most of the structure in data and a perturbation that accounts for…

### Detecting new signals under background mismodeling

- Environmental SciencePhysical Review D
- 2020

Searches for new astrophysical phenomena often involve several sources of non-random uncertainties which can lead to highly misleading results. Among these, model-uncertainty arising from background…

### Random fields of multivariate test statistics, with applications to shape analysis

- Mathematics
- 2008

Our data are random fields of multivariate Gaussian observations, and we fit a multivariate linear model with common design matrix at each point. We are interested in detecting those points where…

### Controlling the false discovery rate: a practical and powerful approach to multiple testing

- Business
- 1995

SUMMARY The common approach to the multiplicity problem calls for controlling the familywise error rate (FWER). This approach, though, has faults, and we point out a few. A different approach to…

### Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests under Nonstandard Conditions

- Mathematics
- 1987

Abstract Large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described. Specifically, the asymptotic distribution of…

### On methods for correcting for the look-elsewhere effect in searches for new physics

- Physics
- 2016

The search for new significant peaks over a energy spectrum often involves a statistical multiple hypothesis testing problem. Separate tests of hypothesis are conducted at different locations over a…

### On the asymptotic performance of the log likelihood ratio statistic for the mixture model and related results

- Mathematics
- 1984

The classical distribution theory of the log likelihood ratio test statistic does not hold for testing homogeneity (i.e., no mixture) against mixture alternatives. Asymptotic theory for this problem…

### Asymptotic distribution of test statistics in the analysis of moment structures under inequality constraints

- Mathematics
- 1985

SUMMARY The analysis of moment structural models has become an important tool of investigation in behavioural, educational and economic studies. The chi-squared largesample test is routinely employed…