This paper discusses inference for ordered parameters of multinomial distributions. We first show that the asymptotic distributions of their maximum likelihood estimators (MLEs) are not always normal and the bootstrap...This paper discusses inference for ordered parameters of multinomial distributions. We first show that the asymptotic distributions of their maximum likelihood estimators (MLEs) are not always normal and the bootstrap distribution estimators of the MLEs can be inconsistent. Then a class of weighted sum estimators (WSEs) of the ordered parameters is proposed. Properties of the WSEs are studied, including their asymptotic normality. Based on those results, large sample inferences for smooth functions of the ordered parameters can be made. Especially, the confidence intervals of the maximum cell probabilities are constructed. Simulation results indicate that this interval estimation performs much better than the bootstrap approaches in the literature. Finally, the above results for ordered parameters of multinomial distributions are extended to more general distribution models.展开更多
We consider testing hypotheses concerning comparing dispersions between two parameter vectors of multinomial distributions in both one-sample and two-sample cases. The comparison criterion is the concept of Schur majo...We consider testing hypotheses concerning comparing dispersions between two parameter vectors of multinomial distributions in both one-sample and two-sample cases. The comparison criterion is the concept of Schur majorization. A new dispersion index is proposed for testing the hypotheses. The corresponding test for the one-sample problem is an exact test. For the two-sample problem, the bootstrap is used to approximate the null distribution of the test statistic and the p-value. We prove that the bootstrap test is asymptotically correct and consistent. Simulation studies for the bootstrap test are reported and a real life example is presented.展开更多
We introduce here the concept of Bayesian networks, in compound Poisson model, which provides a graphical modeling framework that encodes the joint probability distribution for a set of random variables within a direc...We introduce here the concept of Bayesian networks, in compound Poisson model, which provides a graphical modeling framework that encodes the joint probability distribution for a set of random variables within a directed acyclic graph. We suggest an approach proposal which offers a new mixed implicit estimator. We show that the implicit approach applied in compound Poisson model is very attractive for its ability to understand data and does not require any prior information. A comparative study between learned estimates given by implicit and by standard Bayesian approaches is established. Under some conditions and based on minimal squared error calculations, we show that the mixed implicit estimator is better than the standard Bayesian and the maximum likelihood estimators. We illustrate our approach by considering a simulation study in the context of mobile communication networks.展开更多
In 1980's, differential geometric methods are successfully used to study curved exponential families and normal nonlinear repression models. This paper presents a new geometric structure to study multinomial distr...In 1980's, differential geometric methods are successfully used to study curved exponential families and normal nonlinear repression models. This paper presents a new geometric structure to study multinomial distributipn models which contain a set of nonlinear parameters. Based on this geometric structure, the authors study several asymptotic properties for sequential estimation. The bias, the variance and the information loss of the sequeatial estimates are given from geometric viewpoint, and a limit theorem connected with the obServed and expected Fisher information is obtained ill terms of curVature measures. The results show that the sequeotial estimation procedure has some better properties which are generally impossible for nonsequeotial estimation procedures.展开更多
In this paper, we extend to a multivariate setting the bivariate model A introduced by Jin and Ren in 2014 （Recursions and fast Fourier transforms for a new bivariate aggregate claims model, Scandinavian Actuarial Jo...In this paper, we extend to a multivariate setting the bivariate model A introduced by Jin and Ren in 2014 （Recursions and fast Fourier transforms for a new bivariate aggregate claims model, Scandinavian Actuarial Journal 8） to model insurance aggregate claims in the case when different types of claims simulta- neously affect an insurance portfolio. We obtain an exact recursive formula for the probability function of the multivariate compound distribution corresponding to this model under the assumption that the conditional multivariate counting distribution （conditioned by the total number of claims） is multinomial. Our formula extends the corresponding one from Jin and Ren.展开更多
Microsatellite instability(MSI)is a key biomarker for cancer therapy and prognosis.Traditional experimental assays are laborious and time-consuming,and next-generation sequencingbased computational methods do not work...Microsatellite instability(MSI)is a key biomarker for cancer therapy and prognosis.Traditional experimental assays are laborious and time-consuming,and next-generation sequencingbased computational methods do not work on leukemia samples,paraffin-embedded samples,or patient-derived xenografts/organoids,due to the requirement of matched normal samples.Herein,we developed MSIsensor-pro,an open-source single sample MSI scoring method for research and clinical applications.MSIsensor-pro introduces a multinomial distribution model to quantify polymerase slippages for each tumor sample and a discriminative site selection method to enable MSI detection without matched normal samples.We demonstrate that MSIsensor-pro is an ultrafast,accurate,and robust MSI calling method.Using samples with various sequencing depths and tumor purities,MSIsensor-pro significantly outperformed the current leading methods in both accuracy and computational cost.MSIsensor-pro is available at https://github.com/xjtu-omics/msisensor-pro and free for non-commercial use,while a commercial license is provided upon request.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 10371126)
文摘This paper discusses inference for ordered parameters of multinomial distributions. We first show that the asymptotic distributions of their maximum likelihood estimators (MLEs) are not always normal and the bootstrap distribution estimators of the MLEs can be inconsistent. Then a class of weighted sum estimators (WSEs) of the ordered parameters is proposed. Properties of the WSEs are studied, including their asymptotic normality. Based on those results, large sample inferences for smooth functions of the ordered parameters can be made. Especially, the confidence intervals of the maximum cell probabilities are constructed. Simulation results indicate that this interval estimation performs much better than the bootstrap approaches in the literature. Finally, the above results for ordered parameters of multinomial distributions are extended to more general distribution models.
基金Sponsored by the National NSFC (10771126, 10801130)
文摘We consider testing hypotheses concerning comparing dispersions between two parameter vectors of multinomial distributions in both one-sample and two-sample cases. The comparison criterion is the concept of Schur majorization. A new dispersion index is proposed for testing the hypotheses. The corresponding test for the one-sample problem is an exact test. For the two-sample problem, the bootstrap is used to approximate the null distribution of the test statistic and the p-value. We prove that the bootstrap test is asymptotically correct and consistent. Simulation studies for the bootstrap test are reported and a real life example is presented.
文摘We introduce here the concept of Bayesian networks, in compound Poisson model, which provides a graphical modeling framework that encodes the joint probability distribution for a set of random variables within a directed acyclic graph. We suggest an approach proposal which offers a new mixed implicit estimator. We show that the implicit approach applied in compound Poisson model is very attractive for its ability to understand data and does not require any prior information. A comparative study between learned estimates given by implicit and by standard Bayesian approaches is established. Under some conditions and based on minimal squared error calculations, we show that the mixed implicit estimator is better than the standard Bayesian and the maximum likelihood estimators. We illustrate our approach by considering a simulation study in the context of mobile communication networks.
文摘In 1980's, differential geometric methods are successfully used to study curved exponential families and normal nonlinear repression models. This paper presents a new geometric structure to study multinomial distributipn models which contain a set of nonlinear parameters. Based on this geometric structure, the authors study several asymptotic properties for sequential estimation. The bias, the variance and the information loss of the sequeatial estimates are given from geometric viewpoint, and a limit theorem connected with the obServed and expected Fisher information is obtained ill terms of curVature measures. The results show that the sequeotial estimation procedure has some better properties which are generally impossible for nonsequeotial estimation procedures.
文摘In this paper, we extend to a multivariate setting the bivariate model A introduced by Jin and Ren in 2014 （Recursions and fast Fourier transforms for a new bivariate aggregate claims model, Scandinavian Actuarial Journal 8） to model insurance aggregate claims in the case when different types of claims simulta- neously affect an insurance portfolio. We obtain an exact recursive formula for the probability function of the multivariate compound distribution corresponding to this model under the assumption that the conditional multivariate counting distribution （conditioned by the total number of claims） is multinomial. Our formula extends the corresponding one from Jin and Ren.
基金supported by the National Key R&D Program of China(Grant Nos.2018YFC0910400 and 2017YFC0907500)the National Natural Science Foundation of China(Grant Nos.31671372,61702406,31701739,and 31970317)+2 种基金the National Science and Technology Major Project of China(Grant No.2018ZX10302205)the‘‘World-Class Universities and the Characteristic Development Guidance Funds for the Central Universities”the General Financial Grant from the China Postdoctoral Science Foundation(Grant Nos.2017M623178 and 2017M623188)
文摘Microsatellite instability(MSI)is a key biomarker for cancer therapy and prognosis.Traditional experimental assays are laborious and time-consuming,and next-generation sequencingbased computational methods do not work on leukemia samples,paraffin-embedded samples,or patient-derived xenografts/organoids,due to the requirement of matched normal samples.Herein,we developed MSIsensor-pro,an open-source single sample MSI scoring method for research and clinical applications.MSIsensor-pro introduces a multinomial distribution model to quantify polymerase slippages for each tumor sample and a discriminative site selection method to enable MSI detection without matched normal samples.We demonstrate that MSIsensor-pro is an ultrafast,accurate,and robust MSI calling method.Using samples with various sequencing depths and tumor purities,MSIsensor-pro significantly outperformed the current leading methods in both accuracy and computational cost.MSIsensor-pro is available at https://github.com/xjtu-omics/msisensor-pro and free for non-commercial use,while a commercial license is provided upon request.
