In this paper, we explore some weakly consistent properties of quasi-maximum likelihood estimates (QMLE) concerning the quasi-likelihood equation $ \sum\nolimits_{i = 1}^n {X_i (y_i - \mu (X_i^\prime \beta ))} $ for u...In this paper, we explore some weakly consistent properties of quasi-maximum likelihood estimates (QMLE) concerning the quasi-likelihood equation $ \sum\nolimits_{i = 1}^n {X_i (y_i - \mu (X_i^\prime \beta ))} $ for univariate generalized linear model E(y|X) = μ(X′β). Given uncorrelated residuals {e i = Y i ? μ(X i ′ β0), 1 ? i ? n} and other conditions, we prove that $$ \hat \beta _n - \beta _0 = O_p (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n^{ - 1/2} ) $$ holds, where $ \hat \beta _n $ is a root of the above equation, β 0 is the true value of parameter β and $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n $$ denotes the smallest eigenvalue of the matrix S n = ∑ i=1 n X i X i ′ . We also show that the convergence rate above is sharp, provided independent non-asymptotically degenerate residual sequence and other conditions. Moreover, paralleling to the elegant result of Drygas (1976) for classical linear regression models, we point out that the necessary condition guaranteeing the weak consistency of QMLE is S n ?1 → 0, as the sample size n → ∞.展开更多
Regression models for survival time data involve estimation of the hazard rate as a function of predictor variables and associated slope parameters. An adaptive approach is formulated for such hazard regression modeli...Regression models for survival time data involve estimation of the hazard rate as a function of predictor variables and associated slope parameters. An adaptive approach is formulated for such hazard regression modeling. The hazard rate is modeled using fractional polynomials, that is, linear combinations of products of power transforms of time together with other available predictors. These fractional polynomial models are restricted to generating positive-valued hazard rates and decreasing survival times. Exponentially distributed survival times are a special case. Parameters are estimated using maximum likelihood estimation allowing for right censored survival times. Models are evaluated and compared using likelihood cross-validation (LCV) scores. LCV scores and tolerance parameters are used to control an adaptive search through alternative fractional polynomial hazard rate models to identify effective models for the underlying survival time data. These methods are demonstrated using two different survival time data sets including survival times for lung cancer patients and for multiple myeloma patients. For the lung cancer data, the hazard rate depends distinctly on time. However, controlling for cell type provides a distinct improvement while the hazard rate depends only on cell type and no longer on time. Furthermore, Cox regression is unable to identify a cell type effect. For the multiple myeloma data, the hazard rate also depends distinctly on time. Moreover, consideration of hemoglobin at diagnosis provides a distinct improvement, the hazard rate still depends distinctly on time, and hemoglobin distinctly moderates the effect of time on the hazard rate. These results indicate that adaptive hazard rate modeling can provide unique insights into survival time data.展开更多
Overlapped x domain multiplexing(OVXDM) is a promising encoding technique to obtain high spectral efficiency by utilizing inter-symbol interference(ISI) intelligently. However, the computational complexity of maximum ...Overlapped x domain multiplexing(OVXDM) is a promising encoding technique to obtain high spectral efficiency by utilizing inter-symbol interference(ISI) intelligently. However, the computational complexity of maximum likelihood sequence detection(MLSD) increases exponentially with the growth of spectral efficiency in OVXDM, which is unbearable for practical implementations. In this paper, based on a novel path metric associating adjacent symbols, we propose a multi-bit sliding stack decoding(Multi-Bit SSD) algorithm to achieve multiple-bit decoding simultaneously in OVXDM. Theoretical analysis is provided for the algorithm, which indicates the relationship between the performance and parameters including multiplexing waveform, overlapping fold and sliding window size. Simulation results show that the proposed algorithm can achieve better decoding performance and higher spectral efficiency than conventional fast decoding algorithms.展开更多
Effects of many medical procedures appear after a time lag, when a significant change occurs in subjects’ failure rate. This paper focuses on the detection and estimation of such changes which is important for the ev...Effects of many medical procedures appear after a time lag, when a significant change occurs in subjects’ failure rate. This paper focuses on the detection and estimation of such changes which is important for the evaluation and comparison of treatments and prediction of their effects. Unlike the classical change-point model, measurements may still be identically distributed, and the change point is a parameter of their common survival function. Some of the classical change-point detection techniques can still be used but the results are different. Contrary to the classical model, the maximum likelihood estimator of a change point appears consistent, even in presence of nuisance parameters. However, a more efficient procedure can be derived from Kaplan-Meier estimation of the survival function followed by the least-squares estimation of the change point. Strong consistency of these estimation schemes is proved. The finite-sample properties are examined by a Monte Carlo study. Proposed methods are applied to a recent clinical trial of the treatment program for strong drug dependence.展开更多
To test variance homogeneity,various likelihood-ratio based tests such as the Bartlett's test have been proposed.The null distributions of these tests were generally derived asymptotically or approximately.We re-e...To test variance homogeneity,various likelihood-ratio based tests such as the Bartlett's test have been proposed.The null distributions of these tests were generally derived asymptotically or approximately.We re-examine the restrictive maximum likelihood ratio(RELR)statistic,and sug-gest a Monte Carlo algorithm to compute its exact null distribution,and so its p-value.It is much easier to implement than most existing methods.Simulation studies indicate that the proposed procedure is also superior to its competitors in terms of type I error and powers.We analyse an environmental dataset for an illustration.展开更多
It is of great interest to allocate redundant component(s)in a coherent system in order to optimize the lifetime of the resulting system in reliability engineering,and system security.This topic has posed many interes...It is of great interest to allocate redundant component(s)in a coherent system in order to optimize the lifetime of the resulting system in reliability engineering,and system security.This topic has posed many interesting theoretical problems to which many researchers have devoted themselves in the past decades.In this article,we aim to review some recent results on the problem of optimal allocations of active[standby]redundancies in coherent systems.Some open problems in this research line are posed as well.Here we highlight the stochastic orderings as a powerful tool in our discussion.展开更多
One important model in handling the multivariate data is the varying-coefficient partially linear regression model. In this paper, the generalized likelihood ratio test is developed to test whether its coefficient fun...One important model in handling the multivariate data is the varying-coefficient partially linear regression model. In this paper, the generalized likelihood ratio test is developed to test whether its coefficient functions are varying or not. It is showed that the normalized proposed test follows asymptotically x2-distribution and the Wilks phenomenon under the null hypothesis, and its asymptotic power achieves the optimal rate of the convergence for the nonparametric hypotheses testing. Some simulation studies illustrate that the test works well.展开更多
This study proposes a full Bayesian nonparametric procedure to investigate the predictive power of exchange rates in relation to commodity prices for three commodity-exporting countries:Canada,Australia,and New Zealan...This study proposes a full Bayesian nonparametric procedure to investigate the predictive power of exchange rates in relation to commodity prices for three commodity-exporting countries:Canada,Australia,and New Zealand.We propose a new time-dependent infinite mixture of a normal linear regression model of the conditional distribution of the commodity price index.The mixing weights follow a set of Probit stick-breaking priors that are time-varying.We find that exchange rates have a positive predictive effect in general,but accounting for time variation does not improve forecasting performance.By contrast,the intercept in the regression and the lagged dependent variable show signs of parameter change over time in most cases,which is important in forecasting both the mean and the density of commodity prices one period ahead.The results also suggest that the variance is a large source of the time variation in the conditional distribution of commodity prices.展开更多
本文考虑多维广义线性模型的拟似然方程sum from i=1 to n X_i(y_i-μ(X_i^1β))=0,在一定条件下证明了此方程的解(?)渐近存在,并得到了其收敛速度,即■_n-β_0=O_p(■_n^(-1/2)),其中β_0为参数β的真值,■_n是方阵S_n=sum from i=1 to...本文考虑多维广义线性模型的拟似然方程sum from i=1 to n X_i(y_i-μ(X_i^1β))=0,在一定条件下证明了此方程的解(?)渐近存在,并得到了其收敛速度,即■_n-β_0=O_p(■_n^(-1/2)),其中β_0为参数β的真值,■_n是方阵S_n=sum from i=1 to n X_iX_i^1的最小特征值．展开更多
基金supported by the President Foundation (Grant No. Y1050)the Scientific Research Foundation(Grant No. KYQD200502) of GUCAS
文摘In this paper, we explore some weakly consistent properties of quasi-maximum likelihood estimates (QMLE) concerning the quasi-likelihood equation $ \sum\nolimits_{i = 1}^n {X_i (y_i - \mu (X_i^\prime \beta ))} $ for univariate generalized linear model E(y|X) = μ(X′β). Given uncorrelated residuals {e i = Y i ? μ(X i ′ β0), 1 ? i ? n} and other conditions, we prove that $$ \hat \beta _n - \beta _0 = O_p (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n^{ - 1/2} ) $$ holds, where $ \hat \beta _n $ is a root of the above equation, β 0 is the true value of parameter β and $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n $$ denotes the smallest eigenvalue of the matrix S n = ∑ i=1 n X i X i ′ . We also show that the convergence rate above is sharp, provided independent non-asymptotically degenerate residual sequence and other conditions. Moreover, paralleling to the elegant result of Drygas (1976) for classical linear regression models, we point out that the necessary condition guaranteeing the weak consistency of QMLE is S n ?1 → 0, as the sample size n → ∞.
文摘Regression models for survival time data involve estimation of the hazard rate as a function of predictor variables and associated slope parameters. An adaptive approach is formulated for such hazard regression modeling. The hazard rate is modeled using fractional polynomials, that is, linear combinations of products of power transforms of time together with other available predictors. These fractional polynomial models are restricted to generating positive-valued hazard rates and decreasing survival times. Exponentially distributed survival times are a special case. Parameters are estimated using maximum likelihood estimation allowing for right censored survival times. Models are evaluated and compared using likelihood cross-validation (LCV) scores. LCV scores and tolerance parameters are used to control an adaptive search through alternative fractional polynomial hazard rate models to identify effective models for the underlying survival time data. These methods are demonstrated using two different survival time data sets including survival times for lung cancer patients and for multiple myeloma patients. For the lung cancer data, the hazard rate depends distinctly on time. However, controlling for cell type provides a distinct improvement while the hazard rate depends only on cell type and no longer on time. Furthermore, Cox regression is unable to identify a cell type effect. For the multiple myeloma data, the hazard rate also depends distinctly on time. Moreover, consideration of hemoglobin at diagnosis provides a distinct improvement, the hazard rate still depends distinctly on time, and hemoglobin distinctly moderates the effect of time on the hazard rate. These results indicate that adaptive hazard rate modeling can provide unique insights into survival time data.
基金supported by the Fundamental Research Funds for the Central Universities under grant 2016XD-01
文摘Overlapped x domain multiplexing(OVXDM) is a promising encoding technique to obtain high spectral efficiency by utilizing inter-symbol interference(ISI) intelligently. However, the computational complexity of maximum likelihood sequence detection(MLSD) increases exponentially with the growth of spectral efficiency in OVXDM, which is unbearable for practical implementations. In this paper, based on a novel path metric associating adjacent symbols, we propose a multi-bit sliding stack decoding(Multi-Bit SSD) algorithm to achieve multiple-bit decoding simultaneously in OVXDM. Theoretical analysis is provided for the algorithm, which indicates the relationship between the performance and parameters including multiplexing waveform, overlapping fold and sliding window size. Simulation results show that the proposed algorithm can achieve better decoding performance and higher spectral efficiency than conventional fast decoding algorithms.
文摘Effects of many medical procedures appear after a time lag, when a significant change occurs in subjects’ failure rate. This paper focuses on the detection and estimation of such changes which is important for the evaluation and comparison of treatments and prediction of their effects. Unlike the classical change-point model, measurements may still be identically distributed, and the change point is a parameter of their common survival function. Some of the classical change-point detection techniques can still be used but the results are different. Contrary to the classical model, the maximum likelihood estimator of a change point appears consistent, even in presence of nuisance parameters. However, a more efficient procedure can be derived from Kaplan-Meier estimation of the survival function followed by the least-squares estimation of the change point. Strong consistency of these estimation schemes is proved. The finite-sample properties are examined by a Monte Carlo study. Proposed methods are applied to a recent clinical trial of the treatment program for strong drug dependence.
基金The research of Li was supported by Grant 11871294 from National Natural Science Foundation of ChinaLiang’s research was partially supported by NSF grant DMS-1620898.
文摘To test variance homogeneity,various likelihood-ratio based tests such as the Bartlett's test have been proposed.The null distributions of these tests were generally derived asymptotically or approximately.We re-examine the restrictive maximum likelihood ratio(RELR)statistic,and sug-gest a Monte Carlo algorithm to compute its exact null distribution,and so its p-value.It is much easier to implement than most existing methods.Simulation studies indicate that the proposed procedure is also superior to its competitors in terms of type I error and powers.We analyse an environmental dataset for an illustration.
基金supported by the National Natural Science Foundation of China(Grant Nos.11422109and 11271169)Natural Science Foundation of Jiangsu Province(Grant No.BK20141145)a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘It is of great interest to allocate redundant component(s)in a coherent system in order to optimize the lifetime of the resulting system in reliability engineering,and system security.This topic has posed many interesting theoretical problems to which many researchers have devoted themselves in the past decades.In this article,we aim to review some recent results on the problem of optimal allocations of active[standby]redundancies in coherent systems.Some open problems in this research line are posed as well.Here we highlight the stochastic orderings as a powerful tool in our discussion.
基金supported by National Natural Science Foundation of China under Grant No.1117112the Fund of Shanxi Datong University under Grant No.2010K4+1 种基金the Doctoral Fund of Ministry of Education of China under Grant No.20090076110001National Statistical Science Research Major Program of China under Grant No.2011LZ051
文摘One important model in handling the multivariate data is the varying-coefficient partially linear regression model. In this paper, the generalized likelihood ratio test is developed to test whether its coefficient functions are varying or not. It is showed that the normalized proposed test follows asymptotically x2-distribution and the Wilks phenomenon under the null hypothesis, and its asymptotic power achieves the optimal rate of the convergence for the nonparametric hypotheses testing. Some simulation studies illustrate that the test works well.
基金The author acknowledges financial support from the National Natural Science Foundation of China(NSFC,No.71773069).
文摘This study proposes a full Bayesian nonparametric procedure to investigate the predictive power of exchange rates in relation to commodity prices for three commodity-exporting countries:Canada,Australia,and New Zealand.We propose a new time-dependent infinite mixture of a normal linear regression model of the conditional distribution of the commodity price index.The mixing weights follow a set of Probit stick-breaking priors that are time-varying.We find that exchange rates have a positive predictive effect in general,but accounting for time variation does not improve forecasting performance.By contrast,the intercept in the regression and the lagged dependent variable show signs of parameter change over time in most cases,which is important in forecasting both the mean and the density of commodity prices one period ahead.The results also suggest that the variance is a large source of the time variation in the conditional distribution of commodity prices.
基金partly supported by National Natural Science Foundation of China and President Foundation of GUCAS.
文摘本文考虑多维广义线性模型的拟似然方程sum from i=1 to n X_i(y_i-μ(X_i^1β))=0,在一定条件下证明了此方程的解(?)渐近存在,并得到了其收敛速度,即■_n-β_0=O_p(■_n^(-1/2)),其中β_0为参数β的真值,■_n是方阵S_n=sum from i=1 to n X_iX_i^1的最小特征值．
