{"title":"Poisson Quasi-Maximum Likelihood Estimator-based CUSUM Test for Integer-Valued Time Series","authors":"Sangyeol Lee","doi":"10.3844/jmssp.2019.250.258","DOIUrl":"https://doi.org/10.3844/jmssp.2019.250.258","url":null,"abstract":"This study considers the parameter change test for integer-valued time series models based on the Poisson quasi-maximum likelihood estimates. As a change point test, we consider the score vector-based CUSUM test and show that its limiting null distribution takes the form of a function of Brownian bridges. Moreover, the residual-based CUSUM tests are considered as alternatives. For evaluation, we conduct a Monte Carlo simulation study with Poisson, zero-inflated Poisson, negative binomial and Conway-Maxwell integer-valued generalized autoregressive conditional heteroscedastic models andPoisson integer-valued autoregressive models, and compare the performance of the proposed CUSUM tests. Our findings confirm that the proposed test is a functional tool for detecting a change point when the underlying distribution is unspecified.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"30 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78180017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fuzzy Bernstein-Stancu Operator of Rough I-Core of Triple Sequences","authors":"A. Esi, N. Subramanian, M. Ozdemir","doi":"10.3844/JMSSP.2019.323.332","DOIUrl":"https://doi.org/10.3844/JMSSP.2019.323.332","url":null,"abstract":"","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"106 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76106395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Functional Non-Inferiority Hypothesis Testing for Longitudinal Data","authors":"A. Sandie, A. Wanjoya, J. B. Tchatchueng-Mbougua","doi":"10.3844/JMSSP.2019.208.217","DOIUrl":"https://doi.org/10.3844/JMSSP.2019.208.217","url":null,"abstract":"The study pattern of non-inferiority trials is increasingly used to show the non-inferiority of new health intervention. Although in such studies the data are longitudinally collected (data held over a period of time), the conclusion of these non-inferiority trials is based on data observed at a specific time during the study period (usually at the end of the study period). In this study, we present a method that takes into account all the data observed during the study period to perform non-inferiority test. Thus, we approximate the observed data on a statistical unit by a function of time. This allows to transform the observed data on a time grid into functional data on a continuum domain. Although it could have some relevant applications, the functional data analysis for non-inferiority test has not been addressed. In this study, the functional non-inferiority hypothesis testing has been introduced. The optimal point-wise test and simultaneous confidence bands have been adapted and adopted for the purpose. The assessment of the methods has been done through simulations example. Both methods have good performances for large sample sizes. For small sample sizes, the optimal point-wise test would be too conservative while the simultaneous confidence bands based test would be a bit liberal.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"5 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80744508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
L. Chaves, Laerte Dias de Carvalho, Carlos José dos Reis, Devanil Jaques de Souza
{"title":"Explaining the Generalized Cross-Validation on Linear Models","authors":"L. Chaves, Laerte Dias de Carvalho, Carlos José dos Reis, Devanil Jaques de Souza","doi":"10.3844/jmssp.2019.298.307","DOIUrl":"https://doi.org/10.3844/jmssp.2019.298.307","url":null,"abstract":"Cross-Validation is a model validation method widely used by the scientific community. The Generalized Cross-Validation (GCV) is an invariant version of the usual Cross-Validation method. This generalization was obtained using the non usual theory of circulant complex matrices. In this work we intend to give a clear and complete exposition concerning the linear algebra assumptions required by the theory. The aim was to make this text accessible to a wide audience of statisticians and non-statisticians who use the Cross-Validation method in their research activities. It is also intended to supply the absence of a basic reference on this topic in the literature.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"14 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84242930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Constructing Gibbs Measure in a Rigorous Way","authors":"F. Kachapova, Ilias Kachapov","doi":"10.3844/jmssp.2019.308.322","DOIUrl":"https://doi.org/10.3844/jmssp.2019.308.322","url":null,"abstract":"Equilibrium statistical mechanics studies mathematical models for physical systems with many particles interacting with an external force and with one another. In this paper we describe an interaction model that generalizes several of these models in one model. An infinite model is constructed as the limiting case of finite interaction models, that is as a thermodynamic limit. The key point in constructing a thermodynamic limit is a proof of existence of the limiting probability measure (Gibbs measure). Traditional proofs use DLR formalism and are quite complicated. Here we explain a more transparent and more constructive proof for the case of high temperatures. The paper provides a detailed, step-by-step rigorous construction of a statistical model and corresponding proofs. The paper also includes a version of the central limit theorem for a random field transformed by a renormalization group, in a special case of the interaction model.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"10 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87366403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. Tiendrébéogo, B. Somé, S. Kouanda, S. Dossou-Gbété
{"title":"Survival Analysis of Data of HIV Infected Persons Receiving Antiretroviral Therapy Using a Model-Based Binary Tree Approach","authors":"S. Tiendrébéogo, B. Somé, S. Kouanda, S. Dossou-Gbété","doi":"10.3844/jmssp.2019.354.365","DOIUrl":"https://doi.org/10.3844/jmssp.2019.354.365","url":null,"abstract":"Discrete-time approach is used in survival data analysis when only the time interval in which the event of interest has occurred is known or when this event occurs in a discrete - time scale. The work presented in this paper is motivated by the analysis of HIV/AIDS follow-up data collected in Burkina Faso during the 5-YEAR Global Fund program implemented to fight AIDS, Tuberculosis and Malaria. The research question that motivated the work is the likely existence of different mortality risk profiles of people infected with HIV/AIDS, depending on their characteristics and health status at the beginning of their care. In order to answer these questions, we considered a binary tree regression approach for survival data analysis since such a model owns the ability to handle interaction effects between the outcome covariates without a tight specification of such effects during the model statement step. This helps to prevent specification and interpretation errors. The fitted model resulted in splitting patients into three disjoint subgroups, corresponding each to a specific hazard profile.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"3 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87511742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Density Power Downweighting and Robust Inference: Some New Strategies","authors":"Saptarshi Roy, K. Chakraborty, S. Bhadra, A. Basu","doi":"10.3844/JMSSP.2019.333.353","DOIUrl":"https://doi.org/10.3844/JMSSP.2019.333.353","url":null,"abstract":"Preserving the robustness of the procedure has, at the present time, become almost a default requirement for statistical data analysis. Since efficiency at the model and robustness under misspecification of the model are often in conflict, it is important to choose such inference procedures which provide the best compromise between these two concepts. Some minimum Bregman divergence estimators and related tests of hypothesis seem to be able to do well in this respect, with the procedures based on the density power divergence providing the existing standard. In this paper we propose a new family of Bregman divergences which is a superfamily encompassing the density power divergence. This paper describes the inference procedures resulting from this new family of divergences, and makes a strong case for the utility of this divergence family in statistical inference.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"67 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73822126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Subset ARMA Model Identification for Monthly Electricity Consumption Data","authors":"Amaal El Sayed Abd El Ghany Mubarak","doi":"10.3844/jmssp.2019.22.29","DOIUrl":"https://doi.org/10.3844/jmssp.2019.22.29","url":null,"abstract":"Subset models can always be highly influential in series analysis, particularly when the data demonstrate a sort of form in periodic behavior with miscellaneous natural period's ranges, specifically; days, weeks, months and years. Subset models can also be effective as they let the number of parameters lower allowing only the really needed ones to be present in the model. Though subset autoregressive moving-average (ARMA) models always receive much attention, their identification is computationally cumbersome. This paper aims at the identification of Subset ARMA model through utilizing two methods of identification; innovation regression method and genetic algorithm method. The innovation regression method is a traditional one whilst the genetic algorithm methodologies represent a relatively modern approach for identifying Subset ARMA models in recent decades. After encoding every ARMA model as a binary string in the latter method, the iterative algorithm tries tracing the natural evolution of the population in those strings through letting strings to reproduce, producing newer models for competing for survival within upcoming populations. The aim of this research is to show the procedures for identifying the most appropriate order of subset ARMA models for the monthly electricity consumption data in Damietta governorate.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"90 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74624187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Sensitivity of a Dynamic Measure of Financial Inequality","authors":"G. D’Amico, S. Scocchera, L. Storchi","doi":"10.3844/jmssp.2019.280.297","DOIUrl":"https://doi.org/10.3844/jmssp.2019.280.297","url":null,"abstract":"In the present work, we investigate the sensitivity of the dynamic Theil index computed under a Markov reward model with respect to structured perturbations affecting the underlying Markov process. The model is applied to the sovereign credit spread evolution as a proxy for financial risk, which are driven by the sovereign credit rating dynamic. The introduction of such perturbations allows to evaluate the sensitivity of the inequality of the financial risk in a given group of financial entities with respect to the uncertainty in the rating dynamics. To this end we perform a simulation based sensitivity analysis. The methodology is applied to real data concerning sovereign credit ratings and long-term interest rates on government bonds of 24 European countries. Obtained results suggest different sensitivity of the inequality measure to the 12 scenarios built supposing different ways the perturbations could affect the rating process.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"62 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83029496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Model Comparison for the Prediction of Stock Prices in the NYSE","authors":"Victoria Switlyk, Junfeng Shang","doi":"10.3844/JMSSP.2019.233.249","DOIUrl":"https://doi.org/10.3844/JMSSP.2019.233.249","url":null,"abstract":"The stock market is an integral part of investments as well as the economy. The prediction of stock prices is an exciting and challenging problem that has been considered by many due to the complexity and noise within the market and to the potential profit that can be yielded from accurate predictions. We aim to construct and compare models used for the prediction of weekly closing prices for some of the top stocks in the New York Stock Exchange (NYSE) and to discuss the relationship between stock prices and the predictor variables. Relationships explored in the study include that with macroeconomic variables such as the Federal Funds Rate and the M1 money supply and market indexes such as the CBOE Volatility Index, the Wilshire 5000 Total Market Full Cap Index, the CBOE interest rate for 10-year T-notes and bonds, and NYSE commodity indexes including XOI and HUI. Models are built using methods of regression analysis and time series analysis. Models are analyzed and compared with one another by considering their predictive ability, accuracy, fit to the underlying model assumptions, and usefulness in application. The final models considered are a pooled regression model involving the median weekly closing price across all stocks, a varying intercept model considering the weekly closing price for each individual stock, and an ARIMA time series model that predicts the median weekly closing stock price based on past prices.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"34 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76521111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}