Pub Date : 2023-05-15DOI: 10.1080/24754269.2023.2180225
Djoweyda Ghouil, Megdouda Ourbih-Tari
This paper deals with the Monte Carlo Simulation in a Bayesian framework. It shows the importance of the use of Monte Carlo experiments through refined descriptive sampling within the autoregressive model , where and the errors are independent random variables following an exponential distribution of parameter θ. To achieve this, a Bayesian Autoregressive Adaptive Refined Descriptive Sampling (B2ARDS) algorithm is proposed to estimate the parameters ρ and θ of such a model by a Bayesian method. We have used the same prior as the one already used by some authors, and computed their properties when the Normality error assumption is released to an exponential distribution. The results show that B2ARDS algorithm provides accurate and efficient point estimates.
{"title":"Bayesian autoregressive adaptive refined descriptive sampling algorithm in the Monte Carlo simulation","authors":"Djoweyda Ghouil, Megdouda Ourbih-Tari","doi":"10.1080/24754269.2023.2180225","DOIUrl":"https://doi.org/10.1080/24754269.2023.2180225","url":null,"abstract":"This paper deals with the Monte Carlo Simulation in a Bayesian framework. It shows the importance of the use of Monte Carlo experiments through refined descriptive sampling within the autoregressive model , where and the errors are independent random variables following an exponential distribution of parameter θ. To achieve this, a Bayesian Autoregressive Adaptive Refined Descriptive Sampling (B2ARDS) algorithm is proposed to estimate the parameters ρ and θ of such a model by a Bayesian method. We have used the same prior as the one already used by some authors, and computed their properties when the Normality error assumption is released to an exponential distribution. The results show that B2ARDS algorithm provides accurate and efficient point estimates.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"7 1","pages":"177 - 187"},"PeriodicalIF":0.5,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42005573","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}
Pub Date : 2023-05-09DOI: 10.1080/24754269.2023.2201096
G. S. Deepthy, Nicy Sebastian, N. Chandra
{"title":"Applications of Burr III- Weibull quantile function in reliability analysis","authors":"G. S. Deepthy, Nicy Sebastian, N. Chandra","doi":"10.1080/24754269.2023.2201096","DOIUrl":"https://doi.org/10.1080/24754269.2023.2201096","url":null,"abstract":"","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49462581","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}
Pub Date : 2023-04-28DOI: 10.1080/24754269.2023.2201101
Weidong Ma, Fei Ye, Jingsong Xiao, Ying Yang
Cui and Zhong (2019), (Computational Statistics & Data Analysis, 139, 117–133) proposed a test based on the mean variance (MV) index to test independence between a categorical random variable Y with R categories and a continuous random variable X. They ingeniously proved the asymptotic normality of the MV test statistic when R diverges to infinity, which brings many merits to the MV test, including making it more convenient for independence testing when R is large. This paper considers a new test called the integral Pearson chi-square (IPC) test, whose test statistic can be viewed as a modified MV test statistic. A central limit theorem of the martingale difference is used to show that the asymptotic null distribution of the standardized IPC test statistic when R is diverging is also a normal distribution, rendering the IPC test sharing many merits with the MV test. As an application of such a theoretical finding, the IPC test is extended to test independence between continuous random variables. The finite sample performance of the proposed test is assessed by Monte Carlo simulations, and a real data example is presented for illustration.
{"title":"A distribution-free test of independence based on a modified mean variance index","authors":"Weidong Ma, Fei Ye, Jingsong Xiao, Ying Yang","doi":"10.1080/24754269.2023.2201101","DOIUrl":"https://doi.org/10.1080/24754269.2023.2201101","url":null,"abstract":"Cui and Zhong (2019), (Computational Statistics & Data Analysis, 139, 117–133) proposed a test based on the mean variance (MV) index to test independence between a categorical random variable Y with R categories and a continuous random variable X. They ingeniously proved the asymptotic normality of the MV test statistic when R diverges to infinity, which brings many merits to the MV test, including making it more convenient for independence testing when R is large. This paper considers a new test called the integral Pearson chi-square (IPC) test, whose test statistic can be viewed as a modified MV test statistic. A central limit theorem of the martingale difference is used to show that the asymptotic null distribution of the standardized IPC test statistic when R is diverging is also a normal distribution, rendering the IPC test sharing many merits with the MV test. As an application of such a theoretical finding, the IPC test is extended to test independence between continuous random variables. The finite sample performance of the proposed test is assessed by Monte Carlo simulations, and a real data example is presented for illustration.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"7 1","pages":"235 - 259"},"PeriodicalIF":0.5,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42988102","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}
Pub Date : 2023-04-28DOI: 10.1080/24754269.2023.2201108
Mengyao Chen, Yuehua Wu, B. Jin
In this paper, we investigate the COVID-19 pandemic in Canada and evaluate the Canadian government policies on controlling COVID-19 outbreaks. The first case of COVID-19 was reported in Ontario on 25 January 2020. Since then, there have been over million cases by now. During this time period, the federal, provincial and local governments have implemented regulations and policies in order to control the pandemic. To evaluate these government policies, which may be done by analysing the infection rate, infection period and reproductive number of COVID-19, we approach the problem by introducing an extended susceptible-exposed-infectious-removed (SEIR) model and conduct the model inference by using the iterated filter ensemble adjustment Kalman filter (IF-EAKF) algorithm. We first divide the time period into phases according to the policy intensities in each province by segmenting the time period from 4 March 2020 to 31 October 2020 into three time phases: the exploding phase, the strict policy implementation phase, and the provincial reopening phase. We then use IF-EAKF algorithm to obtain the estimates of the model parameters. We show that the infection rate in the second phase is lower than that in both first and third phases. We also discuss the number of new COVID-19 cases under different policy intensities and different policy durations in the third wave of the pandemic.
{"title":"Evaluation of the Canadian government policies on controlling the COVID-19 outbreaks","authors":"Mengyao Chen, Yuehua Wu, B. Jin","doi":"10.1080/24754269.2023.2201108","DOIUrl":"https://doi.org/10.1080/24754269.2023.2201108","url":null,"abstract":"In this paper, we investigate the COVID-19 pandemic in Canada and evaluate the Canadian government policies on controlling COVID-19 outbreaks. The first case of COVID-19 was reported in Ontario on 25 January 2020. Since then, there have been over million cases by now. During this time period, the federal, provincial and local governments have implemented regulations and policies in order to control the pandemic. To evaluate these government policies, which may be done by analysing the infection rate, infection period and reproductive number of COVID-19, we approach the problem by introducing an extended susceptible-exposed-infectious-removed (SEIR) model and conduct the model inference by using the iterated filter ensemble adjustment Kalman filter (IF-EAKF) algorithm. We first divide the time period into phases according to the policy intensities in each province by segmenting the time period from 4 March 2020 to 31 October 2020 into three time phases: the exploding phase, the strict policy implementation phase, and the provincial reopening phase. We then use IF-EAKF algorithm to obtain the estimates of the model parameters. We show that the infection rate in the second phase is lower than that in both first and third phases. We also discuss the number of new COVID-19 cases under different policy intensities and different policy durations in the third wave of the pandemic.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"7 1","pages":"223 - 234"},"PeriodicalIF":0.5,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49622158","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}
Pub Date : 2023-04-28DOI: 10.1080/24754269.2023.2202579
Chi-Shian Dai, Jun Shao
{"title":"Kernel regression utilizing heterogeneous datasets","authors":"Chi-Shian Dai, Jun Shao","doi":"10.1080/24754269.2023.2202579","DOIUrl":"https://doi.org/10.1080/24754269.2023.2202579","url":null,"abstract":"","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42589198","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}
Pub Date : 2023-04-15DOI: 10.1080/24754269.2023.2164943
Naitee Ting
The scientific foundation of a modern clinical trial is randomization – each patient is randomized to a treatment group, and statistical comparisons are made between treatment groups. Because the study units are individual patients, this ‘one patient, one vote’ principle needs to be followed – both in study design and in data analysis. From the physicians' point of view, each patient is equally important, and they need to be treated equally in data analysis. It is critical that statistical analysis should respect design and study design is based on randomization. Hence from both statistical and medical points of view, data analysis needs to follow this ‘one patient, one vote’ principle. Under ICH E9 (R1), five strategies are recommended to establish ‘estimand’. This paper discusses how to implement these strategies using the ‘one patient, one vote’ principle.
{"title":"How to implement the ‘one patient, one vote’ principle under the framework of estimand","authors":"Naitee Ting","doi":"10.1080/24754269.2023.2164943","DOIUrl":"https://doi.org/10.1080/24754269.2023.2164943","url":null,"abstract":"The scientific foundation of a modern clinical trial is randomization – each patient is randomized to a treatment group, and statistical comparisons are made between treatment groups. Because the study units are individual patients, this ‘one patient, one vote’ principle needs to be followed – both in study design and in data analysis. From the physicians' point of view, each patient is equally important, and they need to be treated equally in data analysis. It is critical that statistical analysis should respect design and study design is based on randomization. Hence from both statistical and medical points of view, data analysis needs to follow this ‘one patient, one vote’ principle. Under ICH E9 (R1), five strategies are recommended to establish ‘estimand’. This paper discusses how to implement these strategies using the ‘one patient, one vote’ principle.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"7 1","pages":"202 - 212"},"PeriodicalIF":0.5,"publicationDate":"2023-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49450070","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}
Pub Date : 2023-03-13DOI: 10.1080/24754269.2023.2184607
Muhammad Daniyal, Jignesh kumar Gondaliya, R. Ahmed
Several fields, such as biological, medical, public health, agricultural sciences, etc., require circular balanced repeated measurement designs with fewer unequal number of repeated measurements than the number of treatments. Also, the availability and high cost of experimental subjects in these fields prefer the design in fewer experimental units. However, balancing the carryover effects of the treatments in minimal experimental subjects is one of the problems in this case. In this paper, several new series of minimal circular nearly strongly balanced RMDs in periods of two and three different sizes are constructed. The proposed construction of designs has high efficiency and, therefore, can save the cost of experimentations due to a fewer experimental subjects. Most of the designs are very useful because of the unavailability of strongly balanced RMDs for these combinations of parameters. A list of sets of shifts for the construction of minimal circular nearly SBRMDs has also been mentioned in the Appendix.
{"title":"On the construction of balanced repeated measurements designs with good circular properties","authors":"Muhammad Daniyal, Jignesh kumar Gondaliya, R. Ahmed","doi":"10.1080/24754269.2023.2184607","DOIUrl":"https://doi.org/10.1080/24754269.2023.2184607","url":null,"abstract":"Several fields, such as biological, medical, public health, agricultural sciences, etc., require circular balanced repeated measurement designs with fewer unequal number of repeated measurements than the number of treatments. Also, the availability and high cost of experimental subjects in these fields prefer the design in fewer experimental units. However, balancing the carryover effects of the treatments in minimal experimental subjects is one of the problems in this case. In this paper, several new series of minimal circular nearly strongly balanced RMDs in periods of two and three different sizes are constructed. The proposed construction of designs has high efficiency and, therefore, can save the cost of experimentations due to a fewer experimental subjects. Most of the designs are very useful because of the unavailability of strongly balanced RMDs for these combinations of parameters. A list of sets of shifts for the construction of minimal circular nearly SBRMDs has also been mentioned in the Appendix.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"7 1","pages":"121 - 129"},"PeriodicalIF":0.5,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47136108","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}
Pub Date : 2023-03-13DOI: 10.1080/24754269.2023.2182136
Wenhui Sheng, Qingcong Yuan
In this article, we introduce a flexible model-free approach to sufficient dimension reduction analysis using the expectation of conditional difference measure. Without any strict conditions, such as linearity condition or constant covariance condition, the method estimates the central subspace exhaustively and efficiently under linear or nonlinear relationships between response and predictors. The method is especially meaningful when the response is categorical. We also studied the -consistency and asymptotic normality of the estimate. The efficacy of our method is demonstrated through both simulations and a real data analysis.
{"title":"Dimension reduction with expectation of conditional difference measure","authors":"Wenhui Sheng, Qingcong Yuan","doi":"10.1080/24754269.2023.2182136","DOIUrl":"https://doi.org/10.1080/24754269.2023.2182136","url":null,"abstract":"In this article, we introduce a flexible model-free approach to sufficient dimension reduction analysis using the expectation of conditional difference measure. Without any strict conditions, such as linearity condition or constant covariance condition, the method estimates the central subspace exhaustively and efficiently under linear or nonlinear relationships between response and predictors. The method is especially meaningful when the response is categorical. We also studied the -consistency and asymptotic normality of the estimate. The efficacy of our method is demonstrated through both simulations and a real data analysis.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"7 1","pages":"188 - 201"},"PeriodicalIF":0.5,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45117067","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}
Pub Date : 2023-03-04DOI: 10.1080/24754269.2023.2180185
Jun Shao, Xinyan Wang
We consider maximum likelihood estimation with two or more datasets sampled from different populations with shared parameters. Although more datasets with shared parameters can increase statistical accuracy, this paper shows how to handle heterogeneity among different populations for correctness of estimation and inference. Asymptotic distributions of maximum likelihood estimators are derived under either regular cases where regularity conditions are satisfied or some non-regular situations. A bootstrap variance estimator for assessing performance of estimators and/or making large sample inference is also introduced and evaluated in a simulation study.
{"title":"MLE with datasets from populations having shared parameters","authors":"Jun Shao, Xinyan Wang","doi":"10.1080/24754269.2023.2180185","DOIUrl":"https://doi.org/10.1080/24754269.2023.2180185","url":null,"abstract":"We consider maximum likelihood estimation with two or more datasets sampled from different populations with shared parameters. Although more datasets with shared parameters can increase statistical accuracy, this paper shows how to handle heterogeneity among different populations for correctness of estimation and inference. Asymptotic distributions of maximum likelihood estimators are derived under either regular cases where regularity conditions are satisfied or some non-regular situations. A bootstrap variance estimator for assessing performance of estimators and/or making large sample inference is also introduced and evaluated in a simulation study.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"7 1","pages":"213 - 222"},"PeriodicalIF":0.5,"publicationDate":"2023-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44676372","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}
Pub Date : 2023-03-04DOI: 10.1080/24754269.2023.2179324
C. Kumar, A. Riyaz
In this paper, we discuss some important aspects of the bivariate alternative zero-inflated logarithmic series distribution (BAZILSD) of which the marginals are the alternative zero-inflated logarithmic series distributions of Kumar and Riyaz (2015. An alternative version of zero-inflated logarithmic series distribution and some of its applications. Journal of Statistical Computation and Simulation, 85(6), 1117–1127). We study some important properties of the distribution by deriving expressions for its probability mass function, factorial moments, conditional probability generating functions, and recursion formulae for its probabilities, raw moments and factorial moments. The parameters of the BAZILSD are estimated by the method of maximum likelihood and certain test procedures are also considered. Further certain real-life data applications are cited for illustrating the usefulness of the model. A simulation study is conducted for assessing the performance of the maximum likelihood estimators of the parameters of the BAZILSD.
{"title":"On some aspects of a bivariate alternative zero-inflated logarithmic series distribution","authors":"C. Kumar, A. Riyaz","doi":"10.1080/24754269.2023.2179324","DOIUrl":"https://doi.org/10.1080/24754269.2023.2179324","url":null,"abstract":"In this paper, we discuss some important aspects of the bivariate alternative zero-inflated logarithmic series distribution (BAZILSD) of which the marginals are the alternative zero-inflated logarithmic series distributions of Kumar and Riyaz (2015. An alternative version of zero-inflated logarithmic series distribution and some of its applications. Journal of Statistical Computation and Simulation, 85(6), 1117–1127). We study some important properties of the distribution by deriving expressions for its probability mass function, factorial moments, conditional probability generating functions, and recursion formulae for its probabilities, raw moments and factorial moments. The parameters of the BAZILSD are estimated by the method of maximum likelihood and certain test procedures are also considered. Further certain real-life data applications are cited for illustrating the usefulness of the model. A simulation study is conducted for assessing the performance of the maximum likelihood estimators of the parameters of the BAZILSD.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"7 1","pages":"130 - 143"},"PeriodicalIF":0.5,"publicationDate":"2023-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44798448","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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