scholarly journals Robust functional regression model for marginal mean and subject-specific inferences

2017 ◽  
Vol 27 (11) ◽  
pp. 3236-3254 ◽  
Author(s):  
Chunzheng Cao ◽  
Jian Qing Shi ◽  
Youngjo Lee
Keyword(s):  
Real Data ◽  
Functional Regression ◽  
Conditional Mean ◽  
Data Contamination ◽  
Data Application ◽  
Proposed Model ◽  
Subject Specific ◽  
Heavy Tailed ◽  
Conditional Means ◽  
Functional Regression Models

We introduce flexible robust functional regression models, using various heavy-tailed processes, including a Student t-process. We propose efficient algorithms in estimating parameters for the marginal mean inferences and in predicting conditional means as well as interpolation and extrapolation for the subject-specific inferences. We develop bootstrap prediction intervals (PIs) for conditional mean curves. Numerical studies show that the proposed model provides a robust approach against data contamination or distribution misspecification, and the proposed PIs maintain the nominal confidence levels. A real data application is presented as an illustrative example.

scholarly journals A New Right-Skewed Upside Down Bathtub Shaped Heavy-tailed Distribution and its Applications

2021 ◽  
Vol 19 (1) ◽  
Author(s):  
Sandeep Kumar Maurya ◽  
Sanjay K Singh ◽  
Umesh Singh
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Statistical Properties ◽  
New Right ◽  
Data Sets ◽  
Proposed Model ◽  
Heavy Tailed Distribution ◽  
Heavy Tailed

A one parameter right skewed, upside down bathtub type, heavy-tailed distribution is derived. Various statistical properties and maximum likelihood approaches for estimation purpose are studied. Five different real data sets with four different models are considered to illustrate the suitability of the proposed model.

scholarly journals Two symmetric and computationally efficient Gini correlations

2020 ◽  
Vol 8 (1) ◽  
pp. 373-395
Author(s):  
Courtney Vanderford ◽  
Yongli Sang ◽  
Xin Dang
Keyword(s):  
Influence Function ◽  
Random Variables ◽  
Real Data ◽  
Computationally Efficient ◽  
Gini Correlation ◽  
Heavy Tailed Distributions ◽  
Data Application ◽  
Heavy Tailed ◽  
Log Normal ◽  
Log Normal Distribution

AbstractStandard Gini correlation plays an important role in measuring the dependence between random variables with heavy-tailed distributions. It is based on the covariance between one variable and the rank of the other. Hence for each pair of random variables, there are two Gini correlations and they are not equal in general, which brings a substantial difficulty in interpretation. Recently, Sang et al (2016) proposed a symmetric Gini correlation based on the joint spatial rank function with a computation cost of O(n2) where n is the sample size. In this paper, we study two symmetric and computationally efficient Gini correlations with the computational complexity of O(n log n). The properties of the new symmetric Gini correlations are explored. The influence function approach is utilized to study the robustness and the asymptotic behavior of these correlations. The asymptotic relative efficiencies are considered to compare several popular correlations under symmetric distributions with different tail-heaviness as well as an asymmetric log-normal distribution. Simulation and real data application are conducted to demonstrate the desirable performance of the two new symmetric Gini correlations.

scholarly journals Robust Algorithms for Change-Point Regressions Using the t-Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2394
Author(s):  
Kang-Ping Lu ◽  
Shao-Tung Chang
Keyword(s):  
Change Point ◽  
Regression Models ◽  
Degrees Of Freedom ◽  
Real Data ◽  
Fuzzy Classification ◽  
Robust Algorithms ◽  
Data Contamination ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
T Distribution

Regression models with change-points have been widely applied in various fields. Most methodologies for change-point regressions assume Gaussian errors. For many real data having longer-than-normal tails or atypical observations, the use of normal errors may unduly affect the fit of change-point regression models. This paper proposes two robust algorithms called EMT and FCT for change-point regressions by incorporating the t-distribution with the expectation and maximization algorithm and the fuzzy classification procedure, respectively. For better resistance to high leverage outliers, we introduce a modified version of the proposed method, which fits the t change-point regression model to the data after moderately pruning high leverage points. The selection of the degrees of freedom is discussed. The robustness properties of the proposed methods are also analyzed and validated. Simulation studies show the effectiveness and resistance of the proposed methods against outliers and heavy-tailed distributions. Extensive experiments demonstrate the preference of the t-based approach over normal-based methods for better robustness and computational efficiency. EMT and FCT generally work well, and FCT always performs better for less biased estimates, especially in cases of data contamination. Real examples show the need and the practicability of the proposed method.

scholarly journals A Bayesian Approach to Heavy-Tailed Finite Mixture Autoregressive Models

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 929
Author(s):  
Mohammad Reza Mahmoudi ◽  
Mohsen Maleki ◽  
Dumitru Baleanu ◽  
Vu-Thanh Nguyen ◽  
Kim-Hung Pho
Keyword(s):  
Bayesian Analysis ◽  
Heavy Tails ◽  
Linear Time ◽  
Real Data ◽  
Finite Mixture ◽  
Stochastic Representation ◽  
Bayesian Approaches ◽  
Proposed Model ◽  
Heavy Tailed ◽  
Informative Prior Distributions

In this paper, a Bayesian analysis of finite mixture autoregressive (MAR) models based on the assumption of scale mixtures of skew-normal (SMSN) innovations (called SMSN–MAR) is considered. This model is not simultaneously sensitive to outliers, as the celebrated SMSN distributions, because the proposed MAR model covers the lightly/heavily-tailed symmetric and asymmetric innovations. This model allows us to have robust inferences on some non-linear time series with skewness and heavy tails. Classical inferences about the mixture models have some problematic issues that can be solved using Bayesian approaches. The stochastic representation of the SMSN family allows us to develop a Bayesian analysis considering the informative prior distributions in the proposed model. Some simulations and real data are also presented to illustrate the usefulness of the proposed models.

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

2019 ◽  
Vol XVI (2) ◽  
pp. 1-11
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Muhammad Akbar Ali Shah ◽  
Emrah Altun
Keyword(s):  
Real Data ◽  
Continuous Model ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Probability Weighted Moment ◽  
Record Statistics ◽  
Maximum Likelihood Criterion

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

scholarly journals MIXED CAUSAL-NONCAUSAL AR PROCESSES AND THE MODELLING OF EXPLOSIVE BUBBLES

2019 ◽  
Vol 35 (6) ◽  
pp. 1234-1270 ◽  
Author(s):  
Sébastien Fries ◽  
Jean-Michel Zakoian
Keyword(s):  
Conditional Distribution ◽  
Stable Distribution ◽  
Financial Time Series ◽  
Domain Of Attraction ◽  
Real Data ◽  
Autoregressive Processes ◽  
Financial Time ◽  
Causal Representation ◽  
Heavy Tailed ◽  
Non Gaussian

Noncausal autoregressive models with heavy-tailed errors generate locally explosive processes and, therefore, provide a convenient framework for modelling bubbles in economic and financial time series. We investigate the probability properties of mixed causal-noncausal autoregressive processes, assuming the errors follow a stable non-Gaussian distribution. Extending the study of the noncausal AR(1) model by Gouriéroux and Zakoian (2017), we show that the conditional distribution in direct time is lighter-tailed than the errors distribution, and we emphasize the presence of ARCH effects in a causal representation of the process. Under the assumption that the errors belong to the domain of attraction of a stable distribution, we show that a causal AR representation with non-i.i.d. errors can be consistently estimated by classical least-squares. We derive a portmanteau test to check the validity of the estimated AR representation and propose a method based on extreme residuals clustering to determine whether the AR generating process is causal, noncausal, or mixed. An empirical study on simulated and real data illustrates the potential usefulness of the results.

scholarly journals An adaptive social distancing SIR model for COVID-19 disease spreading and forecasting

2021 ◽  
Vol 10 (s1) ◽  
Author(s):  
Said Gounane ◽  
Yassir Barkouch ◽  
Abdelghafour Atlas ◽  
Mostafa Bendahmane ◽  
Fahd Karami ◽  
...  
Keyword(s):  
Mathematical Theory ◽  
Real Data ◽  
Sir Model ◽  
Epidemic Threshold ◽  
Social Distancing ◽  
Sir Epidemic ◽  
Proposed Model ◽  
Disease Spreading ◽  
The Government ◽  
The Impact

Abstract Recently, various mathematical models have been proposed to model COVID-19 outbreak. These models are an effective tool to study the mechanisms of coronavirus spreading and to predict the future course of COVID-19 disease. They are also used to evaluate strategies to control this pandemic. Generally, SIR compartmental models are appropriate for understanding and predicting the dynamics of infectious diseases like COVID-19. The classical SIR model is initially introduced by Kermack and McKendrick (cf. (Anderson, R. M. 1991. “Discussion: the Kermack–McKendrick Epidemic Threshold Theorem.” Bulletin of Mathematical Biology 53 (1): 3–32; Kermack, W. O., and A. G. McKendrick. 1927. “A Contribution to the Mathematical Theory of Epidemics.” Proceedings of the Royal Society 115 (772): 700–21)) to describe the evolution of the susceptible, infected and recovered compartment. Focused on the impact of public policies designed to contain this pandemic, we develop a new nonlinear SIR epidemic problem modeling the spreading of coronavirus under the effect of a social distancing induced by the government measures to stop coronavirus spreading. To find the parameters adopted for each country (for e.g. Germany, Spain, Italy, France, Algeria and Morocco) we fit the proposed model with respect to the actual real data. We also evaluate the government measures in each country with respect to the evolution of the pandemic. Our numerical simulations can be used to provide an effective tool for predicting the spread of the disease.

An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

2020 ◽  
Vol 70 (4) ◽  
pp. 953-978
Author(s):  
Mustafa Ç. Korkmaz ◽  
G. G. Hamedani
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Lorenz Curves ◽  
Proposed Model ◽  
New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

scholarly journals Transition models for count data: a flexible alternative to fixed distribution models

2021 ◽  
Author(s):  
Moritz Berger ◽  
Gerhard Tutz
Keyword(s):  
Count Data ◽  
Regression Models ◽  
Negative Binomial ◽  
Real Data ◽  
Distribution Models ◽  
Explanatory Variables ◽  
Excess Zeros ◽  
Proposed Model ◽  
Transition Models ◽  
Fixed Distribution

AbstractA flexible semiparametric class of models is introduced that offers an alternative to classical regression models for count data as the Poisson and Negative Binomial model, as well as to more general models accounting for excess zeros that are also based on fixed distributional assumptions. The model allows that the data itself determine the distribution of the response variable, but, in its basic form, uses a parametric term that specifies the effect of explanatory variables. In addition, an extended version is considered, in which the effects of covariates are specified nonparametrically. The proposed model and traditional models are compared in simulations and by utilizing several real data applications from the area of health and social science.

Sign in / Sign up

Export Citation Format

Share Document