Pub Date : 2023-02-13DOI: 10.1080/24754269.2023.2176608
Yanlin Tang, Jing-Long Wang, Zhongyi Zhu
The two-parameter Waring is an important heavy-tailed discrete distribution, which extends the famous Yule-Simon distribution and provides more flexibility when modelling the data. The commonly used EFF (Expectation-First Frequency) for parameter estimation can only be applied when the first moment exists, and it only uses the information of the expectation and the first frequency, which is not as efficient as the maximum likelihood estimator (MLE). However, the MLE may not exist for some sample data. We apply the profile method to the log-likelihood function and derive the necessary and sufficient conditions for the existence of the MLE of the Waring parameters. We use extensive simulation studies to compare the MLE and EFF methods, and the goodness-of-fit comparison with the Yule-Simon distribution. We also apply the Waring distribution to fit an insurance data.
双参数Waring是一种重要的重尾离散分布，它扩展了著名的Yule-Simon分布，为数据建模提供了更大的灵活性。常用的参数估计方法EFF (expectation - first Frequency)只有在第一矩存在的情况下才能应用，而且它只利用了期望和第一频率的信息，效率不如极大似然估计(MLE)。然而，对于某些样本数据，最大似然值可能不存在。将剖面法应用于对数似然函数，得到了Waring参数最大似然值存在的充分必要条件。我们使用了大量的模拟研究来比较MLE和EFF方法，以及与Yule-Simon分布的拟合优度比较。我们还应用沃林分布来拟合保险数据。
{"title":"On the MLE of the Waring distribution","authors":"Yanlin Tang, Jing-Long Wang, Zhongyi Zhu","doi":"10.1080/24754269.2023.2176608","DOIUrl":"https://doi.org/10.1080/24754269.2023.2176608","url":null,"abstract":"The two-parameter Waring is an important heavy-tailed discrete distribution, which extends the famous Yule-Simon distribution and provides more flexibility when modelling the data. The commonly used EFF (Expectation-First Frequency) for parameter estimation can only be applied when the first moment exists, and it only uses the information of the expectation and the first frequency, which is not as efficient as the maximum likelihood estimator (MLE). However, the MLE may not exist for some sample data. We apply the profile method to the log-likelihood function and derive the necessary and sufficient conditions for the existence of the MLE of the Waring parameters. We use extensive simulation studies to compare the MLE and EFF methods, and the goodness-of-fit comparison with the Yule-Simon distribution. We also apply the Waring distribution to fit an insurance data.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"7 1","pages":"144 - 158"},"PeriodicalIF":0.5,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43512864","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 : 2023-01-11DOI: 10.1080/24754269.2023.2164970
Abdisa G. Dufera, Tiantian Liu, Jin Xu
We propose two simple regression models of Pearson correlation coefficient of two normal responses or binary responses to assess the effect of covariates of interest. Likelihood-based inference is established to estimate the regression coefficients, upon which bootstrap-based method is used to test the significance of covariates of interest. Simulation studies show the effectiveness of the method in terms of type-I error control, power performance in moderate sample size and robustness with respect to model mis-specification. We illustrate the application of the proposed method to some real data concerning health measurements.
{"title":"Regression models of Pearson correlation coefficient","authors":"Abdisa G. Dufera, Tiantian Liu, Jin Xu","doi":"10.1080/24754269.2023.2164970","DOIUrl":"https://doi.org/10.1080/24754269.2023.2164970","url":null,"abstract":"We propose two simple regression models of Pearson correlation coefficient of two normal responses or binary responses to assess the effect of covariates of interest. Likelihood-based inference is established to estimate the regression coefficients, upon which bootstrap-based method is used to test the significance of covariates of interest. Simulation studies show the effectiveness of the method in terms of type-I error control, power performance in moderate sample size and robustness with respect to model mis-specification. We illustrate the application of the proposed method to some real data concerning health measurements.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"7 1","pages":"97 - 106"},"PeriodicalIF":0.5,"publicationDate":"2023-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45589134","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 : 2023-01-01Epub Date: 2023-04-28DOI: 10.1080/24754269.2023.2205802
Ting Ye, Marlena Bannick, Yanyao Yi, Jun Shao
To improve precision of estimation and power of testing hypothesis for an unconditional treatment effect in randomized clinical trials with binary outcomes, researchers and regulatory agencies recommend using g-computation as a reliable method of covariate adjustment. However, the practical application of g-computation is hindered by the lack of an explicit robust variance formula that can be used for different unconditional treatment effects of interest. To fill this gap, we provide explicit and robust variance estimators for g-computation estimators and demonstrate through simulations that the variance estimators can be reliably applied in practice.
{"title":"Robust Variance Estimation for Covariate-Adjusted Unconditional Treatment Effect in Randomized Clinical Trials with Binary Outcomes.","authors":"Ting Ye, Marlena Bannick, Yanyao Yi, Jun Shao","doi":"10.1080/24754269.2023.2205802","DOIUrl":"10.1080/24754269.2023.2205802","url":null,"abstract":"<p><p>To improve precision of estimation and power of testing hypothesis for an unconditional treatment effect in randomized clinical trials with binary outcomes, researchers and regulatory agencies recommend using g-computation as a reliable method of covariate adjustment. However, the practical application of g-computation is hindered by the lack of an explicit robust variance formula that can be used for different unconditional treatment effects of interest. To fill this gap, we provide explicit and robust variance estimators for g-computation estimators and demonstrate through simulations that the variance estimators can be reliably applied in practice.</p>","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"7 1","pages":"159-163"},"PeriodicalIF":0.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10665030/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46073039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-20DOI: 10.1080/24754269.2022.2156743
Huijuan Ma, J. Qin, Fang Chen, Yong Zhou
The outbreak of COVID-19 on the Diamond Princess cruise ship has attracted much attention. Motivated by the PCR testing data on the Diamond Princess, we propose a novel cure mixture nonparametric model to investigate the detection pattern. It combines a logistic regression for the probability of susceptible subjects with a nonparametric distribution for the detection of infected individuals. Maximum likelihood estimators are proposed. The resulting estimators are shown to be consistent and asymptotically normal. Simulation studies demonstrate that the proposed approach is appropriate for practical use. Finally, we apply the proposed method to PCR testing data on the Diamond Princess to show its practical utility.
{"title":"A novel nonparametric mixture model for the detection pattern of COVID-19 on Diamond Princess cruise","authors":"Huijuan Ma, J. Qin, Fang Chen, Yong Zhou","doi":"10.1080/24754269.2022.2156743","DOIUrl":"https://doi.org/10.1080/24754269.2022.2156743","url":null,"abstract":"The outbreak of COVID-19 on the Diamond Princess cruise ship has attracted much attention. Motivated by the PCR testing data on the Diamond Princess, we propose a novel cure mixture nonparametric model to investigate the detection pattern. It combines a logistic regression for the probability of susceptible subjects with a nonparametric distribution for the detection of infected individuals. Maximum likelihood estimators are proposed. The resulting estimators are shown to be consistent and asymptotically normal. Simulation studies demonstrate that the proposed approach is appropriate for practical use. Finally, we apply the proposed method to PCR testing data on the Diamond Princess to show its practical utility.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"7 1","pages":"85 - 96"},"PeriodicalIF":0.5,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46674496","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 : 2022-12-12DOI: 10.1080/24754269.2022.2153540
Lei He, R. Yue
This paper concerns with optimal designs for a wide class of nonlinear models with information driven by the linear predictor. The aim of this study is to generate an R-optimal design which minimizes the product of the main diagonal entries of the inverse of the Fisher information matrix at certain values of the parameters. An equivalence theorem for the locally R-optimal designs is provided in terms of the intensity function. Analytic solutions for the locally saturated R-optimal designs are derived for the models having linear predictors with and without intercept, respectively. The particle swarm optimization method has been employed to generate locally non-saturated R-optimal designs. Numerical examples are presented for illustration of the locally R-optimal designs for Poisson regression models and proportional hazards regression models.
{"title":"Locally R-optimal designs for a class of nonlinear multiple regression models","authors":"Lei He, R. Yue","doi":"10.1080/24754269.2022.2153540","DOIUrl":"https://doi.org/10.1080/24754269.2022.2153540","url":null,"abstract":"This paper concerns with optimal designs for a wide class of nonlinear models with information driven by the linear predictor. The aim of this study is to generate an R-optimal design which minimizes the product of the main diagonal entries of the inverse of the Fisher information matrix at certain values of the parameters. An equivalence theorem for the locally R-optimal designs is provided in terms of the intensity function. Analytic solutions for the locally saturated R-optimal designs are derived for the models having linear predictors with and without intercept, respectively. The particle swarm optimization method has been employed to generate locally non-saturated R-optimal designs. Numerical examples are presented for illustration of the locally R-optimal designs for Poisson regression models and proportional hazards regression models.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"7 1","pages":"107 - 120"},"PeriodicalIF":0.5,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45686500","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 : 2022-12-05DOI: 10.1080/24754269.2022.2152591
Jia Kang, Linmin Hu, R. Peng, Yan Li, R. Tian
This paper investigates a warm standby repairable retrial system with two types of components and a single repairman, where type 1 components have priority over type 2 in use. Failure and repair times for each type of component are assumed to be exponential distributions. The retrial feature is considered and the retrial time of each failed component is exponentially distributed. By using Markov process theory and matrix-analytic method, the system steady-state probabilities are derived, and the system steady-state availability and some steady-state performance indices are obtained. Using the Bayesian approach, the system parameters can be estimated. The cost-benefit ratio function of the system is constructed based on the failed components and repairman's states. Numerical experiments are given to evaluate the effect of each parameter on the system steady-state availability and optimize the system cost-benefit ratio with repair rate as a decision variable.
{"title":"Availability and cost-benefit evaluation for a repairable retrial system with warm standbys and priority","authors":"Jia Kang, Linmin Hu, R. Peng, Yan Li, R. Tian","doi":"10.1080/24754269.2022.2152591","DOIUrl":"https://doi.org/10.1080/24754269.2022.2152591","url":null,"abstract":"This paper investigates a warm standby repairable retrial system with two types of components and a single repairman, where type 1 components have priority over type 2 in use. Failure and repair times for each type of component are assumed to be exponential distributions. The retrial feature is considered and the retrial time of each failed component is exponentially distributed. By using Markov process theory and matrix-analytic method, the system steady-state probabilities are derived, and the system steady-state availability and some steady-state performance indices are obtained. Using the Bayesian approach, the system parameters can be estimated. The cost-benefit ratio function of the system is constructed based on the failed components and repairman's states. Numerical experiments are given to evaluate the effect of each parameter on the system steady-state availability and optimize the system cost-benefit ratio with repair rate as a decision variable.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"7 1","pages":"164 - 175"},"PeriodicalIF":0.5,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47099372","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 : 2022-11-21DOI: 10.1080/24754269.2022.2146955
Yuhan Zou, Yingyin Lu, Zuoxiang Peng
Let be a sequence of independent random variables with common general error distribution with shape parameter v>0, and let denote the r-th largest order statistics of . With different normalizing constants the distributional expansions and the uniform convergence rates of normalized powered order statistics are established. An alternative method is presented to estimate the probability of the r-th extremes. Numerical analyses are provided to support the main results.
{"title":"Rates of convergence of powered order statistics from general error distribution","authors":"Yuhan Zou, Yingyin Lu, Zuoxiang Peng","doi":"10.1080/24754269.2022.2146955","DOIUrl":"https://doi.org/10.1080/24754269.2022.2146955","url":null,"abstract":"Let be a sequence of independent random variables with common general error distribution with shape parameter v>0, and let denote the r-th largest order statistics of . With different normalizing constants the distributional expansions and the uniform convergence rates of normalized powered order statistics are established. An alternative method is presented to estimate the probability of the r-th extremes. Numerical analyses are provided to support the main results.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"7 1","pages":"1 - 29"},"PeriodicalIF":0.5,"publicationDate":"2022-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44373673","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 : 2022-10-31DOI: 10.1080/24754269.2022.2136266
Gemechu Abdisa Atomsa, Yingchun Zhou
In this paper, we have constructed Artificial Neural Network models which could capture rainfall pattern of Ethiopia. The data was collected from 147 stations across Ethiopia. Seven homogenized rainfall stations have been created based on both local and global patterns of datasets. Back-of-Word algorithm was used for extracting patterns of the datasets. K-means algorithm was used for clustering purpose. Each of the data of homogenized regions was interpolated using a spatial average. Two time series models, ARMA and Facebook's Prophet, have been fitted for each of spatial averages as baseline models. Both have been shown to perform weak for generalization purpose as spatially averaged datasets lose their strong seasonal pattern. On the other hand, the proposed Long Short Term Memory (LSTM) was found to be the best fitted model in comparison to the baseline models. The hyperparameters of the LSTM have been tuned to get optimal parameters. Besides, the RMSE of the baseline model was used as a benchmark for tuning the LSTM used.
{"title":"Application of neural network to model rainfall pattern of Ethiopia","authors":"Gemechu Abdisa Atomsa, Yingchun Zhou","doi":"10.1080/24754269.2022.2136266","DOIUrl":"https://doi.org/10.1080/24754269.2022.2136266","url":null,"abstract":"In this paper, we have constructed Artificial Neural Network models which could capture rainfall pattern of Ethiopia. The data was collected from 147 stations across Ethiopia. Seven homogenized rainfall stations have been created based on both local and global patterns of datasets. Back-of-Word algorithm was used for extracting patterns of the datasets. K-means algorithm was used for clustering purpose. Each of the data of homogenized regions was interpolated using a spatial average. Two time series models, ARMA and Facebook's Prophet, have been fitted for each of spatial averages as baseline models. Both have been shown to perform weak for generalization purpose as spatially averaged datasets lose their strong seasonal pattern. On the other hand, the proposed Long Short Term Memory (LSTM) was found to be the best fitted model in comparison to the baseline models. The hyperparameters of the LSTM have been tuned to get optimal parameters. Besides, the RMSE of the baseline model was used as a benchmark for tuning the LSTM used.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"7 1","pages":"69 - 84"},"PeriodicalIF":0.5,"publicationDate":"2022-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42947671","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 : 2022-10-20DOI: 10.1080/24754269.2022.2135807
R. Jiang, Yexun Peng
This paper studies the inference problem of index coefficient in single-index models under massive dataset. Analysis of massive dataset is challenging owing to formidable computational costs or memory requirements. A natural method is the averaging divide-and-conquer approach, which splits data into several blocks, obtains the estimators for each block and then aggregates the estimators via averaging. However, there is a restriction on the number of blocks. To overcome this limitation, this paper proposed a computationally efficient method, which only requires an initial estimator and then successively refines the estimator via multiple rounds of aggregations. The proposed estimator achieves the optimal convergence rate without any restriction on the number of blocks. We present both theoretical analysis and experiments to explore the property of the proposed method.
{"title":"A short note on fitting a single-index model with massive data","authors":"R. Jiang, Yexun Peng","doi":"10.1080/24754269.2022.2135807","DOIUrl":"https://doi.org/10.1080/24754269.2022.2135807","url":null,"abstract":"This paper studies the inference problem of index coefficient in single-index models under massive dataset. Analysis of massive dataset is challenging owing to formidable computational costs or memory requirements. A natural method is the averaging divide-and-conquer approach, which splits data into several blocks, obtains the estimators for each block and then aggregates the estimators via averaging. However, there is a restriction on the number of blocks. To overcome this limitation, this paper proposed a computationally efficient method, which only requires an initial estimator and then successively refines the estimator via multiple rounds of aggregations. The proposed estimator achieves the optimal convergence rate without any restriction on the number of blocks. We present both theoretical analysis and experiments to explore the property of the proposed method.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"7 1","pages":"49 - 60"},"PeriodicalIF":0.5,"publicationDate":"2022-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45511628","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 : 2022-10-14DOI: 10.1080/24754269.2022.2133466
Daojiang He, Dongchu Sun, Qing Zhu
The Lomax distribution is an important member in the distribution family. In this paper, we systematically develop an objective Bayesian analysis of data from a Lomax distribution. Noninformative priors, including probability matching priors, the maximal data information (MDI) prior, Jeffreys prior and reference priors, are derived. The propriety of the posterior under each prior is subsequently validated. It is revealed that the MDI prior and one of the reference priors yield improper posteriors, and the other reference prior is a second-order probability matching prior. A simulation study is conducted to assess the frequentist performance of the proposed Bayesian approach. Finally, this approach along with the bootstrap method is applied to a real data set.
{"title":"Bayesian analysis for the Lomax model using noninformative priors","authors":"Daojiang He, Dongchu Sun, Qing Zhu","doi":"10.1080/24754269.2022.2133466","DOIUrl":"https://doi.org/10.1080/24754269.2022.2133466","url":null,"abstract":"The Lomax distribution is an important member in the distribution family. In this paper, we systematically develop an objective Bayesian analysis of data from a Lomax distribution. Noninformative priors, including probability matching priors, the maximal data information (MDI) prior, Jeffreys prior and reference priors, are derived. The propriety of the posterior under each prior is subsequently validated. It is revealed that the MDI prior and one of the reference priors yield improper posteriors, and the other reference prior is a second-order probability matching prior. A simulation study is conducted to assess the frequentist performance of the proposed Bayesian approach. Finally, this approach along with the bootstrap method is applied to a real data set.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"7 1","pages":"61 - 68"},"PeriodicalIF":0.5,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42511670","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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