Interrupted Time Series (ITS) analysis represents a powerful quasi-experimental design in which a discontinuity is enforced at a specific intervention point in a time series, and separate regression functions are fitted before and after the intervention point. Segmented linear/quantile regression can be used in ITS designs to isolate intervention effects by estimating the sudden/level change (change in intercept) and/or the gradual change (change in slope). To our knowledge, the finite-sample properties of quantile segmented regression for detecting level and gradual change remains unaddressed. In this study, we compared the performance of segmented quantile regression and segmented linear regression using a Monte Carlo simulation study where the error distributions were: IID Gaussian, heteroscedastic IID Gaussian, correlated AR(1), and T (with 1, 2 and 3 degrees of freedom, respectively). We also compared segmented quantile regresison and segmented linear regression when applied to a real dataset, employing an ITS design to estimate intervention effects on daily-mean patient prescription volumes. Both the simulation study and applied example illustrate the usefulness of quantile segmented regression as a complementary statistical methodology for assessing the impacts of interventions in ITS designs. Corresponding Author: Rahim Moineddin (Rahim.moineddin@utoronto.ca) Christopher Meaney (Christopher.Meaney@utoronto.ca) Sumeet Kalia (Sumeet.Kalia@utoronto.ca) 248 R. Moineddin et al.
{"title":"Finite Sample Properties of Quantile Interrupted Time Series Analysis: A Simulation Study","authors":"R. Moineddin, C. Meaney, S. Kalia","doi":"10.52547/jirss.20.1.247","DOIUrl":"https://doi.org/10.52547/jirss.20.1.247","url":null,"abstract":"Interrupted Time Series (ITS) analysis represents a powerful quasi-experimental design in which a discontinuity is enforced at a specific intervention point in a time series, and separate regression functions are fitted before and after the intervention point. Segmented linear/quantile regression can be used in ITS designs to isolate intervention effects by estimating the sudden/level change (change in intercept) and/or the gradual change (change in slope). To our knowledge, the finite-sample properties of quantile segmented regression for detecting level and gradual change remains unaddressed. In this study, we compared the performance of segmented quantile regression and segmented linear regression using a Monte Carlo simulation study where the error distributions were: IID Gaussian, heteroscedastic IID Gaussian, correlated AR(1), and T (with 1, 2 and 3 degrees of freedom, respectively). We also compared segmented quantile regresison and segmented linear regression when applied to a real dataset, employing an ITS design to estimate intervention effects on daily-mean patient prescription volumes. Both the simulation study and applied example illustrate the usefulness of quantile segmented regression as a complementary statistical methodology for assessing the impacts of interventions in ITS designs. Corresponding Author: Rahim Moineddin (Rahim.moineddin@utoronto.ca) Christopher Meaney (Christopher.Meaney@utoronto.ca) Sumeet Kalia (Sumeet.Kalia@utoronto.ca) 248 R. Moineddin et al.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43354327","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}
F. Bhatti, Sedigheh Mirzaei Salehabadi, G. Hamedani
We introduce a flexible lifetime distribution called Burr III-Inverse Weibull (BIII-IW). The new proposed distribution has well-known sub-models. The BIII-IW density function includes exponential, left-skewed, right-skewed and symmetrical shapes. The BIII-IW model's failure rate can be monotone and non-monotone depending on the parameter values. To show the importance of the BIII-IW distribution, we establish various mathematical properties such as random number generator, ordinary moments, conditional moments, residual life functions, reliability measures and characterizations. We address the maximum likelihood estimates (MLE) for the BIII-IW parameters and estimate the precision of the maximum likelihood estimators via a simulation study. We consider applications to two COVID-19 data sets to illustrate the potential of the BIII-IW model.
我们引入了一种称为Burr iii -逆威布尔(BIII-IW)的灵活寿命分布。新提出的分布具有众所周知的子模型。BIII-IW密度函数包括指数型、左偏型、右偏型和对称型。根据参数值的不同，BIII-IW模型的故障率可以是单调的，也可以是非单调的。为了说明BIII-IW分布的重要性，我们建立了各种数学性质，如随机数生成器、普通矩、条件矩、剩余寿命函数、可靠性度量和表征。我们解决了BIII-IW参数的最大似然估计(MLE)，并通过模拟研究估计了最大似然估计的精度。我们考虑将其应用于两个COVID-19数据集，以说明BIII-IW模型的潜力。
{"title":"On Burr III-Inverse Weibull Distribution with COVID-19 Applications","authors":"F. Bhatti, Sedigheh Mirzaei Salehabadi, G. Hamedani","doi":"10.52547/jirss.20.1.101","DOIUrl":"https://doi.org/10.52547/jirss.20.1.101","url":null,"abstract":"We introduce a flexible lifetime distribution called Burr III-Inverse Weibull (BIII-IW). The new proposed distribution has well-known sub-models. The BIII-IW density function includes exponential, left-skewed, right-skewed and symmetrical shapes. The BIII-IW model's failure rate can be monotone and non-monotone depending on the parameter values. To show the importance of the BIII-IW distribution, we establish various mathematical properties such as random number generator, ordinary moments, conditional moments, residual life functions, reliability measures and characterizations. We address the maximum likelihood estimates (MLE) for the BIII-IW parameters and estimate the precision of the maximum likelihood estimators via a simulation study. We consider applications to two COVID-19 data sets to illustrate the potential of the BIII-IW model.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43930949","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}
Hossein Ali Mohtashami Borzadaran, H. Jabbari, M. Amini, A. Dolati
. In Demography and modelling mortality (or failure) data the univariate Makeham-Gompertz is well-known for its extension of exponential distribution. Here, a bivariate class of Gompertz–Makeham distribution is constructed based on random number of extremal events. Some reliability properties such as ageing intensity, stress-strength based on competing risks are given. Also dependence properties such as dependence structure, association measures and tail dependence measures are obtained. A simulation study and a performance analysis is given based on estimators such as MLE, Tau-inversion and Rho-inversion.
{"title":"Stress-Strength and Ageing Intensity Analysis via a New Bivariate Negative Gompertz-Makeham Model","authors":"Hossein Ali Mohtashami Borzadaran, H. Jabbari, M. Amini, A. Dolati","doi":"10.52547/jirss.20.1.219","DOIUrl":"https://doi.org/10.52547/jirss.20.1.219","url":null,"abstract":". In Demography and modelling mortality (or failure) data the univariate Makeham-Gompertz is well-known for its extension of exponential distribution. Here, a bivariate class of Gompertz–Makeham distribution is constructed based on random number of extremal events. Some reliability properties such as ageing intensity, stress-strength based on competing risks are given. Also dependence properties such as dependence structure, association measures and tail dependence measures are obtained. A simulation study and a performance analysis is given based on estimators such as MLE, Tau-inversion and Rho-inversion.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46966648","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":"Quantile Approach of Generalized Cumulative Residual Information Measure of Order $(alpha,beta)$","authors":"Vikas Kumar, Rekha Rani, N. Singh","doi":"10.52547/JIRSS.19.2.67","DOIUrl":"https://doi.org/10.52547/JIRSS.19.2.67","url":null,"abstract":"","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":"19 1","pages":"67-99"},"PeriodicalIF":0.4,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46584473","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}
. In this paper we obtain a consistent estimator when there exist some measurement errors and multicollinearity in the instrumental variables in a two stage least square estimation of parameters. We investigate the asymptotic distribution of the proposed estimator and discuss its properties using some theoretical proofs and a simulation study. A real numerical application is also provided for more illustration.
{"title":"Instrumental Variables Regression with Measurement Errors and Multicollinearity in Instruments","authors":"A. Sheikhi, Mohsen Rezapoor, Hamid Hoseenkhani","doi":"10.52547/JIRSS.19.2.15","DOIUrl":"https://doi.org/10.52547/JIRSS.19.2.15","url":null,"abstract":". In this paper we obtain a consistent estimator when there exist some measurement errors and multicollinearity in the instrumental variables in a two stage least square estimation of parameters. We investigate the asymptotic distribution of the proposed estimator and discuss its properties using some theoretical proofs and a simulation study. A real numerical application is also provided for more illustration.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48342386","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}
In this paper, the reconcilability between the P-value and the posterior probability in testing a point null hypothesis against the one-sided hypothesis is considered. Two essential families, non regular and exponential family of distributions, are studied. It was shown in a non regular family of distributions; in some cases, it is possible to find a prior distribution function under which P-value and posterior probability are achieved. However, in the exponential family of distributions, this agreement is based on the complete monotonicity of a function of hazard rate.
{"title":"Testing a Point Null Hypothesis against One-Sided for Non Regular and Exponential Families: The Reconcilability Condition to P-values and Posterior Probability","authors":"Parisa Zolfaghari, R. Chinipardaz, J. Esmaily","doi":"10.52547/JIRSS.19.2.101","DOIUrl":"https://doi.org/10.52547/JIRSS.19.2.101","url":null,"abstract":"In this paper, the reconcilability between the P-value and the posterior probability in testing a point null hypothesis against the one-sided hypothesis is considered. Two essential families, non regular and exponential family of distributions, are studied. It was shown in a non regular family of distributions; in some cases, it is possible to find a prior distribution function under which P-value and posterior probability are achieved. However, in the exponential family of distributions, this agreement is based on the complete monotonicity of a function of hazard rate.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49140209","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}
. This paper focuses on di ff erent methods of estimation and forecasting in first-order integer-valued autoregressive processes with Poisson-Lindley (PLINAR(1)) marginal distribution. For this purpose, the parameters of the model are estimated using Whittle, maximum empirical likelihood and sieve bootstrap methods. Moreover, Bayesian and sieve bootstrap forecasting methods are proposed and predicted value for h -step ahead of the series is obtained. Some simulations and a real data analysis are applied to compare the presented estimations and the prediction methods.
{"title":"Poisson-Lindley INAR(1) Processes: Some Estimation and Forecasting Methods","authors":"R. Nasirzadeh, A. Zamani","doi":"10.52547/JIRSS.19.2.145","DOIUrl":"https://doi.org/10.52547/JIRSS.19.2.145","url":null,"abstract":". This paper focuses on di ff erent methods of estimation and forecasting in first-order integer-valued autoregressive processes with Poisson-Lindley (PLINAR(1)) marginal distribution. For this purpose, the parameters of the model are estimated using Whittle, maximum empirical likelihood and sieve bootstrap methods. Moreover, Bayesian and sieve bootstrap forecasting methods are proposed and predicted value for h -step ahead of the series is obtained. Some simulations and a real data analysis are applied to compare the presented estimations and the prediction methods.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70688015","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}
. This paper focuses on the empirical autocovariance operator of H -valued periodically correlated processes. It will be demonstrated that the empirical estimator converges to a limit with the same periodicity as the main process. Moreover, the rate of convergence of the empirical autocovariance operator in Hilbert-Schmidt norm is derived.
{"title":"Convergence Rate of Empirical Autocovariance Operators in H-Valued Periodically Correlated Processes","authors":"M. Hashemi, A. Zamani","doi":"10.52547/JIRSS.19.2.1","DOIUrl":"https://doi.org/10.52547/JIRSS.19.2.1","url":null,"abstract":". This paper focuses on the empirical autocovariance operator of H -valued periodically correlated processes. It will be demonstrated that the empirical estimator converges to a limit with the same periodicity as the main process. Moreover, the rate of convergence of the empirical autocovariance operator in Hilbert-Schmidt norm is derived.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43350136","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}
When modeling time series data using autoregressive-moving average processes, it is a common practice to presume that the residuals are normally distributed. However, sometimes we encounter non-normal residuals and asymmetry of data marginal distribution. Despite widespread use of pure autoregressive processes for modeling non-normal time series, the autoregressive-moving average models have less been used. The main reason is the difficulty in estimating the autoregressive-moving average model parameters. The purpose of this study is to address this intricacy by approximating maximum likelihood estimators, which is particularly important from model selection perspective. Accordingly, the coefficients and residual distribution parameters of the first-order stationary autoregressive-moving average model with residuals that follow exponential and Weibull families, were estimated. Then based on the simulation study, the obtained theoretical results were investigated and it was shown that the modified maximum likelihood estimators were suitable estimators to estimate the first-order autoregressive-moving average model parameters in nonnormal mode. In a numerical example positive skewness of obtained residuals from fitting the first-order autoregressive-moving average model was shown. Following that, the parameters of candidate residual distributions estimated by modified maximum likelihood estimators and one of the estimated models for modeling the data was selected.
{"title":"Modified Maximum Likelihood Estimation in First-Order Autoregressive Moving Average Models with some Non-Normal Residuals","authors":"M. Kasraie, A. Sayyareh","doi":"10.52547/JIRSS.19.2.33","DOIUrl":"https://doi.org/10.52547/JIRSS.19.2.33","url":null,"abstract":"When modeling time series data using autoregressive-moving average processes, it is a common practice to presume that the residuals are normally distributed. However, sometimes we encounter non-normal residuals and asymmetry of data marginal distribution. Despite widespread use of pure autoregressive processes for modeling non-normal time series, the autoregressive-moving average models have less been used. The main reason is the difficulty in estimating the autoregressive-moving average model parameters. The purpose of this study is to address this intricacy by approximating maximum likelihood estimators, which is particularly important from model selection perspective. Accordingly, the coefficients and residual distribution parameters of the first-order stationary autoregressive-moving average model with residuals that follow exponential and Weibull families, were estimated. Then based on the simulation study, the obtained theoretical results were investigated and it was shown that the modified maximum likelihood estimators were suitable estimators to estimate the first-order autoregressive-moving average model parameters in nonnormal mode. In a numerical example positive skewness of obtained residuals from fitting the first-order autoregressive-moving average model was shown. Following that, the parameters of candidate residual distributions estimated by modified maximum likelihood estimators and one of the estimated models for modeling the data was selected.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42227950","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}
. Di ff erent approaches to goodness of fit (GOF) testing are proposed. This survey intends to present the developments on Goodness of Fit based on entropy during the last 50 years, from the very first origins until the most recent advances for di ff erent data and models. Goodness of fit tests based on Shannon entropy was started by Vasicek in 1976 and were continued by many authors. In this paper, we describe di ff erent GOF tests constructed by authors from the beginning to now. First, the problem of GOF and di ff erent types of GOF are stated. Then, the method of GOF tests based on entropy for complete and censored data is explained and all works proposed by authors in this subject are mentioned.
{"title":"An Updated Review of Goodness of Fit Tests Based on Entropy","authors":"H. A. Noughabi, G. M. Borzadaran","doi":"10.52547/JIRSS.19.2.175","DOIUrl":"https://doi.org/10.52547/JIRSS.19.2.175","url":null,"abstract":". Di ff erent approaches to goodness of fit (GOF) testing are proposed. This survey intends to present the developments on Goodness of Fit based on entropy during the last 50 years, from the very first origins until the most recent advances for di ff erent data and models. Goodness of fit tests based on Shannon entropy was started by Vasicek in 1976 and were continued by many authors. In this paper, we describe di ff erent GOF tests constructed by authors from the beginning to now. First, the problem of GOF and di ff erent types of GOF are stated. Then, the method of GOF tests based on entropy for complete and censored data is explained and all works proposed by authors in this subject are mentioned.","PeriodicalId":42965,"journal":{"name":"JIRSS-Journal of the Iranian Statistical Society","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47712779","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}
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