scholarly journals The Perceived Framework of a Classical Statistic: Is the Non-Invariance of a Wald Statistic Much Ado About Null Thing?

2006 ◽  
Author(s):  
N. K. Dastoor
Keyword(s):  
Wald Statistic ◽  
Classical Statistic

A Simulation Study on a Wald Statistic and Cochran's Q Statistic for Stratified Samples

Biometrics ◽  
1977 ◽  
Vol 33 (4) ◽  
pp. 643 ◽  
Author(s):  
Grant W. Somes ◽  
V. P. Bhapkar
Keyword(s):  
Simulation Study ◽  
Wald Statistic ◽  
Q Statistic

Test procedure and sample size determination for a proportion study using a double-sampling scheme with two fallible classifiers

2017 ◽  
Vol 28 (4) ◽  
pp. 1019-1043 ◽  
Author(s):  
Shi-Fang Qiu ◽  
Xiao-Song Zeng ◽  
Man-Lai Tang ◽  
Wai-Yin Poon
Keyword(s):  
Sample Size ◽  
Null Hypothesis ◽  
Test Procedure ◽  
Sample Size Determination ◽  
Double Sampling ◽  
Score Statistic ◽  
Wald Statistic ◽  
Test Procedures ◽  
Practical Applications ◽  
Logit Transformation

Double sampling is usually applied to collect necessary information for situations in which an infallible classifier is available for validating a subset of the sample that has already been classified by a fallible classifier. Inference procedures have previously been developed based on the partially validated data obtained by the double-sampling process. However, it could happen in practice that such infallible classifier or gold standard does not exist. In this article, we consider the case in which both classifiers are fallible and propose asymptotic and approximate unconditional test procedures based on six test statistics for a population proportion and five approximate sample size formulas based on the recommended test procedures under two models. Our results suggest that both asymptotic and approximate unconditional procedures based on the score statistic perform satisfactorily for small to large sample sizes and are highly recommended. When sample size is moderate or large, asymptotic procedures based on the Wald statistic with the variance being estimated under the null hypothesis, likelihood rate statistic, log- and logit-transformation statistics based on both models generally perform well and are hence recommended. The approximate unconditional procedures based on the log-transformation statistic under Model I, Wald statistic with the variance being estimated under the null hypothesis, log- and logit-transformation statistics under Model II are recommended when sample size is small. In general, sample size formulae based on the Wald statistic with the variance being estimated under the null hypothesis, likelihood rate statistic and score statistic are recommended in practical applications. The applicability of the proposed methods is illustrated by a real-data example.

Condition Monitoring of Wind Turbine Drivetrain Bearings

2019 ◽  
Author(s):  
Konstantinos Gryllias ◽  
Junyu Qi ◽  
Alexandre Mauricio ◽  
Chenyu Liu
Keyword(s):  
Wind Energy ◽  
Condition Monitoring ◽  
Wind Turbines ◽  
Wind Farm ◽  
The Other ◽  
Offshore Wind ◽  
Center Frequency ◽  
Classical Statistic ◽  
Offshore Wind Turbines ◽  
Other Hand

Abstract The current pace of renewable energy development around the world is unprecedented, with offshore wind in particular proving to be an extremely valuable and reliable energy source. The global installed capacity of offshore wind turbines by the end of 2022 is expected to reach the 46.4 GW, among which 33.9 GW in Europe. Costs are critical for the future success of the offshore wind sector. The industry is pushing hard to make cost reductions to show that offshore wind is economically comparable to conventional fossil fuels. Efficiencies in Operations and Maintenance (O&M) offer potential to achieve significant cost savings as it accounts for around 20%–30% of overall offshore wind farm costs. One of the most critical and rather complex assembly of onshore, offshore and floating wind turbines is the gearbox. Gearboxes are designed to last till the end of the lifetime of the asset, according to the IEC 61400-4 standards. On the other hand, a recent study over approximately 350 offshore wind turbines indicate that gearboxes might have to be replaced as early as 6.5 years. Therefore sensing and condition monitoring systems for onshore, offshore and floating wind turbines are needed in order to obtain reliable information on the state and condition of different critical parts, focusing towards the detection and/or prediction of damage before it reaches a critical stage. The development and use of such technologies will allow companies to schedule actions at the right time, and thus will help reducing the costs of operation and maintenance, resulting in an increase of wind energy at a competitive price and thus strengthening productivity of the wind energy sector. At the academic level a plethora of methodologies have been proposed during the last decades for the analysis of vibration signatures focusing towards early and accurate fault detection with limited false alarms and missed detections. Among others, Envelope Analysis is one of the most important methodologies, where an envelope of the vibration signal is estimated, usually after filtering around a selected frequency band excited by impacts due to the faults. Different tools, such as Kurtogram, have been proposed in order to accurately select the optimum filter parameters (center frequency and bandwidth). Cyclostationary Analysis and corresponding methodologies, i.e. the Cyclic Spectral Correlation and the Cyclic Spectral Coherence, have been proved as powerful tools for condition monitoring. On the other hand the application, test and evaluation of such tools on general industrial cases is still rather limited. Therefore the main aim of this paper is the application and evaluation of advanced diagnostic techniques and diagnostic indicators, including the Enhanced Envelope Spectrum and the Spectral Flatness on real world vibration data collected from vibration sensors on gearboxes in multiple wind turbines over an extended period of time of nearly four years. The diagnostic indicators are compared with classical statistic time and frequency indicators, i.e. Kurtosis, Crest Factor etc. and their effectiveness is evaluated based on the successful detection of two failure events.

scholarly journals A power approximation for the Kenward and Roger Wald test in the linear mixed model

PLoS ONE ◽  
2021 ◽  
Vol 16 (7) ◽  
pp. e0254811
Author(s):  
Sarah M. Kreidler ◽  
Brandy M. Ringham ◽  
Keith E. Muller ◽  
Deborah H. Glueck
Keyword(s):  
Mixed Model ◽  
Linear Mixed Model ◽  
Wald Test ◽  
Small Sample ◽  
Power Calculation ◽  
Wald Statistic ◽  
Power Approximation ◽  
Group Randomized Trial ◽  
Approximate Moments ◽  
Image Position

We derive a noncentral F power approximation for the Kenward and Roger test. We use a method of moments approach to form an approximate distribution for the Kenward and Roger scaled Wald statistic, under the alternative. The result depends on the approximate moments of the unscaled Wald statistic. Via Monte Carlo simulation, we demonstrate that the new power approximation is accurate for cluster randomized trials and longitudinal study designs. The method retains accuracy for small sample sizes, even in the presence of missing data. We illustrate the method with a power calculation for an unbalanced group-randomized trial in oral cancer prevention.

A Reminder of the Fallibility of the Wald Statistic

1996 ◽  
Vol 50 (3) ◽  
pp. 226 ◽  
Author(s):  
Thomas R. Fears ◽  
Jacques Benichou ◽  
Mitchell H. Gail
Keyword(s):  
Wald Statistic
Sign in / Sign up

Export Citation Format

Share Document