In this paper a family, called the pivotal family, of distributions is considered.A pivotal family is determined by a generalized pivotal model. Analytical results show that a great many parametric families of distrib...In this paper a family, called the pivotal family, of distributions is considered.A pivotal family is determined by a generalized pivotal model. Analytical results show that a great many parametric families of distributions are pivotal. In a pivotal family of distributions a general method of deriving fiducial distributions of parameters is proposed. In the method a fiducial model plays an important role. A fiducial model is a function of a random variable with a known distribution, called the pivotal random element, when the observation of a statistic is given.The method of this paper includes some other methods of deriving fiducial distributions. Specially the first fiducial distribution given by Fisher can be derived by the method. For the monotone likelihood ratio family of distributions, which is a pivotal family, the fiducial distributions have a frequentist property in the Neyman-Pearson view. Fiducial distributions of regular parametric functions also have the above frequentist property. Some advantages of the fiducial inference are exhibited in four applications of the fiducial distribution. Many examples are given, in which the fiducial distributions cannot be derived by the existing methods.展开更多
In applications, the traditional estimation procedure generally begins with model selection.Once a specific model is selected, subsequent estimation is conducted under the selected model withoutconsideration of the un...In applications, the traditional estimation procedure generally begins with model selection.Once a specific model is selected, subsequent estimation is conducted under the selected model withoutconsideration of the uncertainty from the selection process. This often leads to the underreportingof variability and too optimistic confidence sets. Model averaging estimation is an alternative to thisprocedure, which incorporates model uncertainty into the estimation process. In recent years, therehas been a rising interest in model averaging from the frequentist perspective, and some importantprogresses have been made. In this paper, the theory and methods on frequentist model averagingestimation are surveyed. Some future research topics are also discussed.展开更多
Sample size determination typically relies on a power analysis based on a frequentist conditional approach. This latter can be seen as a particular case of the two-priors approach, which allows to build four distinct ...Sample size determination typically relies on a power analysis based on a frequentist conditional approach. This latter can be seen as a particular case of the two-priors approach, which allows to build four distinct power functions to select the optimal sample size. We revise this approach when the focus is on testing a single binomial proportion. We consider exact methods and introduce a conservative criterion to account for the typical non-monotonic behavior of the power functions, when dealing with discrete data. The main purpose of this paper is to present a Shiny App providing a user-friendly, interactive tool to apply these criteria. The app also provides specific tools to elicit the analysis and the design prior distributions, which are the core of the two-priors approach.展开更多
Various uncertainty quantification methodologies are presented using a combination of several deter-ministic decline curve analysis models and two bootstrapping algorithms.These probabilistic models are applied to 126...Various uncertainty quantification methodologies are presented using a combination of several deter-ministic decline curve analysis models and two bootstrapping algorithms.These probabilistic models are applied to 126 sample wells from the Permian basin.Results are presented for 12-72 months of pro-duction hindcast given an average well production history of 103 months.Based on the coverage rate and the forecast error(with the coverage rate being more significant in our choice of the best probabilistic models)and using up to one-half of the available production history for a group of sample wells from the Permian Basin,we find that the CBM-SEPD combination is the best probabilistic model for the Central Basin Platform,the MBM-Arps combination is the best probabilistic model for the Delaware Basin,the CBM-Arps is the best probabilistic model for the Midland Basin,and the best probabilistic model for the overall Permian Basin is the CBM-Arps when early time data is used as hindcast and CBM-SEPD for when one-quarter to one-half of the data is used as hindcast.When three-quarters or more of the available production history is used for analysis,the MBM-SEPD probabilistic model is the best combination in terms of both coverage rate and forecast error for all the sub-basins in the Permian.The novelty of this work lies in its extension of bootstrapping methods to other decline curve analysis models.This work also offers the engineer guidance on the best choice of probabilistic model whilst attempting to forecast production from the Permian Basin.展开更多
In several instances of statistical practice, it is not uncommon to use the same data for both model selection and inference, without taking account of the variability induced by model selection step. This is usually ...In several instances of statistical practice, it is not uncommon to use the same data for both model selection and inference, without taking account of the variability induced by model selection step. This is usually referred to as post-model selection inference. The shortcomings of such practice are widely recognized, finding a general solution is extremely challenging. We propose a model averaging alternative consisting on taking into account model selection probability and the like-lihood in assigning the weights. The approach is applied to Bernoulli trials and outperforms Akaike weights model averaging and post-model selection estimators.展开更多
In this paper, we propose a new generalized p-value for testing homogeneity of scale parameters λi from k independent inverse Gaussian populations. The proposed generalized p-value is proved to have exact frequentist...In this paper, we propose a new generalized p-value for testing homogeneity of scale parameters λi from k independent inverse Gaussian populations. The proposed generalized p-value is proved to have exact frequentist property, and it is also invariant under the group of scale transformation. Simulation results indicate that the proposed test is better than existing approximate χ^2 test.展开更多
It is quite common in statistical modeling to select a model and make inference as if the model had been known in advance;i.e. ignoring model selection uncertainty. The resulted estimator is called post-model selectio...It is quite common in statistical modeling to select a model and make inference as if the model had been known in advance;i.e. ignoring model selection uncertainty. The resulted estimator is called post-model selection estimator (PMSE) whose properties are hard to derive. Conditioning on data at hand (as it is usually the case), Bayesian model selection is free of this phenomenon. This paper is concerned with the properties of Bayesian estimator obtained after model selection when the frequentist (long run) performances of the resulted Bayesian estimator are of interest. The proposed method, using Bayesian decision theory, is based on the well known Bayesian model averaging (BMA)’s machinery;and outperforms PMSE and BMA. It is shown that if the unconditional model selection probability is equal to model prior, then the proposed approach reduces BMA. The method is illustrated using Bernoulli trials.展开更多
Bayesian model averaging (BMA) is a popular and powerful statistical method of taking account of uncertainty about model form or assumption. Usually the long run (frequentist) performances of the resulted estimator ar...Bayesian model averaging (BMA) is a popular and powerful statistical method of taking account of uncertainty about model form or assumption. Usually the long run (frequentist) performances of the resulted estimator are hard to derive. This paper proposes a mixture of priors and sampling distributions as a basic of a Bayes estimator. The frequentist properties of the new Bayes estimator are automatically derived from Bayesian decision theory. It is shown that if all competing models have the same parametric form, the new Bayes estimator reduces to BMA estimator. The method is applied to the daily exchange rate Euro to US Dollar.展开更多
Parameter estimation is always a difficult issue for crop model users, and inaccurate parameter values will result in deceptive model predictions. Parameter values may vary with different inversion methods due to equi...Parameter estimation is always a difficult issue for crop model users, and inaccurate parameter values will result in deceptive model predictions. Parameter values may vary with different inversion methods due to equifinality and differences in the estimating processes. Therefore, it is of great importance to evaluate the factors which may influence parameter estimates and to make a comparison of the current widely-used methods. In this study, three popular frequentist methods(SCE-UA, GA and PEST) and two Bayesian-based methods(GLUE and MCMC-AM) were applied to estimate nine cultivar parameters using the ORYZA(v3) Model. The results showed that there were substantial differences between the parameter estimates derived by the different methods, and they had strong effects on model predictions. The parameter estimates given by the frequentist methods were obviously sensitive to initial values, and the extent of the sensitivity varied with algorithms and objective functions. Among the frequentist methods, the SCE-UA was recommended due to the balance between stable convergence and high efficiency. All the parameter estimates remarkably improved the goodness of model-fit, and the parameter estimates derived from the Bayesian-based methods had relatively worse performance compared to the frequentist methods. In particular, the parameter estimates with the highest probability density of posterior distributions derived from the MCMC-AM method(MCMC_P_(max)) led to results equivalent to those derived from the frequentist methods, and even better in some situations. Additionally, model accuracy was greatly influenced by the values of phenology parameters in validation.展开更多
The frequentist model averaging(FMA)and the focus information criterion(FIC)under a local framework have been extensively studied in the likelihood and regression setting since the seminal work of Hjort and Claes kens...The frequentist model averaging(FMA)and the focus information criterion(FIC)under a local framework have been extensively studied in the likelihood and regression setting since the seminal work of Hjort and Claes kens in 2003.One inconvenience,however,of the existing works is that they usually require the involved criterion function to be twice differentiable which thus prevents a direct application to the case of quantile regression(QR).This as well as some other intrinsic merits of QR motivate us to study the FIC and FMA in a locally misspecified linear QR model.Specifically,we derive in this paper the explicit asymptotic risk expression for a general submodel-based QR estimator of a focus parameter.Then based on this asymptotic result,we develop the FIC and FMA in the current setting.Our theoretical development depends crucially on the convexity of the objective function,which makes possible to establish the asymptotics based on the existing convex stochastic process theory.Simulation studies are presented to illustrate the finite sample performance of the proposed method.The low birth weight data set is analyzed.展开更多
Frequentist model averaging has received much attention from econometricians and statisticians in recent years.A key problem with frequentist model average estimators is the choice of weights.This paper develops a new...Frequentist model averaging has received much attention from econometricians and statisticians in recent years.A key problem with frequentist model average estimators is the choice of weights.This paper develops a new approach of choosing weights based on an approximation of generalized cross validation.The resultant least squares model average estimators are proved to be asymptotically optimal in the sense of achieving the lowest possible squared errors.Especially,the optimality is built under both discrete and continuous weigh sets.Compared with the existing approach based on Mallows criterion,the conditions required for the asymptotic optimality of the proposed method are more reasonable.Simulation studies and real data application show good performance of the proposed estimators.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.10271013,10071090).
文摘In this paper a family, called the pivotal family, of distributions is considered.A pivotal family is determined by a generalized pivotal model. Analytical results show that a great many parametric families of distributions are pivotal. In a pivotal family of distributions a general method of deriving fiducial distributions of parameters is proposed. In the method a fiducial model plays an important role. A fiducial model is a function of a random variable with a known distribution, called the pivotal random element, when the observation of a statistic is given.The method of this paper includes some other methods of deriving fiducial distributions. Specially the first fiducial distribution given by Fisher can be derived by the method. For the monotone likelihood ratio family of distributions, which is a pivotal family, the fiducial distributions have a frequentist property in the Neyman-Pearson view. Fiducial distributions of regular parametric functions also have the above frequentist property. Some advantages of the fiducial inference are exhibited in four applications of the fiducial distribution. Many examples are given, in which the fiducial distributions cannot be derived by the existing methods.
基金supported by the National Natural Science Foundation of China under Grant Nos. 70625004, 10721101, and 70221001
文摘In applications, the traditional estimation procedure generally begins with model selection.Once a specific model is selected, subsequent estimation is conducted under the selected model withoutconsideration of the uncertainty from the selection process. This often leads to the underreportingof variability and too optimistic confidence sets. Model averaging estimation is an alternative to thisprocedure, which incorporates model uncertainty into the estimation process. In recent years, therehas been a rising interest in model averaging from the frequentist perspective, and some importantprogresses have been made. In this paper, the theory and methods on frequentist model averagingestimation are surveyed. Some future research topics are also discussed.
文摘Sample size determination typically relies on a power analysis based on a frequentist conditional approach. This latter can be seen as a particular case of the two-priors approach, which allows to build four distinct power functions to select the optimal sample size. We revise this approach when the focus is on testing a single binomial proportion. We consider exact methods and introduce a conservative criterion to account for the typical non-monotonic behavior of the power functions, when dealing with discrete data. The main purpose of this paper is to present a Shiny App providing a user-friendly, interactive tool to apply these criteria. The app also provides specific tools to elicit the analysis and the design prior distributions, which are the core of the two-priors approach.
文摘Various uncertainty quantification methodologies are presented using a combination of several deter-ministic decline curve analysis models and two bootstrapping algorithms.These probabilistic models are applied to 126 sample wells from the Permian basin.Results are presented for 12-72 months of pro-duction hindcast given an average well production history of 103 months.Based on the coverage rate and the forecast error(with the coverage rate being more significant in our choice of the best probabilistic models)and using up to one-half of the available production history for a group of sample wells from the Permian Basin,we find that the CBM-SEPD combination is the best probabilistic model for the Central Basin Platform,the MBM-Arps combination is the best probabilistic model for the Delaware Basin,the CBM-Arps is the best probabilistic model for the Midland Basin,and the best probabilistic model for the overall Permian Basin is the CBM-Arps when early time data is used as hindcast and CBM-SEPD for when one-quarter to one-half of the data is used as hindcast.When three-quarters or more of the available production history is used for analysis,the MBM-SEPD probabilistic model is the best combination in terms of both coverage rate and forecast error for all the sub-basins in the Permian.The novelty of this work lies in its extension of bootstrapping methods to other decline curve analysis models.This work also offers the engineer guidance on the best choice of probabilistic model whilst attempting to forecast production from the Permian Basin.
文摘In several instances of statistical practice, it is not uncommon to use the same data for both model selection and inference, without taking account of the variability induced by model selection step. This is usually referred to as post-model selection inference. The shortcomings of such practice are widely recognized, finding a general solution is extremely challenging. We propose a model averaging alternative consisting on taking into account model selection probability and the like-lihood in assigning the weights. The approach is applied to Bernoulli trials and outperforms Akaike weights model averaging and post-model selection estimators.
基金Supported by the National Natural Science Foundation of China(Grant No.11201478,11471030,11126197 and11471035)
文摘In this paper, we propose a new generalized p-value for testing homogeneity of scale parameters λi from k independent inverse Gaussian populations. The proposed generalized p-value is proved to have exact frequentist property, and it is also invariant under the group of scale transformation. Simulation results indicate that the proposed test is better than existing approximate χ^2 test.
文摘It is quite common in statistical modeling to select a model and make inference as if the model had been known in advance;i.e. ignoring model selection uncertainty. The resulted estimator is called post-model selection estimator (PMSE) whose properties are hard to derive. Conditioning on data at hand (as it is usually the case), Bayesian model selection is free of this phenomenon. This paper is concerned with the properties of Bayesian estimator obtained after model selection when the frequentist (long run) performances of the resulted Bayesian estimator are of interest. The proposed method, using Bayesian decision theory, is based on the well known Bayesian model averaging (BMA)’s machinery;and outperforms PMSE and BMA. It is shown that if the unconditional model selection probability is equal to model prior, then the proposed approach reduces BMA. The method is illustrated using Bernoulli trials.
文摘Bayesian model averaging (BMA) is a popular and powerful statistical method of taking account of uncertainty about model form or assumption. Usually the long run (frequentist) performances of the resulted estimator are hard to derive. This paper proposes a mixture of priors and sampling distributions as a basic of a Bayes estimator. The frequentist properties of the new Bayes estimator are automatically derived from Bayesian decision theory. It is shown that if all competing models have the same parametric form, the new Bayes estimator reduces to BMA estimator. The method is applied to the daily exchange rate Euro to US Dollar.
基金supported by the National Natural Science Foundation of China(NSFC 51909004)。
文摘Parameter estimation is always a difficult issue for crop model users, and inaccurate parameter values will result in deceptive model predictions. Parameter values may vary with different inversion methods due to equifinality and differences in the estimating processes. Therefore, it is of great importance to evaluate the factors which may influence parameter estimates and to make a comparison of the current widely-used methods. In this study, three popular frequentist methods(SCE-UA, GA and PEST) and two Bayesian-based methods(GLUE and MCMC-AM) were applied to estimate nine cultivar parameters using the ORYZA(v3) Model. The results showed that there were substantial differences between the parameter estimates derived by the different methods, and they had strong effects on model predictions. The parameter estimates given by the frequentist methods were obviously sensitive to initial values, and the extent of the sensitivity varied with algorithms and objective functions. Among the frequentist methods, the SCE-UA was recommended due to the balance between stable convergence and high efficiency. All the parameter estimates remarkably improved the goodness of model-fit, and the parameter estimates derived from the Bayesian-based methods had relatively worse performance compared to the frequentist methods. In particular, the parameter estimates with the highest probability density of posterior distributions derived from the MCMC-AM method(MCMC_P_(max)) led to results equivalent to those derived from the frequentist methods, and even better in some situations. Additionally, model accuracy was greatly influenced by the values of phenology parameters in validation.
基金This paper is supported by the National Natural Science Foundation of China(No.11771049).
文摘The frequentist model averaging(FMA)and the focus information criterion(FIC)under a local framework have been extensively studied in the likelihood and regression setting since the seminal work of Hjort and Claes kens in 2003.One inconvenience,however,of the existing works is that they usually require the involved criterion function to be twice differentiable which thus prevents a direct application to the case of quantile regression(QR).This as well as some other intrinsic merits of QR motivate us to study the FIC and FMA in a locally misspecified linear QR model.Specifically,we derive in this paper the explicit asymptotic risk expression for a general submodel-based QR estimator of a focus parameter.Then based on this asymptotic result,we develop the FIC and FMA in the current setting.Our theoretical development depends crucially on the convexity of the objective function,which makes possible to establish the asymptotics based on the existing convex stochastic process theory.Simulation studies are presented to illustrate the finite sample performance of the proposed method.The low birth weight data set is analyzed.
基金by National Key R&D Program of China(2020AAA0105200)the Ministry of Science and Technology of China(Grant no.2016YFB0502301)+1 种基金the National Natural Science Foundation of China(Grant nos.11871294,12031016,11971323,71925007,72042019,72091212 and 12001559)a joint grant from the Academy for Multidisciplinary Studies,Capital Normal University.
文摘Frequentist model averaging has received much attention from econometricians and statisticians in recent years.A key problem with frequentist model average estimators is the choice of weights.This paper develops a new approach of choosing weights based on an approximation of generalized cross validation.The resultant least squares model average estimators are proved to be asymptotically optimal in the sense of achieving the lowest possible squared errors.Especially,the optimality is built under both discrete and continuous weigh sets.Compared with the existing approach based on Mallows criterion,the conditions required for the asymptotic optimality of the proposed method are more reasonable.Simulation studies and real data application show good performance of the proposed estimators.
