On robust regression estimation for shape parameters of Pareto distribution

2015 ◽  
Author(s):  
Y. M. Kantar
Keyword(s):  
Pareto Distribution ◽  
Robust Regression ◽  
Regression Estimation ◽  
Shape Parameters

Stochastic comparison of parallel systems with Pareto components

2021 ◽  
pp. 1-13
Author(s):  
Sameen Naqvi ◽  
Weiyong Ding ◽  
Peng Zhao
Keyword(s):  
Order Statistics ◽  
Extreme Value Theory ◽  
Pareto Distribution ◽  
Parallel Systems ◽  
Value Theory ◽  
Extreme Value ◽  
Stochastic Comparison ◽  
Shape Parameters ◽  
Scale Parameters ◽  
Dispersive Ordering

Abstract Pareto distribution is an important distribution in extreme value theory. In this paper, we consider parallel systems with Pareto components and study the effect of heterogeneity on skewness of such systems. It is shown that, when the lifetimes of components have different shape parameters, the parallel system with heterogeneous Pareto component lifetimes is more skewed than the system with independent and identically distributed Pareto components. However, for the case when the lifetimes of components have different scale parameters, the result gets reversed in the sense of star ordering. We also establish the relation between star ordering and dispersive ordering by extending the result of Deshpande and Kochar [(1983). Dispersive ordering is the same as tail ordering. Advances in Applied Probability 15(3): 686–687] from support $(0, \infty )$ to general supports $(a, \infty )$ , $a > 0$ . As a consequence, we obtain some new results on dispersion of order statistics from heterogeneous Pareto samples with respect to dispersive ordering.

scholarly journals Least Absolute Deviation Support Vector Regression

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Kuaini Wang ◽  
Jingjing Zhang ◽  
Yanyan Chen ◽  
Ping Zhong
Keyword(s):  
Support Vector Regression ◽  
Loss Function ◽  
Robust Regression ◽  
Support Vector ◽  
Regression Estimation ◽  
Least Absolute Deviation ◽  
Absolute Deviation ◽  
Robust Model ◽  
Benchmark Datasets ◽  
Classification And Regression

Least squares support vector machine (LS-SVM) is a powerful tool for pattern classification and regression estimation. However, LS-SVM is sensitive to large noises and outliers since it employs the squared loss function. To solve the problem, in this paper, we propose an absolute deviation loss function to reduce the effects of outliers and derive a robust regression model termed as least absolute deviation support vector regression (LAD-SVR). The proposed loss function is not differentiable. We approximate it by constructing a smooth function and develop a Newton algorithm to solve the robust model. Numerical experiments on both artificial datasets and benchmark datasets demonstrate the robustness and effectiveness of the proposed method.

Nonparametric robust regression estimation for censored data

2015 ◽  
Vol 58 (2) ◽  
pp. 505-525 ◽  
Author(s):  
Mohamed Lemdani ◽  
Elias Ould Saïd
Keyword(s):  
Censored Data ◽  
Robust Regression ◽  
Regression Estimation

scholarly journals Bayesian inference for Pareto distribution with prior conjugate and prior non conjugate

2020 ◽  
Vol 16 (3) ◽  
pp. 382
Author(s):  
Ferra YANUAR ◽  
Cici Saputri
Keyword(s):  
Parameter Estimation ◽  
Bayesian Inference ◽  
Prior Distribution ◽  
Pareto Distribution ◽  
Scale Parameter ◽  
Simulation Studies ◽  
Shape Parameters ◽  
Conjugate Prior ◽  
Absolute Bias ◽  
Best Estimator

The purpose of this study is to determine the best estimator for estimating the shape   parameters of the Pareto distribution with the known  scale parameter. Estimation of these parameters is done by using the Gamma distribution as the prior distribution of the conjugate and the Uniform distribution as the non-conjugate prior distribution. A comparison of the two prior distributions is done through simulation studies with various sample sizes. The best estimator net is a method that produces the smallest posterior variance, absolute bias, and Bayes confidence interval. This study proves that the Bayes estimator by using the prior conjugate distribution produces all indicators of the goodness of the model with a smaller value than the non-conjugate prior distribution. Thus it can be concluded that the estimator with prior conjugate will produce a better predictive value than prior non-conjugate.

scholarly journals Robust Regression Estimation Methods and Intercept Bias: A Capital Asset Pricing Model Application

2009 ◽  
Vol 13 (3/4) ◽  
pp. 293-321 ◽  
Author(s):  
James B. McDonald ◽  
◽  
Richard A. Michelfelder ◽  
Panayiotis Theodossiou ◽  
◽  
...  
Keyword(s):  
Asset Pricing ◽  
Robust Regression ◽  
Capital Asset Pricing Model ◽  
Estimation Methods ◽  
Capital Asset Pricing ◽  
Regression Estimation ◽  
Pricing Model ◽  
Capital Asset ◽  
Model Application ◽  
Asset Pricing Model
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