On procrustean mean shapes and the shape of the means

1996 ◽  
Vol 28 (02) ◽  
pp. 336-337
Author(s):  
Hulling Le
Keyword(s):  
Statistical Models ◽  
Nuisance Parameters ◽  
Finite Set

Two sets of k labelled points, or configurations, in ℝ m are defined to have the same shape if they differ only in translation, rotation and scaling. An important matter in practice is the estimation of the shape of the means; the shape determined by the means of data on the vertices of configurations. However, statistical models for vertices-based shapes always involve some unknown samplewise nuisance parameters associated with ambiguity of location, rotation and scaling. The use of procrustean mean shapes for a finite set of configurations, which are usually formulated directly in terms of their vertices, will enable one to eliminate these nuisance parameters.

On procrustean mean shapes and the shape of the means

1996 ◽  
Vol 28 (2) ◽  
pp. 336-337
Author(s):  
Hulling Le
Keyword(s):  
Statistical Models ◽  
Nuisance Parameters ◽  
Finite Set

Two sets of k labelled points, or configurations, in ℝm are defined to have the same shape if they differ only in translation, rotation and scaling. An important matter in practice is the estimation of the shape of the means; the shape determined by the means of data on the vertices of configurations. However, statistical models for vertices-based shapes always involve some unknown samplewise nuisance parameters associated with ambiguity of location, rotation and scaling. The use of procrustean mean shapes for a finite set of configurations, which are usually formulated directly in terms of their vertices, will enable one to eliminate these nuisance parameters.

scholarly journals On the Correction of the Asymptotic Distribution of the Likelihood Ratio Statistic If Nuisance Parameters Are Estimated Based on an External Source

2014 ◽  
Vol 10 (2) ◽  
Author(s):  
Marianne Jonker ◽  
Aad Van der Vaart
Keyword(s):  
Confidence Interval ◽  
Asymptotic Distribution ◽  
Confidence Intervals ◽  
Likelihood Ratio ◽  
Statistical Models ◽  
Likelihood Ratio Statistic ◽  
External Source ◽  
Nuisance Parameters ◽  
Testing Hypotheses

AbstractIn practice, nuisance parameters in statistical models are often replaced by estimates based on an external source, for instance if estimates were published before or a second dataset is available. Next these estimates are assumed to be known when the parameter of interest is estimated, a hypothesis is tested or confidence intervals are constructed. By this assumption, the level of the test is, in general, higher than supposed and the coverage of the confidence interval is too low. In this article, we derive the asymptotic distribution of the likelihood ratio statistic if the nuisance parameters are estimated based on a dataset that is independent of the data used for estimating the parameter of interest. This distribution can be used for correctly testing hypotheses and constructing confidence intervals. Four theoretical and practical examples are given as illustration.

Nuisance parameters, mixture models, and the efficiency of partial likelihood estimators

1980 ◽  
Vol 296 (1427) ◽  
pp. 639-662 ◽  
Keyword(s):  
Lower Bounds ◽  
Statistical Models ◽  
Asymptotic Variance ◽  
Partial Likelihood ◽  
Nuisance Parameters ◽  
Direct Proportion ◽  
Likelihood Estimator ◽  
Unbiased Estimators ◽  
Asymptotically Normal ◽  
Independent Observations

This paper establishes lower bounds for estimation in parametric statistical models in which one wishes to estimate a real-valued parameter of interest in the presence of nuisance parameters which are accruing in number in direct proportion to the number of independent observations. The formal setting requires that the nuisance parameters be independent observations from an unknown distribution. In this setting an information measure analogous to the Fisher information is derived. It is then used to generate lower bounds for the variance of unbiased estimators and also for the asymptotic variance of consistent asymptotically normal estimators. Under certain conditions, consistent asymptotically normal estimators can be generated by maximizing factors of the complete likelihood, even though the maximum likelihood estimator is inconsistent. These estimators can be fully efficient in the sense of meeting the lower bounds despite their apparent wasteful use of the likelihood, as is demonstrated, in several important examples, by the use of a natural sufficient condition.

CONSISTENT SPECIFICATION TESTING WITH NUISANCE PARAMETERS PRESENT ONLY UNDER THE ALTERNATIVE

1998 ◽  
Vol 14 (3) ◽  
pp. 295-325 ◽  
Author(s):  
Maxwell B. Stinchcombe ◽  
Halbert White
Keyword(s):  
Statistical Models ◽  
Nuisance Parameter ◽  
Nuisance Parameters ◽  
Law Of Iterated Logarithm ◽  
Specification Testing ◽  
Specification Tests ◽  
Recent Developments ◽  
Topological Measures ◽  
Parameter Approach ◽  
Tests Of Hypotheses

The nonparametric and the nuisance parameter approaches to consistently testing statistical models are both attempts to estimate topological measures of distance between a parametric and a nonparametric fit, and neither dominates in experiments. This topological unification allows us to greatly extend the nuisance parameter approach. How and why the nuisance parameter approach works and how it can be extended bear closely on recent developments in artificial neural networks. Statistical content is provided by viewing specification tests with nuisance parameters as tests of hypotheses about Banach-valued random elements and applying the Banach central limit theorem and law of iterated logarithm, leading to simple procedures that can be used as a guide to when computationally more elaborate procedures may be warranted.

Statistical models with nuisance parameters as applied to an experiment performed by a group of devices

1994 ◽  
Vol 38 (4) ◽  
pp. 333-351
Author(s):  
Ludmila Kubáčková ◽  
Lubomír Kubáček
Keyword(s):  
Statistical Models ◽  
Nuisance Parameters

scholarly journals Building and steering binned template fits with cabinetry

2021 ◽  
Vol 251 ◽  
pp. 03067
Author(s):  
Kyle Cranmer ◽  
Alexander Held
Keyword(s):  
Statistical Models ◽  
Goodness Of Fit ◽  
High Energy Physics ◽  
Model Building ◽  
High Energy ◽  
Nuisance Parameters ◽  
Modular Approach ◽  
Key Steps ◽  
Data Visualizations ◽  
Energy Physics

The cabinetry library provides a Python-based solution for building and steering binned template fits. It tightly integrates with the pythonic High Energy Physics ecosystem, and in particular with pyhf for statistical inference. cabinetry uses a declarative approach for building statistical models, with a JSON schema describing possible configuration choices. Model building instructions can additionally be provided via custom code, which is automatically executed when applicable at key steps of the workflow. The library implements interfaces for performing maximum likelihood fitting, upper parameter limit determination, and discovery significance calculation. cabinetry also provides a range of utilities to study and disseminate fit results. These include visualizations of the fit model and data, visualizations of template histograms and fit results, ranking of nuisance parameters by their impact, a goodness-of-fit calculation, and likelihood scans. The library takes a modular approach, allowing users to include some or all of its functionality in their workflow.

Statistical Models: Theory and Practice

2005 ◽  
Author(s):  
David Freedman
Keyword(s):  
Statistical Models ◽  
Theory And Practice

Is That Measure Really One-Dimensional?

Methodology ◽  
2018 ◽  
Vol 14 (4) ◽  
pp. 188-196 ◽  
Author(s):  
Esther T. Beierl ◽  
Markus Bühner ◽  
Moritz Heene
Keyword(s):  
Model Fit ◽  
Nuisance Parameters ◽  
Factorial Validity ◽  
Fit Indices ◽  
Analysis Model ◽  
Factor Analysis Model ◽  
One Dimensional ◽  
Confirmatory Factor Analysis Model ◽  
Cutoff Values ◽  
Confirmatory Factor

Abstract. Factorial validity is often assessed using confirmatory factor analysis. Model fit is commonly evaluated using the cutoff values for the fit indices proposed by Hu and Bentler (1999) . There is a body of research showing that those cutoff values cannot be generalized. Model fit does not only depend on the severity of misspecification, but also on nuisance parameters, which are independent of the misspecification. Using a simulation study, we demonstrate their influence on measures of model fit. We specified a severe misspecification, omitting a second factor, which signifies factorial invalidity. Measures of model fit showed only small misfit because nuisance parameters, magnitude of factor loadings and a balanced/imbalanced number of indicators per factor, also influenced the degree of misfit. Drawing from our results, we discuss challenges in the assessment of factorial validity.

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