Statistics, Optimization & Information Computing

Robust Forecasting of Sequences with Periodically Stationary Long Memory Multiplicative Seasonal Increments Observed with Noise and Cointegrated Sequences

Maksym Luz — 2022-03-23

The problem of optimal estimation of linear functionals constructed from unobserved values of stochastic sequence with periodically stationary increments based on observations of the sequence with a periodically stationary noise is considered. For sequences with known spectral densities, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal estimates of the functionals. Formulas that determine the least favorable spectral densities and minimax (robust) spectral characteristics of the optimal linear estimates of functionals are proposed in the case where spectral densities of the sequence are not exactly known while some sets of admissible spectral densities are given.

A Basis Approach to Surface Clustering

Adriano Zanin Zambom — 2022-02-19

This paper presents a novel method for clustering surfaces. The proposal involves first using natural splines basis functions in a tensor product to smooth the data and thus reduce the dimension to a finite number of coefficients, and then using these estimated coefficients to cluster the surfaces via k-means or spectral clustering. An extension of the algorithm to clustering higher-dimensional tensors is also discussed. We show that the proposed algorithm exhibits the property of strong consistency, with or without measurement errors, in correctly clustering the data as the sample size increases. Simulation studies suggest that the proposed method outperforms the benchmark k-means and spectral algorithm which use the original data. In addition, an EGG real data example is considered to illustrate the practical application of the proposal.

The Discrete Inverse Burr Distribution with Characterizations, Properties, Applications, Bayesian and Non-Bayesian Estimations

Christophe Chesneau — 2022-02-05

A new one-parameter heavy tailed discrete distribution with infinite mean is defined and studied. The probability mass function of the new distribution can be "unimodal and right skewed" and its failure rate can be monotonically decreasing. Some of its relevant properties are discussed. Some characterizations based on: (i) the conditional expectation of a certain function of the random variable and (ii) in terms of the reversed hazard function are presented. Different Bayesian and non-Bayesian estimation methods are described and compared using simulations and two real data applications are given. The new model is used to model carious teeth data and counts of cysts in kidneys datasets, and it outperforms many well-known competitive discrete models.

Testing the Validity of Lindley Model Based on Informational Energy with Application to Real Medical Data

Hadi Alizadeh Noughabi — 2021-07-30

In this article, a test statistic for testing the validity of the Lindley model based on the informational energy is proposed. Consistency of our test is shown. Through a simulation study, we obtain the critical values of the test statistic and then the power of the test is computed by Monte Carlo method against various alternatives. The performance of the proposed test with some competing tests is compared. Our results show that our test is superior to the classical nonparametric tests and can apply to a testing problem in practice. A real medical data set is presented and analyzed.

Extreme Value Modelling of the Monthly South African Industrial Index (J520) Returns

Owen Jakata — 2021-12-13

This study uses Extreme Value Theory (EVT), Value-at-Risk (VaR) and Expected Shortfall (ES) analysis as a unified tool for managing extreme financial risk. The study extends the application of the generalised Pareto distribution (GPD) by modelling monthly South African Industrial Index (J520) returns (years: 1995-2018) to quantify the tail-related risk measures. The GPD is used to estimate the tail-related risk measures using the Peak over Threshold (PoT) method. Maximum Likelihood Estimates (MLE) of model parameters were obtained and the models goodness of fit was assessed graphically using Quantile-Quantile (QCQ) plots, Probability (PCP) plots, scatter plots, residuals, return levels and density plots. The findings are that the GPD provides an adequate fit to the data of excesses (extreme losses or gains). Low frequency but very high or very low returns impact on investment decisions. Calculations of the VaR and ES tail-related risk measures based on the fitted GPD model are given. The results reveal that for an investment in the South African Industrial Index (J520), the prospect of potential extreme losses is less than the prospect of potential extreme gains. There seems to be an upper bound where losses do not seem to exceed easily. The study concluded that EVT, together with VaR and ES analysis are useful tools that can be applied in practice to manage index/stock price risk and help investors improve their investment decisions and trading strategies through better quality information derived from the tools. This study contributes to empirical evidence on EVT methods that help to protect financial systems against unpredictable fluctuations and losses of extreme nature.

On F-implicit Minimal Vector Variational Inequalities

Mehdi Roohi — 2022-03-23

In this paper, by introducing some new concepts in minimal spaces, we prove a generalized form of the Fan-KKM theorem in minimal vector spaces. A new class of minimal generalized vector F-implicit variational inequality problems and, as an application of Fan-KKM theorem is investigated. Moreover, an existence theorem for this kind of problems under some suitable assumptions in minimal vector spaces is given.

Necessary and Sufficient Optimality Conditions for Semi-infinite Programming with Multiple Fuzzy-valued Objective Functions

Tung Thanh Le — 2022-01-07

This paper deals with semi-infifinite programming with multiple fuzzy-valued objective functions. Firstly, some types of effificient solutions are proposed and illustrated in some examples. Then, necessary and suffificient Karush-Kuhn-Tucker optimality conditions for semi-infifinite programming with multiple fuzzy-valued objective functions are established.

Necessary Conditions to A Fractional Variational Problem

Melani Barrios — 2022-02-05

The fractional variational calculus is a recent fifield, where classical variational problems are considered, but in the presence of fractional derivatives. Since there are several defifinitions of fractional derivatives, it is logical to think of different types of optimality conditions. For this reason, in order to solve fractional variational problems, two theorems of necessary conditions are well known: an Euler-Lagrange equation which involves Caputo and Riemann-Liouville fractional derivatives, and other Euler-Lagrange equation that involves only Caputo derivatives. However, it is undecided which of these two methods is convenient to work with. In this article, we make a comparison solving a particular fractional variational problem with both methods to obtain some conclusions about which one gives the optimal solution.

Three-step Iterative Algorithm with Error Terms of Convergence and Stability Analysis for New NOMVIP in Ordered Banach Spaces

Iqbal Ahmad — 2021-07-30

This article undertakes to study a NOMVIP involving XNOR-operation and solved by employing a proposed three-step iterative algorithm in ordered Banach Space. Under suitable conditions, we obtain the strong convergence and existence results of NOMVIP involving XNOR-operation by applying the resolvent operator technique with XNOR and XOR operations and discuss the stability of the proposed algorithm. Finally, we provide a numerical example to confirm the convergence of the suggested algorithm in support of our considered problem which gives the grantee that all the proposed conditions of our main result have been formulated by using MATLAB programming.

Validation of Xgamma Exponential Model via Nikulin-Rao-Robson Goodness-of- Fit-Test under Complete and Censored Sample with Different Methods of Estimation

Abhimanyu Singh Yadav — 2022-02-28

In this article, a new extension of the one parameter Xgamma distribution has been proposed. Also the associated different statistical properties are derived. The unknown parameter of the proposed distribution is estimated by using different classical estimation methods and by using Bayesian estimation method. Under classical methods of estimation, we brieflfly describe the method of moment estimators, maximum likelihood estimators, maximum product of spacing estimators, least squares and weighted least squares estimators and Cramer-von-Mises estimators. The Bayesian estimation using gamma prior under squared error loss function has been discussed and computed via Lindley’s approximation and Markov Chain Monte Carlo techniques. Furthermore, the 100(1 − α)% asymptotic confifidence interval and credible interval along with the coverage probability are also discussed. The obtained classical and the Bayesian estimators are compared through Monte Carlo simulations. Next, we construct a modifified Chi-squared goodness of fifit test based on the Nikulin-Rao-Robson (NRR) statistic in presence of censored and complete data. The applicability of our proposed model has been illustrated for both complete data and right censored data by using two real data sets for each.

A New Compound Generalization of the Lomax Lifetime Model: Properties, Copulas and Modeling Real Data

Mohamed Refaie — 2022-01-01

A new compound generalization of the Lomax lifetime model is presented and studied. The novel model is established based on the Poisson Topp-Leone family of Merovci et al. (2020). The novel density can be “right skewedwith heavy tail”, “symmetric” and “left skewedwith heavy tail”. The corresponding failure rate can be “monotonically decreasing”, “increasingconstant”, “upside down”, “upside down-constant” and “reversed J-shape”. Relevant characteristics are derived and discussed. numerical and graphical analysis for some statistical properties are presented. we derived some new bivariate extensions via some common copulas. Graphical assessment for the maximum likelihood estimation is presented. Graphical assessment for the maximum likelihood estimation is presented. Two real-life data sets are analyzed and modelled using the novel model. The new model proven its superiority against fourteen competitive Lomax extensions.

A Different Way of Choosing a Threshold in a Bivariate Extreme Value Study

Andrehette Verster — 2021-12-15

The choice of optimum threshold in Extreme Value Theory, peaks over threshold, has been a topic of discussion
for decades. A threshold must be chosen high enough to control the bias of the extreme value index. On the other hand, if a threshold is chosen too high the variance becomes a problem. This is a very difficult trade-off and has been studied over the years from various viewpoints. More often these studies aim at methods for choosing the threshold in univariate settings. Not as many literature are available for choosing the threshold in a multivariate setting. In this paper we consider an approach for choosing the threshold when working with bivariate extreme values above a threshold. This approach makes use of Bayesian methodology. It adds value to the existing literature since it is also possible to use this approach without visual inspection.

A New Lifetime Distribution with Properties, Characterizations, Validation Testing and Different Estimation Methods

Haitham M. Yousof — 2021-12-15

A new lifetime distribution is proposed and its properties are studied. The new density function has a heavy right skew tails with different shapes. The new failure rate function can be “constant”, “bathtub (U)”, “increasing-constant”, “decreasing-constant”, “upside down” and “upside down-U”. Complexity of the most integrals related to statistical properties is solved and numerically analyzed. Simple type copula is presented. Numerical calculations for analyzing the skewness and kurtosis are presented. Different estimation methods such as the maximum likelihood estimation method, Cramer-von-Mises estimation method, ordinary least square estimation method, weighted least square estimation method, Anderson Darling estimation method, right tail Anderson Darling estimation method and left tail-Anderson Darling estimation method are considered. Numerical simulation studies are performed. An example of environmental real data set is employed to compare the estimation methods. Another example is presented to measure importance and flflexibility of the new model. Using the validation approach proposed by Bagdonavicius and Nikulin (2011) for censored data, we propose the construction of modifified chi-square goodness-of-fifit tests for the new model. Based on the maximum likelihood estimators on initial data, the modifified statistics recover the information lost while grouping data and follow chi-square models. All elements of the modifified criteria tests are given explicitly. Numerical example from simulated samples and four real data sets have been analyzed to illustrate the feasibility of the modifified test.

Exponentiated Weibull Models Applied to Medical Data in Presence of Right-censoring, Cure Fraction and Covariates

Edson Zangiacomi Martinez — 2021-11-29

Cure fraction models have been widely used to analyze survival data in which a proportion of the individuals is
not susceptible to the event of interest. This article considers frequentist and Bayesian methods to estimate the unknown model parameters of the exponentiated Weibull (EW) distribution considering right-censored survival data with a cure fraction and covariates. The EW distribution is as an extension to the Weibull distribution by considering an additional shape parameter to the model. We consider four types of cure fraction models: the mixture cure fraction (MCF), the nonmixture cure fraction (NMCF), the complementary promotion time cure (CPTC), and the cure rate proportional odds (CRPO) models. Bayesian inferences are obtained by using MCMC (Markov Chain Monte Carlo) methods. A simulation study was conducted to examine the performance of the maximum likelihood estimators for different sample sizes. Two real datasets were considered to illustrate the applicability of the proposed model. The EW distribution and its sub-models have the flexibility to accommodate different shapes for the hazard function and should be an attractive choice for survival data analysis when a cure fraction is present.

Polynomials Shrinkage Estimators of a Multivariate Normal Mean

Abdelkader Benkhaled — 2021-08-17

In this work, the estimation of the multivariate normal mean by different classes of shrinkage estimators is investigated. The risk associated with the balanced loss function is used to compare two estimators. We start by considering estimators that generalize the James-Stein estimator and show that these estimators dominate the maximum likelihood estimator (MLE), therefore are minimax, when the shrinkage function satisfifies some conditions. Then, we treat estimators of polynomial form and prove the increase of the degree of the polynomial allows us to build a better estimator from the one previously constructed.

A New Two-parameter Modified Half-logistic Distribution: Properties and Applications

Gorgees Shaheed — 2021-05-24

This article aims to present and analyse a modified two-parameter version of the Half-Logistic lifetime model.
The hazard function, quantile function, asymptotic, linear combination, extreme value, moments, incomplete moments, residual entropies, moment generating function and order statistics, all theoretical properties of this model that are derived and discussed in depth. By performing a simulation analysis, the various techniques of estimation are compared to the estimates of the maximum likelihood of parameters.Finally, two actual data sets have been applied to illustrate the goals of this article.

Extended Exponentiated Chen Distribution: Mathematical Properties and Applications

Zohreh Zamani — 2021-07-10

In this paper, we introduce a new four-parameter distribution which is called Extended Exponentiated Chen (EE-C) distribution. Theoretical properties of this model including the hazard function, moments, conditional moments, mean residual life, mean past lifetime, coefficients of skewness and kurtosis, order statistics and asymptotic properties are derived and studied. The maximum likelihood estimation technique is used to estimate the parameters of this model. The estimation of the model parameters by Least squares, Weighted Least Squares, Crammer-von-Mises, Anderson-Darling and right-tailed Anderson-Darling methods are also briefly introduced and numerically investigated. Moreover, simulation schemes are derived. At the end, three applications of the model with two real data sets are presented for the illustration of the flexibility of the proposed distribution.

Statistical Inference of Chen Distribution Based on Type I Progressive Hybrid Censored Samples

Tanmay Kayal — 2022-03-23

In this paper we study the problem of estimating unknown parameters of a two-parameter distribution with bathtub shape under the assumption that data are type I progressive hybrid censored. We derive maximum likelihood estimators and then obtain the observed Fisher information matrix. Bayes estimators are also obtained under the squared error loss function and highest posterior density intervals are constructed as well. We perform a simulation study to compare proposed methods and analyzed a real data set for illustration purposes. Finally we establish optimal plans with respect to cost constraints and obtain comments based on a numerical study.

Data Envelopment Analysis in Three-Stage Network Structure with Slack Based Measure (SBM)

Qaiser Farooq Dar — 2022-03-23

Data envelopment analysis (DEA) is a non-parametric technique for measuring and analyzing the relative efficiency of the Decision-Making Unit (DMU) having multiple homogeneous types of inputs and outputs. Traditional DEA treats DMU as black boxes and calculates their efficiencies by considering their initial inputs and final outputs. But the overall efficiency of DMU is directly depended upon the performances of intermediate processes of operations. In many situations, DMUs have a three-stage network structure. Against the aforesaid backdrop, this paper introduces a non-oriented and non-radial the slacks-based measure (SBM) of efficiency framework for the three-stage network production process. In the proposed model we have considered both series and parallel relationship between the inputs and outputs of different independent and dependent stages. Additionally, this research is aimed at measuring the Indian banking efficiency by using the three-stage network DEA model.