scholarly journals On the Arcsecant Hyperbolic Normal Distribution. Properties, Quantile Regression Modeling and Applications

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 117 ◽  
Author(s):  
Mustafa Ç. Korkmaz ◽  
Christophe Chesneau ◽  
Zehra Sedef Korkmaz
Keyword(s):  
Quantile Regression ◽  
Regression Model ◽  
Normal Distribution ◽  
Order Statistics ◽  
Random Variable ◽  
Unit Interval ◽  
Parametric Estimation ◽  
Simulation Studies ◽  
Quantile Regression Model ◽  
New Distribution

This work proposes a new distribution defined on the unit interval. It is obtained by a novel transformation of a normal random variable involving the hyperbolic secant function and its inverse. The use of such a function in distribution theory has not received much attention in the literature, and may be of interest for theoretical and practical purposes. Basic statistical properties of the newly defined distribution are derived, including moments, skewness, kurtosis and order statistics. For the related model, the parametric estimation is examined through different methods. We assess the performance of the obtained estimates by two complementary simulation studies. Also, the quantile regression model based on the proposed distribution is introduced. Applications to three real datasets show that the proposed models are quite competitive in comparison to well-established models.

A nonparametric method for assessment of interactions in a median regression model for analyzing right censored data

2018 ◽  
Vol 28 (4) ◽  
pp. 1170-1187
Author(s):  
MinJae Lee ◽  
Mohammad H Rahbar ◽  
Hooshang Talebi
Keyword(s):  
Quantile Regression ◽  
Regression Model ◽  
Survival Data ◽  
Real Life ◽  
Simulation Studies ◽  
Median Regression ◽  
Right Censored Data ◽  
Censored Quantile Regression ◽  
Quantile Regression Model ◽  
The Impact

We propose a nonparametric test for interactions when we are concerned with investigation of the simultaneous effects of two or more factors in a median regression model with right censored survival data. Our approach is developed to detect interaction in special situations, when the covariates have a finite number of levels with a limited number of observations in each level, and it allows varying levels of variance and censorship at different levels of the covariates. Through simulation studies, we compare the power of detecting an interaction between the study group variable and a covariate using our proposed procedure with that of the Cox Proportional Hazard (PH) model and censored quantile regression model. We also assess the impact of censoring rate and type on the standard error of the estimators of parameters. Finally, we illustrate application of our proposed method to real life data from Prospective Observational Multicenter Major Trauma Transfusion (PROMMTT) study to test an interaction effect between type of injury and study sites using median time for a trauma patient to receive three units of red blood cells. The results from simulation studies indicate that our procedure performs better than both Cox PH model and censored quantile regression model based on statistical power for detecting the interaction, especially when the number of observations is small. It is also relatively less sensitive to censoring rates or even the presence of conditionally independent censoring that is conditional on the levels of covariates.

scholarly journals Modeling of Quantile Regression to Know the Factors Affecting the High Spread Api Malaria in Indonesia

2020 ◽  
Vol 16 (3) ◽  
pp. 417
Author(s):  
Yahya Matdoan
Keyword(s):  
Quantile Regression ◽  
Regression Model ◽  
Normal Distribution ◽  
Factors Affecting ◽  
Quantile Regression Model ◽  
A Value ◽  
Main Factors ◽  
Poor Population

The OLS method estimation is based on a normal distribution, so it is not appropriate to analyze a number of data that are not symmetrical or contain outliers. Therefore, quantile regression was developed which was not affected by outliers. This study compares quantile regression with OLS in the case of factors affecting malaria in Indonesia. The results show that the value of the Quantil Regression model is 0,832 and the MSE value is 0,182. In addition, the OLS model obtained a value of 0,681 and an MSE value of 0,231. So we get the conclusion that the best model is a quantile regression model. Further results were obtained that the main factors causing the spread of malaria in Indonesia were the factor of livable houses, poor population factors and physician factors.

scholarly journals Improving estimations in quantile regression model with autoregressive errors

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 97-107 ◽  
Author(s):  
Bahadır Yuzbasi ◽  
Yasin Asar ◽  
Samil Sik ◽  
Ahmet Demiralp
Keyword(s):  
Quantile Regression ◽  
Regression Model ◽  
Simulation Experiment ◽  
Ordinary Least Squares ◽  
Least Squares Regression ◽  
White Noise Process ◽  
Respiratory Mortality ◽  
Explanatory Variables ◽  
Quantile Regression Model ◽  
Regression Approach

An important issue is that the respiratory mortality may be a result of air pollution which can be measured by the following variables: temperature, relative humidity, carbon monoxide, sulfur dioxide, nitrogen dioxide, hydrocarbons, ozone, and particulates. The usual way is to fit a model using the ordinary least squares regression, which has some assumptions, also known as Gauss-Markov assumptions, on the error term showing white noise process of the regression model. However, in many applications, especially for this example, these assumptions are not satisfied. Therefore, in this study, a quantile regression approach is used to model the respiratory mortality using the mentioned explanatory variables. Moreover, improved estimation techniques such as preliminary testing and shrinkage strategies are also obtained when the errors are autoregressive. A Monte Carlo simulation experiment, including the quantile penalty estimators such as lasso, ridge, and elastic net, is designed to evaluate the performances of the proposed techniques. Finally, the theoretical risks of the listed estimators are given.

scholarly journals ASYMPTOTIC THEORY FOR NONLINEAR QUANTILE REGRESSION UNDER WEAK DEPENDENCE

2015 ◽  
Vol 32 (3) ◽  
pp. 686-713 ◽  
Author(s):  
Walter Oberhofer ◽  
Harry Haupt
Keyword(s):  
Quantile Regression ◽  
Asymptotic Normality ◽  
Regression Model ◽  
Asymptotic Theory ◽  
Asymptotic Properties ◽  
Covariance Estimation ◽  
First Order ◽  
Regression Quantiles ◽  
Quantile Regression Model ◽  
Consistency And Asymptotic Normality

This paper studies the asymptotic properties of the nonlinear quantile regression model under general assumptions on the error process, which is allowed to be heterogeneous and mixing. We derive the consistency and asymptotic normality of regression quantiles under mild assumptions. First-order asymptotic theory is completed by a discussion of consistent covariance estimation.

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