模逆算法的分析、改进及测试

公钥密码实现中,模逆算法经常是算法实现的瓶颈。通常求模逆的运算方法牵涉到大量的除法和减法操作,而除法操作需要大量的运算开销。基于现有的求最大公因子的方法,分析利用扩展欧几里德求模逆的方法,以及二进制扩展欧几里德算法,提出了利用二进制扩展欧几里德算法求模逆的方法,给出了几种算法性能比较的测试环境和测试结果。测试结果表明:改进的算法比利用扩展欧几里德求模逆的方法速度更快,对硬件实现更具有普遍性。     

r-循环矩阵求逆和广义逆的Euclid算法

利用多项式的Euclid算法给出了非奇异的r-循环矩阵求逆矩阵的一个新算法,该算法同时推广到用于求奇异r-循环矩阵的群逆和Moore-Penrose逆。最后给出了应用该算法的数值例子。     

Accelerated Degradation Models for Failure Based on Geometric Brownian Motion and Gamma Processes

Based on a generalized cumulative damage approach with a stochastic process describing degradation, new accelerated life test models are presented in which both observed failures and degradation measures can be considered for parametric inference of system lifetime. Incorporating an accelerated test variable, we provide several new accelerated degradation models for failure based on the geometric Brownian motion or gamma process. It is shown that in most cases, our models for failure can be approximated closely by accelerated test versions of Birnbaum–Saunders and inverse Gaussian distributions. Estimation of model parameters and a model selection procedure are discussed, and two illustrative examples using real data for carbon-film resistors and fatigue crack size are presented.     

函子的群逆

定义了函子的群逆,给出了函子的群逆存在的充要条件。     

Bayesian deconvolution of oil well test data using Gaussian processes

We use Bayesian methods to infer an unobserved function that is convolved with a known kernel. Our method is based on the assumption that the function of interest is a Gaussian process and, assuming a particular correlation structure, the resulting convolution is also a Gaussian process. This fact is used to obtain inferences regarding the unobserved process, effectively providing a deconvolution method. We apply the methodology to the problem of estimating the parameters of an oil reservoir from well-test pressure data. Here, the unknown process describes the structure of the well. Applications to data from Mexican oil wells show very accurate results.     

An efficient correction to the density-based empirical likelihood ratio goodness-of-fit test for the inverse Gaussian distribution

The inverse Gaussian (IG) distribution is widely used to model positively skewed data. An important issue is to develop a powerful goodness-of-fit test for the IG distribution. We propose and examine novel test statistics for testing the IG goodness of fit based on the density-based empirical likelihood (EL) ratio concept. To construct the test statistics, we use a new approach that employs a method of the minimization of the discrimination information loss estimator to minimize Kullback–Leibler type information. The proposed tests are shown to be consistent against wide classes of alternatives. We show that the density-based EL ratio tests are more powerful than the corresponding classical goodness-of-fit tests. The practical efficiency of the tests is illustrated by using real data examples.     

Empirical likelihood for nonlinear regression models with nonignorable missing responses

This article develops three empirical likelihood (EL) approaches to estimate parameters in nonlinear regression models in the presence of nonignorable missing responses. These are based on the inverse probability weighted (IPW) method, the augmented IPW (AIPW) method and the imputation technique. A logistic regression model is adopted to specify the propensity score. Maximum likelihood estimation is used to estimate parameters in the propensity score by combining the idea of importance sampling and imputing estimating equations. Under some regularity conditions, we obtain the asymptotic properties of the maximum EL estimators of these unknown parameters. Simulation studies are conducted to investigate the finite sample performance of our proposed estimation procedures. Empirical results provide evidence that the AIPW procedure exhibits better performance than the other two procedures. Data from a survey conducted in 2002 are used to illustrate the proposed estimation procedure. The Canadian Journal of Statistics 48: 386–416; 2020 © 2020 Statistical Society of Canada     

Poisson-mixed Inverse Gaussian Regression Model and Its Application

In this article, we have developed a Poisson-mixed inverse Gaussian (PMIG) distribution. The mixed inverse Gaussian distribution is a mixture of the inverse Gaussian distribution and its length-biased counterpart. A PMIG regression model is developed and the maximum likelihood estimation of the parameters is studied. A dataset dealing with the number of hospital stays among the elderly population is analyzed by using the PMIG and the PIG (Poisson-inverse Gaussian) regression models and it has been shown that the PMIG model fits the data better than the PIG model.     

Shared frailty models based on reversed hazard rate for modified inverse Weibull distribution as baseline distribution

The unknown or unobservable risk factors in the survival analysis cause heterogeneity between individuals. Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyze the bivariate data on related survival times, the shared frailty models were suggested. The most common shared frailty model is a model in which frailty act multiplicatively on the hazard function. In this paper, we introduce the shared gamma frailty model and the inverse Gaussian frailty model with the reversed hazard rate. We introduce the Bayesian estimation procedure using Markov chain Monte Carlo (MCMC) technique to estimate the parameters involved in the model. We present a simulation study to compare the true values of the parameters with the estimated values. We also apply the proposed models to the Australian twin data set and a better model is suggested.     

Response and predictor folding to counter symmetric dependency in dimension reduction

In the regression setting, dimension reduction allows for complicated regression structures to be detected via visualisation in a low‐dimensional framework. However, some popular dimension reduction methodologies fail to achieve this aim when faced with a problem often referred to as symmetric dependency. In this paper we show how vastly superior results can be achieved when carrying out response and predictor transformations for methods such as least squares and sliced inverse regression. These transformations are simple to implement and utilise estimates from other dimension reduction methods that are not faced with the symmetric dependency problem. We highlight the effectiveness of our approach via simulation and an example. Furthermore, we show that ordinary least squares can effectively detect multiple dimension reduction directions. Methods robust to extreme response values are also considered.