Precise asymptotics for the first moment of the error variance estimator in linear models

Abstract We define and compute asymptotically optimal difference sequences for estimating error variance in homoscedastic nonparametric regression. Our optimal difference sequences do not depend on unknowns, such as the mean function, and provide substantial improvements over the suboptimal sequences commonly used in practice. For example, in the case of normal data the usual variance estimator based on symmetric second-order differences is only 64% efficient relative to the estimator based on optimal second-order differences. The efficiency of an optimal mth-order difference estimator relative to the error sample variance is 2m/(2m + 1). Again this is for normal data, and increases as the tails of the error distribution become heavier.

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Experience in Applying the New UK Procedure for Creep Rupture Data Assessment to Gas Turbine Materials

Volume 4: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education; IGTI Scholar Award ◽

10.1115/97-gt-118 ◽

1997 ◽

Cited By ~ 1

Author(s):

Chris K. Bullough

Keyword(s):

Gas Turbine ◽

Linear Models ◽

Rupture Strength ◽

Statistical Tests ◽

Error Variance ◽

Creep Rupture ◽

Data Sets ◽

Data Assessment ◽

Rupture Data ◽

Turbine Blading

A new procedure being developed in British Standards for the assessment of creep-rupture data is described, and evaluated with trial data sets of gas turbine blading materials. The procedure is applied in phases. An important development by statistical experts is a framework for the main assessment phase which uses maximum-likelihood fitting methods for the treatment of unfailed test points and error variance. The framework selects models from a standard suite (together with any other linear models supplied by the assessor) using statistical criteria, but also incorporates metallurgical judgement. The improved representation of the experimental data compared with previous fitting methods, and the associated statistical tests indicate that the new procedure can be used to derive rupture strength values for gas turbine materials with confidence.

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Information criteria for nonlinear time series models

Studies in Nonlinear Dynamics & Econometrics ◽

10.1515/snde-2015-0026 ◽

2016 ◽

Vol 20 (3) ◽

Author(s):

Saskia Rinke ◽

Philipp Sibbertsen

Keyword(s):

Error Term ◽

Linear Models ◽

Nonlinear Models ◽

General Information ◽

Information Criteria ◽

Order Selection ◽

Simulation Studies ◽

Variance Estimator ◽

Linear And Nonlinear ◽

The Impact

AbstractIn this paper the performance of different information criteria for simultaneous model class and lag order selection is evaluated using simulation studies. We focus on the ability of the criteria to distinguish linear and nonlinear models. In the simulation studies, we consider three different versions of the commonly known criteria AIC, SIC and AICc. In addition, we also assess the performance of WIC and evaluate the impact of the error term variance estimator. Our results confirm the findings of different authors that AIC and AICc favor nonlinear over linear models, whereas weighted versions of WIC and all versions of SIC are able to successfully distinguish linear and nonlinear models. However, the discrimination between different nonlinear model classes is more difficult. Nevertheless, the lag order selection is reliable. In general, information criteria involving the unbiased error term variance estimator overfit less and should be preferred to using the usual ML estimator of the error term variance.

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First Order Difference-Based Error Variance Estimator in Nonparametric Regression with a Single Outlier

Communications for Statistical Applications and Methods ◽

10.5351/ckss.2012.19.3.333 ◽

2012 ◽

Vol 19 (3) ◽

pp. 333-344 ◽

Cited By ~ 1

Author(s):

Chun-Gun Park

Keyword(s):

Nonparametric Regression ◽

Error Variance ◽

Variance Estimator ◽

Order Difference ◽

First Order

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