Maximum likelihood estimation in the proportional hazards cure model

The proportional hazards cure model generalizes Cox’s proportional hazards model which allows that a proportion of study subjects may never experience the event of interest. Here nonparametric maximum likelihood approach is proposed to estimating the cumulative hazard and the regression parameters. The asymptotic properties of the resulting estimators are established using the modern empirical process theory. And the estimators for the regression parameters are shown to be semiparametric efficient.     

The population-sample decomposition approach to multivariate estimation methods

In this paper it is argued that all multivariate estimation methods, such as OLS regression, simultaneous linear equations systems and, more widely, what are known as LISREL methods, have merit as geometric approximation methods, even if the observations are not drawn from a multivariate normal parent distribution and consequently cannot be viewed as ML estimators. It is shown that for large samples the asymptotical distribution of any estimator, being a totally differentiable covariance function, may be assessed by the δ method. Finally, we stress that the design of the sample and a priori knowledge about the parent distribution may be incorporated to obtain more specific results. It turns out that some fairly traditional assumptions, such as assuming some variables to be non-random, fixed over repeated samples, or the existence of a parent normal distribution, may have dramatic effects on the assessment of standard deviations and confidence bounds, if such assumptions are not realistic. The method elaborated by us does not make use of such assumptions.     

A New Technique to Determine Horizontal and Vertical Permeabilities from the Time-Delayed Response of a Vertical Interference Test

To determine the permeabilities from a vertical interference test, earlier investigators proposed correlations or type curves based on point source solutions or partially penetrated well solutions. However, it is impossible for these correlations or type curves to cover all possible scenarios in the real world. In more recent years, people use regression analysis to simultaneously match the pressure responses at the source interval and the observation point. With regression analysis, we face the problem of non-unique solutions. Sometimes, estimated permeability could be outside a reasonable range when analyzing noisy data from real tests. In this paper, a new technique is presented to estimate horizontal and vertical permeabilities from the time-delayed response in a wireline vertical interference test. In a vertical test, a pressure drawdown test period is followed by a pressure buildup test period. Because of the delay in response, the pressure at the observation probe continues to drop for some time while the pressure at the source interval is being built up. The maximum pressure drop at the observation probe with regard to the maximum pressure drop in the source interval is time-delayed. Using this time delay and the maximum pressure drop at the observation probe, vertical and horizontal permeabilities can be estimated. A novel numerical scheme is used. The new technique is compared with the previous methods, and it shows its superiority in accuracy. In addition, it can be used in different test configurations. Application issues in real testing conditions are discussed. Finally, two field tests are analyzed using this technique, while an earlier effort to analyze the tests using a conventional method was not successful due to poor data quality.     

回归分析中参数估计的一种新方法

本文根据矩阵的广义逆理论，建立了回归分析中进行参数估计的一种新方法，该方法更简单更精确。     

非参数可修系统可用度的评定

考虑可修的串联系统,其单元产品在出现故障时,由于种种原因,故障不能得到及时维修,形成了一段保障延误时间.于是这一更新过程为:正常工作(直到出现故障)-保障延误-故障维修-正常工作…….假设每一时段的分布未知,且相互独立,给出了可用度的点估计和置信下限.     

频率选择性衰落信道中的频偏盲估计

根据频率选择性衰落信道的抽头延迟线模型,将针对平坦衰落信道的CS(周期平稳过程理论)频偏盲估计算法扩展到了频率选择性衰落信道,并通过仿真证明这种扩展是可行的.仿真结果还表明CS算法不仅有好的抗平坦衰落能力,而且有很好的抗频率选择性衰落性能.     

部分线性变系数模型的Profile Lagrange乘子检验

对于部分线性变系数模型附有约束条件时的估计与检验问题,基于Profile最小二乘方法给出了参数部分以及非参数部分的约束估计并研究了它们的渐近性质,并针对约束条件构造了Profile Lagrange乘子检验统计量,证明了该统计量在原假设下的渐近分布为χ2分布,从而将Lagrange乘子检验方法推广到了半参数模型上.     

厚尾相依序列的均值变点估计

本文研究了厚尾相依序列的均值变点估计. 证明了变点的CUSUM估计的一致性并得到了收敛速度.在方差无穷的情况下推广了H\'{a}jek--R\'{e}nyi不等式.     

The Asymptotic Variance of the Continuous-Time Kernel Estimator with Applications to Bandwidth Selection

We derive simple expressions for the asymptotic variance of the kernel-density estimator of a stationary continuous-time process in one and d dimensions and relate convergence rates to sample path smoothness. Important applications include methods for selecting optimal smoothing parameters and construction of confidence bands for testing hypotheses about the density. In a simulation study the results are applied to bandwidth selection for discrete-time processes that can be modelled as continuous-time processes sampled at a high rate.     

Estimation of investment project profitability in the modified Cantor-Lipman model

The profitability of investment projects in the modified Cantor-Lipman model is analyzed. The possibility of making lower estimates of the investment project profitability by searching for periodic trajectories is studied. The necessary and sufficient conditions for the existence of a trajectory with the period 2 are derived. The sufficient conditions ensuring the existence of a certain trajectory with the period 2 are derived in the form of explicit requirements on the investment project structure.