scholarly journals The robust estimation of examinee ability based on the four-parameter logistic model when guessing and carelessness responses exist

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0250268
Author(s):  
Xiaozhu Jian ◽  
Dai Buyun ◽  
Deng Yuanping
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Robust Estimation ◽  
Logistic Model ◽  
Simulation Studies ◽  
Critical Probability ◽  
Likelihood Estimator ◽  
New Approach ◽  
Two Parameter ◽  
Random Guessing

The three-parameter Logistic model (3PLM) and the four-parameter Logistic model (4PLM) have been proposed to reduce biases in cases of response disturbances, including random guessing and carelessness. However, they could also influence the examinees who do not guess or make careless errors. This paper proposes a new approach to solve this problem, which is a robust estimation based on the 4PLM (4PLM-Robust), involving a critical-probability guessing parameter and a carelessness parameter. This approach is compared with the 2PLM-MLE(two-parameter Logistic model and a maximum likelihood estimator), the 3PLM-MLE, the 4PLM-MLE, the Biweight estimation and the Huber estimation in terms of bias using an example and three simulation studies. The results show that the 4PLM-Robust is an effective method for robust estimation, and its calculation is simpler than the Biweight estimation and the Huber estimation.

scholarly journals Direct fast estimator for recombination frequency in the F2 cross

2021 ◽  
Author(s):  
Mathias Lorieux
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Maximum Likelihood Estimator ◽  
Recombination Frequency ◽  
Short Note ◽  
Simulation Studies ◽  
Likelihood Estimator ◽  
Simple Estimate ◽  
Efficient Simulation

AbstractIn this short note, a new unbiased maximum-likelihood estimator is proposed for the recombination frequency in the F2 cross. The estimator is much faster to calculate than its EM algorithm equivalent, yet as efficient. Simulation studies are carried to illustrate the gain over another simple estimate proposed by Benito & Gallego (2004).

scholarly journals Reliability for Lindley Distribution with an Outlier

2013 ◽  
Vol 3 ◽  
pp. 20-23
Author(s):  
Hossein Jabbari Khamnei
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Studies ◽  
Likelihood Estimator ◽  
Lindley Distribution

In this paper, we consider the problem of estimating R=P(Y<X) , when Y has lindleydistribution with parameter a and x has lindley distribution with presence of one outlier withparameters b and c , such that X and Y are independent. The maximum likelihood estimator of R isderived and some results of simulation studies are presented.

On the distribution of the Cauchy maximum-likelihood estimator

1993 ◽  
Vol 440 (1909) ◽  
pp. 475-479
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Linear Group ◽  
Joint Density ◽  
Likelihood Estimator ◽  
Remarkable Property ◽  
Large Sample ◽  
The Real ◽  
Two Parameter ◽  
Explicit Expressions

The two-parameter Cauchy maximum-likelihood estimator T ( y ) = ( T 1 ( y ), T 2 ( y )) is known to be unique for samples of size n ≽ 3 (J. Copas, Biometrika 62, 701-704 (1975)). In this paper we exploit equivariance under the real fractional linear group to show that the joint density of T has the form p n ( X )/(4 πt 2 2 ) where X = | t ─ θ | 2 / (4 t 2 θ 2 ). Explicit expressions are given for p 3 ( X ) and p 4 ( X ) and the asymptotic large-sample limit. All such densities are shown to have the remarkable property that E ( u(>T )) = u ( θ ) if u(⋅) is harmonic and the expectation is finite. In particular, both components of the maximum -likelihood estimator are unbiased for ≽ 3, E log{ T 1 2 + T 2 2 ) = log ( θ 1 2 + θ 2 2 ), E ( T 1 2 - T 2 2 ) = θ 1 2 - θ 2 2 , E { T 1 T 2 ) = θ 1 θ 2 for n ≽ 4, and so on.

SELECTING THE BEST PERFORMING WEIBULL ESTIMATION METHOD FOR RANDOMLY RIGHT CENSORED DATA

2010 ◽  
Vol 17 (02) ◽  
pp. 105-118
Author(s):  
JONATHAN J. BATES ◽  
JOSÉ L. ZAYAS-CASTRO
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Censored Data ◽  
Estimation Method ◽  
Estimation Methods ◽  
Likelihood Estimator ◽  
Right Censored Data ◽  
Kaplan Meier ◽  
Piecewise Exponential ◽  
Two Parameter

A total of nine methods are compared and tables are presented for selecting the best performing estimator for a two-parameter Weibull distribution using randomly right censored data. The results indicate that a best performing method can be selected given a certain sample size, censoring level, and shape parameter range. Such a comparison of estimators is necessary as the best performing method is shown to vary across these values. The estimation methods tested include the Maximum Likelihood Estimator, Kaplan-Meier Estimator, Piecewise Exponential Estimator, Földes, Rejt, and Winter Estimator, Klein, Lee, and Moeschberger Partially Parametric Estimator, Ross Estimator, White Estimator, Bain and Engelhardt Estimator, and the Modified Profile Maximum Likelihood Estimator. Recommendations are provided for applying the studied approach to other types of data and distributions.

A SIMPLE ESTIMATOR FOR THE WEIBULL SHAPE PARAMETER

2012 ◽  
Vol 12 (02) ◽  
pp. 395-402 ◽  
Author(s):  
MAHDI TEIMOURI ◽  
SARALEES NADARAJAH
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Closed Form ◽  
Maximum Likelihood Estimator ◽  
Shape Parameter ◽  
Scale Parameter ◽  
Maximum Likelihood Estimators ◽  
Simulation Studies ◽  
Likelihood Estimator

The Weibull distribution is the most popular model for lifetimes. However, the maximum likelihood estimators for the Weibull distribution are not available in closed form. In this note, we derive a simple, consistent, closed form estimator for the Weibull shape parameter. This estimator is independent of the Weibull scale parameter. Simulation studies show that this estimator performs as well as the maximum likelihood estimator.

The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

2018 ◽  
pp. 439
Author(s):  
Hazim Mansour Gorgees ◽  
Bushra Abdualrasool Ali ◽  
Raghad Ibrahim Kathum
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Reliability Function ◽  
Bayes Estimator ◽  
Likelihood Estimator ◽  
Monte Carlo Simulation Technique ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Better Than

     In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

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