Variational Principles for Asymptotic Variance of General Markov Processes

A variational formula for the asymptotic variance of general Markov processes is obtained.As application,we get an upper bound of the mean exit time of reversible Markov processes,and some comparison theorems between the reversible and non-reversible diffusion processes.

Nearly best linear estimates of logistic parameters based on complete ordered statistics

Deals with the determination of the nearly best linear estimates of location and scale parameters of a logistic population, when both parameters are unknown, by introducing Blom’s semi empirical ’α,β correction’ into the asymptotic mean and covariance formulae with complete and ordered samples taken into consideration and various nearly best linear estimates established and points out the high efficiency of these estimators relative to the best linear unbiased estimators (BLUEs) and other linear estimators makes them useful in practice.

Multiple Objective Test Design for Accelerated Destructive Degradation Tests

Accelerated destructive degradation tests(ADDTs)are powerful to provide reliability information in the degradation processes with destructive measurements.In order to carry out an ADDT efficiently,both the estimation precision of parameters and the test cost should be considered.On the basis of the given degradation model and failure criterion,a multiple-objective optimization model for the design of ADDTs is proposed.Under constrains of the maximum measurement time,the total sample size and the number of stress levels,a comprehensive target function is suggested to reflect both the precision of lifetime estimation and total cost,and the optimal test plan is obtained,which is composed by optimal choices for samples size,measurement frequency,and the number of measurements at each stress level.A real example is illustrated to demonstrate the implementation of the proposed approach.

Uncertainty Comparison Between Value-at-Risk and Expected Shortfall

Value-at-Risk(VaR)and expected shortfall(ES)are two key risk measures in financial risk management.Comparing these two measures has been a hot debate,and most discussions focus on risk measure properties.This paper uses independent data and autoregressive models with normal or t-distribution to examine the effect of the heavy tail and dependence on comparing the nonparametric inference uncertainty of these two risk measures.Theoretical and numerical analyses suggest that VaR at 99%level is better than ES at 97.5%level for distributions with heavier tails.

Delete-group Jackknife Estimate in Partially Linear Regression Models with Heteroscedasticity

Consider a partially linear regression model with an unknown vector parameter , an unknown function g(·), and unknown heteroscedastic error variances. Chen, You[23] proposed a semiparametric generalized least squares estimator (SGLSE) for , which takes the heteroscedasticity into account to increase efficiency. For inference based on this SGLSE, it is necessary to construct a consistent estimator for its asymptotic covariance matrix. However, when there exists within-group correlation, the traditional delta method and the delete-1 jackknife estimation fail to offer such a consistent estimator. In this paper, by deleting grouped partial residuals a delete-group jackknife method is examined. It is shown that the delete-group jackknife method indeed can provide a consistent estimator for the asymptotic covariance matrix in the presence of within-group correlations. This result is an extension of that in [21].

Impact of sufficient dimension reduction in nonparametric estimation of causal effect

We consider the estimation of causal treatment effect using nonparametric regression orinverse propensity weighting together with sufficient dimension reduction for searching lowdimensional covariate subsets. A special case of this problem is the estimation of a responseeffect with data having ignorable missing response values. An issue that is not well addressedin the literature is whether the estimation of the low-dimensional covariate subsets by sufficient dimension reduction has an impact on the asymptotic variance of the resulting causaleffect estimator. With some incorrect or inaccurate statements, many researchers believe thatthe estimation of the low-dimensional covariate subsets by sufficient dimension reduction doesnot affect the asymptotic variance. We rigorously establish a result showing that this is nottrue unless the low-dimensional covariate subsets include some covariates superfluous for estimation, and including such covariates loses efficiency. Our theory is supplemented by somesimulation results.