For two normal populations with unknown means μ and unknown variances σ2, assume that there are simple order restrictions among the means and variances: μ1 < μ2 and σ12 >σ22 > 0. This case is said to be...For two normal populations with unknown means μ and unknown variances σ2, assume that there are simple order restrictions among the means and variances: μ1 < μ2 and σ12 >σ22 > 0. This case is said to be simultaneous order restriction by Shi (Maximum likelihood estimation of means and variances from normal populations under simultaneous order restrictions, J. Multivariate Anal., 50(1994), 282-293.) and an iterative algorithm of computing the order restricted maximum likelihood estimates of μi and σi2 was given in that paper. This paper shows that the restricted maximum likelihood estimate of μi has smaller mean square loss than the usual estimate xi under some conditions.展开更多
This paper considers the well known problem of estimating reliability in discrete reliability growth context with sequence of dichotomous success-failure outcomes. More precisely, the authors generalize the simple ord...This paper considers the well known problem of estimating reliability in discrete reliability growth context with sequence of dichotomous success-failure outcomes. More precisely, the authors generalize the simple order relationship constraint with some coefficients. The authors prove that under some mild conditions, the generalized constraint MLE problem can be transformed to a traditional isotonic problem. The authors also study the lower confidence limit estimation of reliability with sample space ranking method. A simulation is conducted to illustrate the superiority of the proposed method.展开更多
Nonparametric stochastic volatility models,although providing great flexibility for modelling thevolatility equation,often fail to account for useful shape information.For example,a model maynot use the knowledge that...Nonparametric stochastic volatility models,although providing great flexibility for modelling thevolatility equation,often fail to account for useful shape information.For example,a model maynot use the knowledge that the autoregressive component of the volatility equation is monotonically increasing as the lagged volatility increases.We propose a class of additive stochasticvolatility models that allow for different shape constraints and can incorporate the leverageeffect–asymmetric impact of positive and negative return shocks on volatilities.We developa Bayesian fitting algorithm and demonstrate model performance on simulated and empiricaldatasets.Unlike general nonparametric models,our model sacrifices little when the true volatility equation is linear.In nonlinear situations we improve the model fit and the ability to estimatevolatilities over general,unconstrained,nonparametric models.展开更多
文摘For two normal populations with unknown means μ and unknown variances σ2, assume that there are simple order restrictions among the means and variances: μ1 < μ2 and σ12 >σ22 > 0. This case is said to be simultaneous order restriction by Shi (Maximum likelihood estimation of means and variances from normal populations under simultaneous order restrictions, J. Multivariate Anal., 50(1994), 282-293.) and an iterative algorithm of computing the order restricted maximum likelihood estimates of μi and σi2 was given in that paper. This paper shows that the restricted maximum likelihood estimate of μi has smaller mean square loss than the usual estimate xi under some conditions.
基金supported by the Natural Science Foundation of China under Grant No.11171007/A011103
文摘This paper considers the well known problem of estimating reliability in discrete reliability growth context with sequence of dichotomous success-failure outcomes. More precisely, the authors generalize the simple order relationship constraint with some coefficients. The authors prove that under some mild conditions, the generalized constraint MLE problem can be transformed to a traditional isotonic problem. The authors also study the lower confidence limit estimation of reliability with sample space ranking method. A simulation is conducted to illustrate the superiority of the proposed method.
基金Peter Craigmile and Jiangyong Yin were supported in part by the National Science Foundation(NSF)under grant DMS-0906864Xinyi Xu,Jiangyong Yin and Steven MacEachern were supported in part by the NSF under grant DMS-1209194+2 种基金Peter Craigmile is additionally supported in part by the NSF under grants SES-1024709,DMS-1407604 and SES-1424481the National Cancer Institute of the National Institutes of Health under Award Number 1R21CA212308-01the project title is‘Evaluating how licensing-law strategies will change neighborhood disparities in tobacco retailer density’.Xinyi Xu and Steven MacEachern are supported under grant DMS-1613110.
文摘Nonparametric stochastic volatility models,although providing great flexibility for modelling thevolatility equation,often fail to account for useful shape information.For example,a model maynot use the knowledge that the autoregressive component of the volatility equation is monotonically increasing as the lagged volatility increases.We propose a class of additive stochasticvolatility models that allow for different shape constraints and can incorporate the leverageeffect–asymmetric impact of positive and negative return shocks on volatilities.We developa Bayesian fitting algorithm and demonstrate model performance on simulated and empiricaldatasets.Unlike general nonparametric models,our model sacrifices little when the true volatility equation is linear.In nonlinear situations we improve the model fit and the ability to estimatevolatilities over general,unconstrained,nonparametric models.
