Quadratic Loss of Isotonic Normal Means under Simultaneous Order Restrictions

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.

SEMIPARAMETRIC ANALYSIS OF ISOTONIC ERRORS-IN-VARIABLES REGRESSION MODELS WITH RANDOMLY RIGHT CENSORED RESPONSE

This paper considers the estimation of a semiparametric isotonic regression model when the covariates are measured with additive errors and the response is randomly right censored by a censoring time.The authors show that the proposed estimator of the regression parameter is rootn consistent and asymptotically normal.The authors also show that the isotonic estimator of the functional component,at a fixed point,is cubic root-n consistent and converges in distribution to the slope at zero of the greatest convex minorant of the sum of a two-sided standard Brownian motion and the square of the time parameter.A simulation study is carried out to investigate the performance of the estimators proposed in this article.

Estimation in Discrete Reliability Growth,a Growth Model with Coefficient Condition

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.

Shape-constrained semiparametric additive stochastic volatility models

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.