Sequential Monitoring Variance Changes in Location Model

In this paper, a moving monitoring procedure is proposed to detect potential variance change of the location model with dependent errors. The procedure is motivated by the problem that the existing square CUSUM test is insensitive to a late variance change of the location model. The asymptotic distribution of the statistics under the null hypothesis and the consistency under the alternative hypothesis are derived. Simulations show that our monitoring procedure compared to the square CUSUM test offers better power and can more quickly detect change. Moreover, the effectiveness of our procedure is illustrated by applying it to two data sets.     

Phase I Monitoring of Polynomial Profiles

In some statistical process control applications, quality of a process or product is characterized by a relationship between two or more variables which is referred to as profile. In many practical situations, a profile can be modeled as a polynomial regression. In this article, three methods are developed for monitoring polynomial profiles in Phase I. Their performance is evaluated using power criterion. Furthermore, a method based on likelihood ratio test is developed to identify the location of shifts. Numerical simulation is used to evaluate the performance of the developed method.     

Bootstrap Procedures for Online Monitoring of Changes in Autoregressive Models

We compare the behavior of several bootstrap procedures for monitoring changes in the error distribution of autoregressive time series. The proposed procedures are designed to control the overall significance level and include classical tests based on the empirical distribution function as well as Fourier-type methods that utilize the empirical characteristic function, both functions being computed on the basis of properly estimated residuals. The Monte Carlo study incorporates different estimators and a variety of sampling situations with and without outliers.     

医疗费用预测的贝叶斯多项式混合效应模型

医疗费用预测是健康保险费率厘定的前提和基础。对于多年期的医疗费用数据,通常使用线性混合效应模型对其进行拟合,但线性混合效应模型对非线性关系的纵向数据建模具有一定的局限性。本文对线性混合效应模型进行扩展,根据医疗费用数据中变量之间的非线性关系,建立了多项式混合效应模型,并将其应用于一组医疗费用数据进行实证研究。结果表明,多项式混合效应模型对住院医疗费用的拟合效果显著优于通常使用的线性混合模型,在医疗费用管理和健康保险的费率厘定中具有重要的应用价值。     

Sequential Estimation of Expectations in the Presence of Trend2

A sequence of independent random variables {Z_n:n≥ 1} with unknown probability distributions is considered and the problem of estimating their expectations {M_n+1: n≥ 1} is examined. The estimation of M_n+1 is based on a finite set {z_k:1≤k≤n}, each z_k being an observed value of Z_k, 1 ≤k≤n, and also based on the assumption that {M_n:n≥ 1} follows an unknown trend of a specified form.     

正交多项式逼近下非线性趋势序列单位根检验

 传统单位根检验方法常常假设带有线性的确定性趋势,但如果趋势是非线性的,通常将因为检验功效大幅下降而导致检验失败。本文研究用正交多项式逼近非线性趋势,然后对残差进行单位根检验的方法。研究了用正交多项式进行趋势逼近的性质,推导了这种方法进行单位根检验时统计量的极限分布,提出了正交多项式最高阶数的确定方法,仿真研究了残差相关与不相关时的检验功效。结果表明,检验方法是有效的。     

动态面板阈模型的一种序贯两步估计

动态面板阈模型可以刻画经济变量动态调整过程的非对称性,在实证分析中有广泛的运用,但阈值参数的引入同时增加了参数估计的困难,理论上尚有许多问题没有解决。针对此类模型,本文提出了一种简单而实用的序贯两步估计方法,首先利用格点搜索获得阈值参数的一致估计,基于该参数对数据结构进行合理划分并引入不同类型的矩条件,然后利用广义矩方法获得自回归参数的估计。理论研究与模拟结果表明,序贯两步估计具有良好的大样本性质和有限样本表现;与现有文献的方法相比,序贯两步估计能够有效避免不同类型参数估计偏差的相互影响,减小估计量的偏差与均方根误差。     

因子模型的一种结构突变检验及其统计性质研究

为了内生地识别动态因子模型因子载荷矩阵的结构突变（包括因子个数的变化）,本文利用主成分估计得伪因子序列构造累积平方和统计量检验因子载荷矩阵的结构突变性,进一步利用迭代累积平方和算法对多个结构突变点的位置进行探测。研究发现,本文提出的检验统计量对于因子个数误设具有稳健性;并且该检验具有良好的有限样本性质和渐近性;另外,实证分析发现,中国沪市A股市场制造业上市公司的对数收益率序列存在结构突变的共同因子。     

Monitoring Structural Changes in Generalized Linear Models

In this article, we introduce two monitoring schemes to (sequentially) detect structural changes in generalized linear models and develop asymptotic theories for them. The first method is based on cumulative sums (CUSUM) of weighted residuals, in which the unknown in-control parameters have been replaced by its maximum likelihood (ML) estimate from the training sample, whereas the second scheme makes use of moving sums (MOSUM) of weighted residuals. We characterize the limit distribution of the test statistic and show that these tests are consistent. Moreover, we also obtain and tabulate the asymptotic critical values of the tests. Finally, we study the speed of detection under different conditions. The methods are illustrated and compared in several simulations.     

Sequential analysis methodology for a Poisson GLMM with applications to multicenter randomized clinical trials

Sequential analyses in clinical trials have ethical and economic advantages over fixed sample size methods. The sequential probability ratio test (SPRT) is a hypothesis testing procedure which evaluates data as it is collected. The original SPRT was developed by Wald for one-parameter families of distributions and later extended by Bartlett to handle the case of nuisance parameters. However, Bartlett's SPRT requires independent and identically distributed observations. In this paper we show that Bartlett's SPRT can be applied to generalized linear model (GLM) contexts. Then we propose an SPRT analysis methodology for a Poisson generalized linear mixed model (GLMM) that is suitable for our application to the design of a multicenter randomized clinical trial that compares two preventive treatments for surgical site infections. We validate the methodology with a simulation study that includes a comparison to Neyman–Pearson and Bayesian fixed sample size test designs and the Wald SPRT.     

Polynomial regression with errors in the variables

A polynomial functional relationship with errors in both variables can be consistently estimated by constructing an ordinary least squares estimator for the regression coefficients, assuming hypothetically the latent true regressor variable to be known, and then adjusting for the errors. If normality of the error variables can be assumed, the estimator can be simplified considerably. Only the variance of the errors in the regressor variable and its covariance with the errors of the response variable need to be known. If the variance of the errors in the dependent variable is also known, another estimator can be constructed.     

Sequential Fixed-Width Confidence Interval for a Function of the Parameters

Let X₁…, X_m and Y₁…, Y_n be two independent sequences of i.i.d. random variables with distribution functions F_x(.|θ) and F_y(. | φ) respectively. Let g(θ, φ) be a real-valued function of the unknown parameters θ and φ. The purpose of this paper is to suggest a sequential procedure which gives a fixed-width confidence interval for g(θ, φ) so that the coverage probability is approximately α (preas-signed). Certain asymptotic optimality properties of the sequential procedure are established. A Monte Carlo study is presented.     

Algebraic Methods for Polynomial Statistical Models

We describe applications of computational algebra to statistical problems of parameter identifiability, sufficiency, and estimation. The methods work for a family of statistical models that includes Poisson and binomial examples in network tomography.     

Sequential Hypothesis Tests for Identifying the Minimum Dose with a Threshold Effect

We propose a procedure to identify a lowest dose having greater effect than a threshold dose under the assumption of monotonicity of dose mean response in dose response test. So, we use statistics based on contrasts among sample means and apply a group sequential procedure to our procedure to identify effectively the dose. If we can identify the dose at an early step in the sequential test, since we can terminate the procedure with a few observations, the procedure is useful from an economical point of view. In a simulation studies, we compare the superiority among these procedures based on three contrasts.     

Structural Change Monitoring for Random Coefficient Autoregressive Time Series

A monitoring scheme is proposed to sequentially detect a structural change in random coefficient autoregressive time series of order p (RCA(p)) after a training period of size T. It extends structural change monitoring to RCA(p) time series. The asymptotic properties of our monitoring statistic are established under both the null of no change in parameters and the alternative of a change in coefficient. The finite sample properties are investigated by a simulation study.     

Monitoring distributional changes of squared residuals in GARCH models

Change point monitoring for distributional changes in time-series models is an important issue. In this article, we propose two monitoring procedures to detect distributional changes of squared residuals in GARCH models. The asymptotic properties of our monitoring statistics are derived under both the null of no change in distribution and the alternative of a change in distribution. The finite sample properties are investigated by a simulation.     

Sequential estimation for nonhomogeneous Ornstein-Uhlenbeck processes

In this paper, we propose a stochastic process, which is a class of nonhomogeneous diffusion process from the perspective of the corresponding nonlinear stochastic differential equation. The parameter included in the drift term are estimated by sequential maximum likelihood methodology on the basis of continuous sampling of the process. The sequential estimators are proved to be closed, unbiased, strongly consistent, normally distributed, and optimal in the mean square sense.     

Sequential testing of gradual changes in the drift of a stochastic process

In this paper, some sequential monitoring procedures are constructed and analyzed for detecting a “gradual” change in the drift parameter of a general stochastic process satisfying a certain (weak) invariance principle. It is shown that the tests can be constructed such that the “false alarm rate” attains a prescribed level (say) α and that the tests have “asymptotic power 1”. A more precise analysis of the procedures under the alternative proves that the stopping times, suitably normalized, have a standard normal limiting distribution. A few results from a small simulation study are also presented in order to give an idea of the finite sample behaviour of the suggested procedures.