Some New Results on the Multinomial Randomized Response Model

ABSTRACT

The randomized response technique is an effective survey method designed to elicit sensitive information while ensuring the privacy of the respondents. In this article, we present some new results on the randomization response model in situations wherein one or two response variables are assumed to follow a multinomial distribution. For a single sensitive question, we use the well-known Hopkins randomization device to derive estimates, both under the assumption of truthful and untruthful responses, and present a technique for making pairwise comparisons. When there are two sensitive questions of interest, we derive a Pearson product moment correlation estimator based on the multinomial model assumption. This estimator may be used to quantify the linear relationship between two variables when multinomial response data are observed according to a randomized-response protocol.     

Profile information matrix for nonlinear transformation models

For semiparametric models, interval estimation and hypothesis testing based on the information matrix for the full model is a challenge because of potentially unlimited dimension. Use of the profile information matrix for a small set of parameters of interest is an appealing alternative. Existing approaches for the estimation of the profile information matrix are either subject to the curse of dimensionality, or are ad-hoc and approximate and can be unstable and numerically inefficient. We propose a numerically stable and efficient algorithm that delivers an exact observed profile information matrix for regression coefficients for the class of Nonlinear Transformation Models [A. Tsodikov (2003) J R Statist Soc Ser B 65:759-774]. The algorithm deals with the curse of dimensionality and requires neither large matrix inverses nor explicit expressions for the profile surface.     

一种基于加权F-范数的半正定矩阵的逼近方法

正定性是许多金融预测模型的重要假设前提，然而从实际样本中得到的相关系数矩阵并不能保证其正定性。为此在介绍如何根据样本设定相关系数矩阵以及范数逼近原理的基础上，如何根据该原理找到与之最接近的相关系数矩阵，即最接近的单位对角半正定对称矩阵。通过实证，验证了其方法的有效性。     

圆锥轴受扭时静、动力的传递矩阵法求解

本文提出了圆锥轴受扭时静、动力的传递矩阵。该方法简便实用,适于工程技术人员在微机上应用。     

分析Chiral分层媒质特性的一般方法(英文)

提出了一套系统方法用于求解任意导体片位于界面的Chiral分层媒质的谐振频率,衰减因子和电磁场分布。文中的分析是在Fourier变换域的并矢格林函数和矩阵分析的基础上来进行的,给出的公式的最大价值在于它提供了求解Chiral分层媒质问题的方法论。     

《高等代数》教程之我见

《高等代数》是一门普遍让学生感到头疼的课,这与所用教材的教程有一定关系,本文就目前所用的教材提出了一种较为适宜的教程,并论述了实施它的可能性与有利因素.     

Analysis of some ruin-related quantities in a Markov-modulated risk model

In this paper, we study the joint Laplace transform and probability generating function of some random quantities that occur in each environment state by the time of ruin in a Markov-modulated risk process. These quantities include the duration spent in each state, the number of claims and the aggregate amount of claims that occurred in each state by the time of ruin. Explicit formulae for the joint transforms, given the initial surplus, and the initial and terminal environment states, are expressed in terms of a matrix version of the scale function. Moments and covariances of these ruin-related quantities are obtained and numerical illustrations are presented. The joint transform of the duration spent in each state, the number of claims, and the aggregate amount of claims that occurred in each state by the time the surplus attains a certain level are also investigated.     

Multivariate process dispersion monitoring without subgrouping

The memory-type adaptive and non-adaptive control charts are among the best control charts for detecting small-to-moderate changes in the process parameter(s). In this paper, we propose the Crosier CUSUM (CCUSUM), EWMA, adaptive CCUSUM (ACCUSUM) and adaptive EWMA (AEWMA) charts for efficiently monitoring the changes in the covariance matrix of a multivariate normal process without subgrouping. Using extensive Monte Carlo simulations, the length characteristics of these control charts are computed. It turns out that the ACCUSUM and AEWMA charts perform uniformly and substantially better than the CCUSUM and EWMA charts when detecting a range of shift sizes in the covariance matrix. Moreover, the AEWMA chart outperforms the ACCUSUM chart. A real dataset is used to explain the implementation of the proposed control charts.     

Accurate computation of single and product moments of order statistics under progressive censoring

An accurate procedure is proposed to calculate approximate moments of progressive order statistics in the context of statistical inference for lifetime models. The study analyses the performance of power series expansion to approximate the moments for location and scale distributions with high precision and smaller deviations with respect to the exact values. A comparative analysis between exact and approximate methods is shown using some tables and figures. The different approximations are applied in two situations. First, we consider the problem of computing the large sample variance–covariance matrix of maximum likelihood estimators. We also use the approximations to obtain progressively censored sampling plans for log-normal distributed data. These problems illustrate that the presented procedure is highly useful to compute the moments with precision for numerous censoring patterns and, in many cases, is the only valid method because the exact calculation may not be applicable.