scholarly journals Equivariance and Generalized Inference in Two-Sample Location-Scale Families

2011 ◽  
Vol 2011 ◽  
pp. 1-16
Author(s):  
Sévérien Nkurunziza ◽  
Fuqi Chen
Keyword(s):  
Monte Carlo Simulation ◽  
Maximum Likelihood Estimators ◽  
Conditional Inference ◽  
Simulation Studies ◽  
Pivotal Quantity ◽  
Minimum Risk ◽  
Generalized Pivotal Quantity ◽  
Location Parameters ◽  
Generalized Inference ◽  
The Difference

We are interested in-typical Behrens-Fisher problem in general location-scale families. We present a method of constructing generalized pivotal quantity (GPQ) and generalizedPvalue (GPV) for the difference between two location parameters. The suggested method is based on the minimum risk equivariant estimators (MREs), and thus, it is an extension of the methods based on maximum likelihood estimators and conditional inference, which have been, so far, applied to some specific distributions. The efficiency of the procedure is illustrated by Monte Carlo simulation studies. Finally, we apply the proposed method to two real datasets.

scholarly journals Validation and Measurement Uncertainty Assessment of a Microbiological Method Using Generalized Pivotal Quantity Procedure and Monte-Carlo Simulation

2018 ◽  
Vol 101 (4) ◽  
pp. 1205-1211
Author(s):  
Saad Alaoui Sossé ◽  
Taoufiq Saffaj ◽  
Bouchaib Ihssane
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Measurement Uncertainty ◽  
Uncertainty Assessment ◽  
Tolerance Interval ◽  
Alternative Procedure ◽  
Pivotal Quantity ◽  
Statistical Tool ◽  
Generalized Pivotal Quantity ◽  
Escherichia Coli Bacteria

Abstract Recently, a novel and effective statistical tool called the uncertainty profile has been developed with the purpose of graphically assessing the validity and estimating the measurement uncertainty of analytical procedures. One way to construct the uncertainty profile is to compute the β-content, γ-confidence tolerance interval. In this study, we propose a tolerance interval based on the combination of the generalized pivotal quantity procedure and Monte-Carlo simulation. The uncertainty profile has been applied successfully in several fields. However, in order to further confirm its universality, this newer approach has been applied to assess the performance of an alternative procedure versus a reference procedure for counting of Escherichia coli bacteria in drinking water. Hence, the aims of this research were to expose how the uncertainty profile can be powerfully applied pursuant to ISO 16140 standards in the frame of interlaboratory study and how to easily make a decision concerning the validity of the procedure. The analysis of the results shows that after the introduction of a correction factor, the alternative procedure is deemed valid over the studied range because the uncertainty limits lie within the acceptability limits set at ±−0.3 log unit/100 ml for a β = 66.7% and γ = 90%.

ESTIMATING THE SHAPE PARAMETER OF THE LOG-LOGISTIC DISTRIBUTION

2006 ◽  
Vol 13 (03) ◽  
pp. 257-266 ◽  
Author(s):  
ZHENMIN CHEN
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Confidence Intervals ◽  
Shape Parameter ◽  
Interval Estimation ◽  
Maximum Likelihood Estimators ◽  
Logistic Distribution ◽  
Pivotal Quantity ◽  
Estimation Problems ◽  
Exact Confidence Intervals

The log-logistic distribution is a useful distribution in survival analysis. Parameter estimation problems have been discussed by many authors. This paper focuses on the interval estimation for the shape parameter of the log-logistic distribution. Bain and Engelhardt3 gave confidence intervals for the parameters of a logistic distribution based on pivotal quantities formed by maximum likelihood estimators. Chen10 proposed another method for obtaining exact confidence intervals of the shape parameter of the log-logistic distribution. Compared with the existing methods for constructing confidence intervals for the parameters of the log-logistic distribution, the method given in Chen10 is easier to use. In the present paper, the pivotal quantity used in Chen10 is adjusted to improve the performance of statistical analysis. Monte Carlo simulation is conducted to compare the performance of different pivotal quantities. The simulation result shows that the adjusted pivotal quantity has better performance, and then should be recommended to the statistics users.

Monte Carlo simulation studies of the catalytic combustion of methane

2006 ◽  
Vol 112 (1-2) ◽  
pp. 121-128 ◽  
Author(s):  
Joaquín Cortés ◽  
Eliana Valencia ◽  
Paulo Araya
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Catalytic Combustion ◽  
Simulation Studies ◽  
Catalytic Combustion Of Methane

Measurement error-filtered machine learning in digital soil mapping

2021 ◽  
Author(s):  
Stephan van der Westhuizen ◽  
Gerard Heuvelink ◽  
David Hofmeyr
Keyword(s):  
Machine Learning ◽  
Measurement Error ◽  
Soil Property ◽  
Soil Mapping ◽  
Digital Soil Mapping ◽  
Simulation Studies ◽  
True Value ◽  
Linear Relationships ◽  
The Difference ◽  
The Relationship

<p>Digital soil mapping (DSM) may be defined as the use of a statistical model to quantify the relationship between a certain observed soil property at various geographic locations, and a collection of environmental covariates, and then using this relationship to predict the soil property at locations where the property was not measured. It is also important to quantify the uncertainty with regards to prediction of these soil maps. An important source of uncertainty in DSM is measurement error which is considered as the difference between a measured and true value of a soil property.</p><p>The use of machine learning (ML) models such as random forests (RF) has become a popular trend in DSM. This is because ML models tend to be capable of accommodating highly non-linear relationships between the soil property and covariates. However, it is not clear how to incorporate measurement error into ML models. In this presentation we will discuss how to incorporate measurement error into some popular ML models, starting with incorporating weights into the objective function of ML models that implicitly assume a Gaussian error. We will discuss the effect that these modifications have on prediction accuracy, with reference to simulation studies.</p>

Sign in / Sign up

Export Citation Format

Share Document