Shape averages and their Bias

1994 ◽  
Vol 26 (2) ◽  
pp. 334-340 ◽  
Author(s):  
K. V. Mardia ◽  
I. L. Dryden
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Normal Model ◽  
Likelihood Estimator ◽  
Distributional Properties ◽  
Exact Maximum Likelihood

The paper considers the bias of Bookstein's mean estimator for shape under the isotropic normal model. This work depends on certain distributional properties of shape variables. An alternative unbiased modified estimator is proposed and its performance is compared with various estimators, including Procrustes and the exact maximum likelihood estimator, in a simulation study.

Shape averages and their Bias

1994 ◽  
Vol 26 (02) ◽  
pp. 334-340 ◽  
Author(s):  
K. V. Mardia ◽  
I. L. Dryden
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Normal Model ◽  
Likelihood Estimator ◽  
Distributional Properties ◽  
Exact Maximum Likelihood

The paper considers the bias of Bookstein's mean estimator for shape under the isotropic normal model. This work depends on certain distributional properties of shape variables. An alternative unbiased modified estimator is proposed and its performance is compared with various estimators, including Procrustes and the exact maximum likelihood estimator, in a simulation study.

scholarly journals Transforming variables to central normality

2021 ◽  
Author(s):  
Jakob Raymaekers ◽  
Peter J. Rousseeuw
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Real Data ◽  
Data Sets ◽  
Transformation Parameter ◽  
Likelihood Estimator ◽  
Extensive Simulation ◽  
Highly Sensitive

AbstractMany real data sets contain numerical features (variables) whose distribution is far from normal (Gaussian). Instead, their distribution is often skewed. In order to handle such data it is customary to preprocess the variables to make them more normal. The Box–Cox and Yeo–Johnson transformations are well-known tools for this. However, the standard maximum likelihood estimator of their transformation parameter is highly sensitive to outliers, and will often try to move outliers inward at the expense of the normality of the central part of the data. We propose a modification of these transformations as well as an estimator of the transformation parameter that is robust to outliers, so the transformed data can be approximately normal in the center and a few outliers may deviate from it. It compares favorably to existing techniques in an extensive simulation study and on real data.

A good property of the maximum likelihood estimator in a restricted normal model

Test ◽  
1997 ◽  
Vol 6 (1) ◽  
pp. 127-135
Author(s):  
C. Rueda ◽  
B. Salvador ◽  
M. A. Fernández
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Good Property ◽  
Normal Model ◽  
Likelihood Estimator

scholarly journals Classical and Bayesian Approach in Estimation of Scale Parameter of Nakagami Distribution

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Kaisar Ahmad ◽  
S. P. Ahmad ◽  
A. Ahmed
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Bayesian Approach ◽  
Simulation Study ◽  
Bayesian Method ◽  
Scale Parameter ◽  
Loss Functions ◽  
Likelihood Estimator ◽  
R Software ◽  
Nakagami Distribution

Nakagami distribution is considered. The classical maximum likelihood estimator has been obtained. Bayesian method of estimation is employed in order to estimate the scale parameter of Nakagami distribution by using Jeffreys’, Extension of Jeffreys’, and Quasi priors under three different loss functions. Also the simulation study is conducted in R software.

A mutual information estimator with exponentially decaying bias

2015 ◽  
Vol 14 (3) ◽  
Author(s):  
Zhiyi Zhang ◽  
Lukun Zheng
Keyword(s):  
Maximum Likelihood ◽  
Mutual Information ◽  
Asymptotic Normality ◽  
Sample Size ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Type I Error ◽  
Type I ◽  
Nonparametric Estimator ◽  
Likelihood Estimator

AbstractA nonparametric estimator of mutual information is proposed and is shown to have asymptotic normality and efficiency, and a bias decaying exponentially in sample size. The asymptotic normality and the rapidly decaying bias together offer a viable inferential tool for assessing mutual information between two random elements on finite alphabets where the maximum likelihood estimator of mutual information greatly inflates the probability of type I error. The proposed estimator is illustrated by three examples in which the association between a pair of genes is assessed based on their expression levels. Several results of simulation study are also provided.

scholarly journals Estimation of Reliability for a Two Component Survival Stress-Strength Model

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
S. B. Munoli ◽  
Rohit R. Mutkekar
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Maximum Likelihood Estimators ◽  
Reliability Function ◽  
Strength Model ◽  
Life Testing ◽  
Likelihood Estimator ◽  
Two Component ◽  
Testing Experiment

The reliability function for a parallel system of two identical components is derived from a stress-strength model, where failure of one component increases the stress on the surviving component of the system. The Maximum Likelihood Estimators of parameters and their asymptotic distribution are obtained. Further the Maximum Likelihood Estimator and Bayes Estimator of reliability function are obtained using the data from a life-testing experiment. Computation of estimators is illustrated through simulation study.

scholarly journals Estimation of P{X < Y} for gamma exponential model

2014 ◽  
Vol 24 (2) ◽  
pp. 283-291 ◽  
Author(s):  
Milan Jovanovic ◽  
Vesna Rajic
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Asymptotic Distribution ◽  
Simulation Study ◽  
Random Variables ◽  
Exponential Model ◽  
Independent Random Variables ◽  
Likelihood Estimator

In this paper, we estimate probability P{X < Y} when X and Y are two independent random variables from gamma and exponential distribution, respectively. We obtain maximum likelihood estimator and its asymptotic distribution. We perform some simulation study.

scholarly journals Maximum Likelihood Estimator of AUC for a Bi-Exponentiated Weibull Model

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Fazhe Chang ◽  
Lianfen Qian
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Asymptotic Property ◽  
Simulation Study ◽  
Weibull Model ◽  
Finite Sample ◽  
Property A ◽  
Likelihood Estimator ◽  
Exponentiated Weibull ◽  
Finite Sample Size

For a Bi-Exponentiated Weibull model, the authors obtain a general AUC formula and derive the maximum likelihood estimator of AUC and its asymptotic property. A simulation study is carried out to illustrate the finite sample size performance.

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