Profile likelihood function is introduced to analyze the uncertainty of hydrometeorological extreme inference and the theory of estimating confidence intervals of the key parameters and quantiles of extreme value dist...Profile likelihood function is introduced to analyze the uncertainty of hydrometeorological extreme inference and the theory of estimating confidence intervals of the key parameters and quantiles of extreme value distribution by profile likelihood function is described.GEV(generalized extreme value)distribution and GP(generalized Pareto)distribution are used respectively to fit the annual maximum daily flood discharge sample of the Yichang station in the Yangtze River and the daily rainfall sample in10 big cities including Guangzhou.The parameters of the models are estimated by maximum likelihood method and the fitting results are tested by probability plot,quantile plot,return level plot and density plot.The return levels and confidence intervals of flood and rainstorm in different return periods are calculated by profile likelihood function.The results show that the asymmetry of the profile likelihood function curve increases with the return period,which can reflect the effect of the length of sample series and return periods on confidence interval.As an effective tool for estimating confidence interval of the key parameters and quantiles of extreme value distribution,profile likelihood function can lead to a more accurate result and help to analyze the uncertainty of extreme values of hydrometeorology.展开更多
Hydrological risk is highly dependent on the occurrence of extreme rainfalls.This fact has led to a wide range of studies on the estimation and uncertainty analysis of the extremes.In most cases,confidence intervals(C...Hydrological risk is highly dependent on the occurrence of extreme rainfalls.This fact has led to a wide range of studies on the estimation and uncertainty analysis of the extremes.In most cases,confidence intervals(CIs)are constructed to represent the uncertainty of the estimates.Since the accuracy of CIs depends on the asymptotic normality of the data and is questionable with limited observations in practice,a Bayesian highest posterior density(HPD)interval,bootstrap percentile interval,and profile likelihood(PL)interval have been introduced to analyze the uncertainty that does not depend on the normality assumption.However,comparison studies to investigate their performances in terms of the accuracy and uncertainty of the estimates are scarce.In addition,the strengths,weakness,and conditions necessary for performing each method also must be investigated.Accordingly,in this study,test experiments with simulations from varying parent distributions and different sample sizes were conducted.Then,applications to the annual maximum rainfall(AMR)time series data in South Korea were performed.Five districts with 38-year(1973–2010)AMR observations were fitted by the three aforementioned methods in the application.From both the experimental and application results,the Bayesian method is found to provide the lowest uncertainty of the design level while the PL estimates generally have the highest accuracy but also the largest uncertainty.The bootstrap estimates are usually inferior to the other two methods,but can perform adequately when the distribution model is not heavy-tailed and the sample size is large.The distribution tail behavior and the sample size are clearly found to affect the estimation accuracy and uncertainty.This study presents a comparative result,which can help researchers make decisions in the context of assessing extreme rainfall uncertainties.展开更多
In this paper,we study the hazard rate by a semiparametric model with an unspecified functional form and involving an index structure.We propose a random censored local linear kernel-weighted least squares estimator f...In this paper,we study the hazard rate by a semiparametric model with an unspecified functional form and involving an index structure.We propose a random censored local linear kernel-weighted least squares estimator for the nonparametric component,treating it as a bivariate function,and this estimator enjoys uniform consistency.The induced profile likelihood estimator of the index coefficient vector achieves the information lower bound.This semiparametric efficient result inspires the construction of a class of efficient estimating equations.For computational feasibility,another two sets of estimating equations are presented based on double robustness.The efficient estimation can be readily implemented by an adapted Newton-Raphson algorithm.Asymptotic properties of all estimators are rigorously established and derived.Numerical results validate the performance of the proposed estimators.展开更多
This paper considers partially linear additive models with the number of parameters diverging when some linear cons train ts on the parame trie par t are available.This paper proposes a constrained profile least-squar...This paper considers partially linear additive models with the number of parameters diverging when some linear cons train ts on the parame trie par t are available.This paper proposes a constrained profile least-squares estimation for the parametrie components with the nonparametric functions being estimated by basis function approximations.The consistency and asymptotic normality of the restricted estimator are given under some certain conditions.The authors construct a profile likelihood ratio test statistic to test the validity of the linear constraints on the parametrie components,and demonstrate that it follows asymptotically chi-squared distribution under the null and alternative hypo theses.The finite sample performance of the proposed method is illus trated by simulation studies and a data analysis.展开更多
Prediction of the progression of an infectious disease outbreak is important for planning and coordinating a response.Differential equations are often used to model an epidemic outbreak's behaviour but are challen...Prediction of the progression of an infectious disease outbreak is important for planning and coordinating a response.Differential equations are often used to model an epidemic outbreak's behaviour but are challenging to parameterise.Furthermore,these models can suffer from misspecification,which biases predictions and parameter estimates.Stochastic models can help with misspecification but are even more expensive to simulate and perform inference with.Here,we develop an explicitly likelihood-based variation of the generalised profiling method as a tool for prediction and inference under model mis-specification.Our approach allows us to carry out identifiability analysis and uncertainty quantification using profile likelihood-based methods without the need for marginalisation.We provide justification for this approach by introducing a new interpretation of the model approximation component as a stochastic constraint.This preserves the rationale for using profiling rather than integration to remove nuisance parameters while also providing a link back to stochastic models.We applied an initial version of this method during an outbreak of measles in Samoa in 2019e2020 and found that it achieved relatively fast,accurate predictions.Here we present the most recent version of our method and its application to this measles outbreak,along with additional validation.展开更多
We propose the single-index hazards model for censored survival data.As an extension of the Cox model and many transformation models,this model allows nonparametric modeling of covariate effects in a parsimonious way ...We propose the single-index hazards model for censored survival data.As an extension of the Cox model and many transformation models,this model allows nonparametric modeling of covariate effects in a parsimonious way via a single index.In addition,the relative importance of covariates can be assessed via this model.We consider two commonly used profile likelihood methods for parameter estimation:the local profile likelihood method and the stratified profile likelihood method.It is shown that both methods may give consistent estimators under certain restrictive conditions,but in general they can yield biased estimation.Simulation studies are also conducted to demonstrate these bias phenomena.The existence and nature of the failures of these two commonly used approaches is somewhat surprising.展开更多
In this paper we study the practical procedure for getting the maximumlikelihood estimates in a semi-parametric regression model with interval censored data.On the basis of the on previous theoretical results, we give...In this paper we study the practical procedure for getting the maximumlikelihood estimates in a semi-parametric regression model with interval censored data.On the basis of the on previous theoretical results, we give the detailed algorithms when there are one or two covariates in the model.展开更多
This paper considers a semi-varying coefficient model for panel data with fixed effects,proposes the profile-likelihood-based estimators for the parametric and nonparametric components,and establishes convergence rate...This paper considers a semi-varying coefficient model for panel data with fixed effects,proposes the profile-likelihood-based estimators for the parametric and nonparametric components,and establishes convergence rates and asymptotic normality properties for both estimators.Simulation results show that the proposed estimators behave well in finite sample cases.展开更多
In this paper, we investigate the estimation of semi-varying coefficient models when the nonlinear covariates are prone to measurement error. With the help of validation sampling, we propose two estimators of the para...In this paper, we investigate the estimation of semi-varying coefficient models when the nonlinear covariates are prone to measurement error. With the help of validation sampling, we propose two estimators of the parameter and the coefficient functions by combining dimension reduction and the profile likelihood methods without any error structure equation specification or error distribution assumption. We establish the asymptotic normality of proposed estimators for both the parametric and nonparametric parts and show that the proposed estimators achieves the best convergence rate. Data-driven bandwidth selection methods are also discussed. Simulations are conducted to evaluate the finite sample property of the estimation methods proposed.展开更多
In this paper,we consider the statistical inferences in a partially linear model when the model error follows an autoregressive process.A two-step procedure is proposed for estimating the unknown parameters by taking ...In this paper,we consider the statistical inferences in a partially linear model when the model error follows an autoregressive process.A two-step procedure is proposed for estimating the unknown parameters by taking into account of the special structure in error.Since the asymptotic matrix of the estimator for the parametric part has a complex structure,an empirical likelihood function is also developed.We derive the asymptotic properties of the related statistics under mild conditions.Some simulations,as well as a real data example,are conducted to illustrate the finite sample performance.展开更多
基金supported by the National Basic Research Program of China("973" Program)(Grant Nos.2013CB036406,2010CB951102)the National Natural Science Foundation of China(Grant No.51109224)
文摘Profile likelihood function is introduced to analyze the uncertainty of hydrometeorological extreme inference and the theory of estimating confidence intervals of the key parameters and quantiles of extreme value distribution by profile likelihood function is described.GEV(generalized extreme value)distribution and GP(generalized Pareto)distribution are used respectively to fit the annual maximum daily flood discharge sample of the Yichang station in the Yangtze River and the daily rainfall sample in10 big cities including Guangzhou.The parameters of the models are estimated by maximum likelihood method and the fitting results are tested by probability plot,quantile plot,return level plot and density plot.The return levels and confidence intervals of flood and rainstorm in different return periods are calculated by profile likelihood function.The results show that the asymmetry of the profile likelihood function curve increases with the return period,which can reflect the effect of the length of sample series and return periods on confidence interval.As an effective tool for estimating confidence interval of the key parameters and quantiles of extreme value distribution,profile likelihood function can lead to a more accurate result and help to analyze the uncertainty of extreme values of hydrometeorology.
基金supported by Hanyang University(Grant No.HY-2014)
文摘Hydrological risk is highly dependent on the occurrence of extreme rainfalls.This fact has led to a wide range of studies on the estimation and uncertainty analysis of the extremes.In most cases,confidence intervals(CIs)are constructed to represent the uncertainty of the estimates.Since the accuracy of CIs depends on the asymptotic normality of the data and is questionable with limited observations in practice,a Bayesian highest posterior density(HPD)interval,bootstrap percentile interval,and profile likelihood(PL)interval have been introduced to analyze the uncertainty that does not depend on the normality assumption.However,comparison studies to investigate their performances in terms of the accuracy and uncertainty of the estimates are scarce.In addition,the strengths,weakness,and conditions necessary for performing each method also must be investigated.Accordingly,in this study,test experiments with simulations from varying parent distributions and different sample sizes were conducted.Then,applications to the annual maximum rainfall(AMR)time series data in South Korea were performed.Five districts with 38-year(1973–2010)AMR observations were fitted by the three aforementioned methods in the application.From both the experimental and application results,the Bayesian method is found to provide the lowest uncertainty of the design level while the PL estimates generally have the highest accuracy but also the largest uncertainty.The bootstrap estimates are usually inferior to the other two methods,but can perform adequately when the distribution model is not heavy-tailed and the sample size is large.The distribution tail behavior and the sample size are clearly found to affect the estimation accuracy and uncertainty.This study presents a comparative result,which can help researchers make decisions in the context of assessing extreme rainfall uncertainties.
基金supported by the Humanities and Social Sciences Youth Foundation of the Ministry of Education of China(Grant No.23YJC910003)supported by the Ph D Scholarship,The Hong Kong Polytechnic University+4 种基金supported by the Research Grant(Grant No.P0034390)The Hong Kong Polytechnic Universitysupported by National Natural Science Foundation of China(Grant No.12271060)supported by the General Research Fund(Grant Nos.13245116 and 15327216)Research Grants of Council,Hong Kong Special Administrative Region,China。
文摘In this paper,we study the hazard rate by a semiparametric model with an unspecified functional form and involving an index structure.We propose a random censored local linear kernel-weighted least squares estimator for the nonparametric component,treating it as a bivariate function,and this estimator enjoys uniform consistency.The induced profile likelihood estimator of the index coefficient vector achieves the information lower bound.This semiparametric efficient result inspires the construction of a class of efficient estimating equations.For computational feasibility,another two sets of estimating equations are presented based on double robustness.The efficient estimation can be readily implemented by an adapted Newton-Raphson algorithm.Asymptotic properties of all estimators are rigorously established and derived.Numerical results validate the performance of the proposed estimators.
基金supported by the National Natural Science Foundation of China under Grant No.11771250the Natural Science Foundation of Shandong Province under Grant No.ZR2019MA002the Program for Scientific Research Innovation of Graduate Dissertation under Grant No.LWCXB201803
文摘This paper considers partially linear additive models with the number of parameters diverging when some linear cons train ts on the parame trie par t are available.This paper proposes a constrained profile least-squares estimation for the parametrie components with the nonparametric functions being estimated by basis function approximations.The consistency and asymptotic normality of the restricted estimator are given under some certain conditions.The authors construct a profile likelihood ratio test statistic to test the validity of the linear constraints on the parametrie components,and demonstrate that it follows asymptotically chi-squared distribution under the null and alternative hypo theses.The finite sample performance of the proposed method is illus trated by simulation studies and a data analysis.
文摘Prediction of the progression of an infectious disease outbreak is important for planning and coordinating a response.Differential equations are often used to model an epidemic outbreak's behaviour but are challenging to parameterise.Furthermore,these models can suffer from misspecification,which biases predictions and parameter estimates.Stochastic models can help with misspecification but are even more expensive to simulate and perform inference with.Here,we develop an explicitly likelihood-based variation of the generalised profiling method as a tool for prediction and inference under model mis-specification.Our approach allows us to carry out identifiability analysis and uncertainty quantification using profile likelihood-based methods without the need for marginalisation.We provide justification for this approach by introducing a new interpretation of the model approximation component as a stochastic constraint.This preserves the rationale for using profiling rather than integration to remove nuisance parameters while also providing a link back to stochastic models.We applied an initial version of this method during an outbreak of measles in Samoa in 2019e2020 and found that it achieved relatively fast,accurate predictions.Here we present the most recent version of our method and its application to this measles outbreak,along with additional validation.
文摘We propose the single-index hazards model for censored survival data.As an extension of the Cox model and many transformation models,this model allows nonparametric modeling of covariate effects in a parsimonious way via a single index.In addition,the relative importance of covariates can be assessed via this model.We consider two commonly used profile likelihood methods for parameter estimation:the local profile likelihood method and the stratified profile likelihood method.It is shown that both methods may give consistent estimators under certain restrictive conditions,but in general they can yield biased estimation.Simulation studies are also conducted to demonstrate these bias phenomena.The existence and nature of the failures of these two commonly used approaches is somewhat surprising.
基金This research is supported by the National Natural Science Foundation of China(10071004) and RFDP, Liping Liu was supported in part by the National Basic Research Program of China under Grant 2003CB716101.
文摘In this paper we study the practical procedure for getting the maximumlikelihood estimates in a semi-parametric regression model with interval censored data.On the basis of the on previous theoretical results, we give the detailed algorithms when there are one or two covariates in the model.
基金supported by the National Natural Science Foundation of China under Grant No.11101452the Natural Science Foundation Project of CQ CSTC under Grant No.2012jjA00035+2 种基金the National Basic Research Program of China under Grant No.2011CB808000the National Social Science Foundation of China under Grant No.12XTJ001the Natural Science Foundation Project of CTBU of China under Grant No.1352001
文摘This paper considers a semi-varying coefficient model for panel data with fixed effects,proposes the profile-likelihood-based estimators for the parametric and nonparametric components,and establishes convergence rates and asymptotic normality properties for both estimators.Simulation results show that the proposed estimators behave well in finite sample cases.
基金Supported by the National Natural Science Foundation of China(No.10871072,11171112 and 11101114)the Scientific Research Fund of Zhejiang Provincial Education Department(Grant No.Y201121276)the Doctoral Fund of Ministry of Education of China(200900076110001)
文摘In this paper, we investigate the estimation of semi-varying coefficient models when the nonlinear covariates are prone to measurement error. With the help of validation sampling, we propose two estimators of the parameter and the coefficient functions by combining dimension reduction and the profile likelihood methods without any error structure equation specification or error distribution assumption. We establish the asymptotic normality of proposed estimators for both the parametric and nonparametric parts and show that the proposed estimators achieves the best convergence rate. Data-driven bandwidth selection methods are also discussed. Simulations are conducted to evaluate the finite sample property of the estimation methods proposed.
基金supported by the NSF of China(Nos.11971208,11601197)the NSSF of China(Grant No.21&ZD152)+2 种基金the China Postdoctoral Science Foundation(Nos.2016M600511,2017T100475)the NSF of Jiangxi Province(Nos.2018ACB21002,20171ACB21030)the Post graduate Innovation Project of Jiangxi Province(No.YC2021CB124)。
文摘In this paper,we consider the statistical inferences in a partially linear model when the model error follows an autoregressive process.A two-step procedure is proposed for estimating the unknown parameters by taking into account of the special structure in error.Since the asymptotic matrix of the estimator for the parametric part has a complex structure,an empirical likelihood function is also developed.We derive the asymptotic properties of the related statistics under mild conditions.Some simulations,as well as a real data example,are conducted to illustrate the finite sample performance.
