HAZARD RATE ESTIMATION FOR CENSORED DATA BY WAVELET METHODS

ABSTRACT

We study the estimation of a hazard rate function based on censored data by non-linear wavelet method. We provide an asymptotic formula for the mean integrated squared error (MISE) of nonlinear wavelet-based hazard rate estimators under randomly censored data. We show this MISE formula, when the underlying hazard rate function and censoring distribution function are only piecewise smooth, has the same expansion as analogous kernel estimators, a feature not available for the kernel estimators. In addition, we establish an asymptotic normality of the nonlinear wavelet estimator.     

Estimation of the mean of the exponential distribution with an outlying observation

Given a life testing experiment consisting of n items, n-1 of which have the expected life λ while one could have an expected life λ/α with 0 < α < 1 the problem is. to find a mean square error (MSE) minimizing estimation function. The standard estimators for the homogeneous case (α = 1) overestimate the expected life and their MSE tend to infinity when a tends to 0.

Looking at the estimation problem as an insurance (see Anscombe (1960)) two different “testimators” are compared with respect to their MSE, Numerical results show that an estimation function based on the “Epstein-statistic” x_(n)/[xbar] is the best one.     

Simulation of the p-generalized Gaussian distribution

In this paper, we introduce the p-generalized polar methods for the simulation of the p-generalized Gaussian distribution. On the basis of geometric measure representations, the well-known Box–Muller method and the Marsaglia–Bray rejecting polar method for the simulation of the Gaussian distribution are generalized to simulate the p-generalized Gaussian distribution, which fits much more flexibly to data than the Gaussian distribution and has already been applied in various fields of modern sciences. To prove the correctness of the p-generalized polar methods, we give stochastic representations, and to demonstrate their adequacy, we perform a comparison of six simulation techniques w.r.t. the goodness of fit and the complexity. The competing methods include adapted general methods and another special method. Furthermore, we prove stochastic representations for all the adapted methods.     

弱电解质溶液中c／ka^o比值对解离度误差的影响

介绍了溶液中弱电解质平衡体系的pH计算是《无机化学》课程中的重要基础理论知识。为简化计算经常需要引入近似条件，这样必然造成误差。通过理论计算解释了不同c／ka^o值与解离度误差的关系和不同解离度误差对应的c／ka^o值，对学生正确理解相关内容大有助益，是教材内容的必要补充。     

On Comparison Of Estimates Of Dispersion Using Generalized Pitman Nearness Criterion

In this paper, estimates QP dispersion matrix and its functions are compared based on generalized Pitman nearness criterion, Various Iosa functions are considered for the purpose. Locally superior estimates are defined and obtained. Comparison of these estimates are made with other standard ones. It is snown that within certain classes, defined in the paper, these are the best estimatcrs ia the generalized Fitman nearness sense     

对外汉语教材生词英语译释和汉语词语学习偏误

通过对对外汉语初级教材中生词英语译释存在的译释方式不妥、译释不够准确、忽略生词的附属义、忽略生词的用法等方面问题进行例举分析，指出这些问题会诱发英语干扰，导致语际负迁移，造成词语理解错误，以致留学生学习汉语词汇时容易出现语义及语法层面的偏误。     

Tolerance‐based error reduction in multi‐agent bioassays

Some degree of error is inevitable in multi‐agent bioassays regardless of design or measurement technology. Estimation error can be reduced post facto by exploiting the matrix partial ordering of the bioassay survival estimates. The standard method for this is order‐restricted regression (ORR). If the joint action of the bioassay agents admits a tolerance‐based interpretation, additional structure beyond matrix partial ordering is available, leading to a new method of error reduction. This tolerance‐based error reduction (TBER) procedure almost always outperforms ORR. Like ORR, TBER applies to complete factorial bioassay designs and, using weighting, to incomplete designs.     

Challenges to the Acceptance of Probabilistic Risk Analysis

This paper discusses a number of the key challenges to the acceptance and application of probabilistic risk analysis (PRA). Those challenges include: (a) the extensive reliance on subjective judgment in PRA, requiring the development of guidance for the use of PRA in risk-informed regulation, and possibly the development of robust or reference prior distributions to minimize the reliance on judgment; and (b) the treatment of human performance in PRA, including not only human error per se but also management and organizational factors more broadly. All of these areas are seen as presenting interesting research challenges at the interface between engineering and other disciplines.     

人机工程学的发展及人机系统的可靠性

本文介绍了人机工程学(工效学)这一新兴边缘学科的研究内容、发展及现状,讨论了人-机系统的可靠性并着重讨论了人的操作可靠性,探讨了按人为差错进行可靠性分析与可靠性估计的人为差错和可靠性分析逻辑推演法(HERALD法)及系统能力方法(SC方法)。 本文的结论可供系统管理工作者及设计工作者,特别是可靠性管理及可靠性设计工作者参考。