Non parametric regression analysis for longitudinal data with time-depending autoregressive error process

This paper considers a non parametric longitudinal model, where the within-subject correlation structure is represented by a time-depending autoregressive error process. An initial estimator without taking into account the within-subject correlation is obtained to fit the time-depending autoregressive error process. With the initial estimator, we construct a two-stage local linear estimator of the mean function. According to the asymptotic normality of the initial and two-stage estimators, it is discovered that the two-stage estimator has a smaller asymptotic variance. The simulation results show us that the two-stage estimation has some good properties. The analysis of a data set demonstrates its application.     

Test for the existence of finite moments via bootstrap

This paper develops a bootstrap hypothesis test for the existence of finite moments of a random variable, which is nonparametric and applicable to both independent and dependent data. The test is based on a property in bootstrap asymptotic theory, in which the m out of n bootstrap sample mean is asymptotically normal when the variance of the observations is finite. Consistency of the test is established. Monte Carlo simulations are conducted to illustrate the finite sample performance and compare it with alternative methods available in the literature. Applications to financial data are performed for illustration.     

Conditional estimation using prior information in 2‐stage group sequential designs assuming asymptotic normality when the trial terminated early

Two‐stage designs are widely used to determine whether a clinical trial should be terminated early. In such trials, a maximum likelihood estimate is often adopted to describe the difference in efficacy between the experimental and reference treatments; however, this method is known to display conditional bias. To reduce such bias, a conditional mean‐adjusted estimator (CMAE) has been proposed, although the remaining bias may be nonnegligible when a trial is stopped for efficacy at the interim analysis. We propose a new estimator for adjusting the conditional bias of the treatment effect by extending the idea of the CMAE. This estimator is calculated by weighting the maximum likelihood estimate obtained at the interim analysis and the effect size prespecified when calculating the sample size. We evaluate the performance of the proposed estimator through analytical and simulation studies in various settings in which a trial is stopped for efficacy or futility at the interim analysis. We find that the conditional bias of the proposed estimator is smaller than that of the CMAE when the information time at the interim analysis is small. In addition, the mean‐squared error of the proposed estimator is also smaller than that of the CMAE. In conclusion, we recommend the use of the proposed estimator for trials that are terminated early for efficacy or futility.     

抽样调查中基于平衡样本的稳健预测

抽样调查中基于模型推断方法获得的估计量性质是依赖于模型的。在恰当的模型下比率估计和扩张估计是最优线性无偏估计。当模型设定错误时,比率估计和扩张估计是有偏估计,但如果样本是平衡的,可以消除偏倚,从而实现了复杂问题简单处理的思想。     

Improved CUSUM charts for monitoring process mean

In this paper, we propose new cumulative sum (CUSUM) and Shewhart-CUSUM (SCUSUM) control charts for monitoring the process mean using ranked-set sampling (RSS) and ordered RSS (ORSS) schemes. The proposed CUSUM charts include the Crosier's CUSUM (CCUSUM) and Shewhart-CCUSUM (SCCUSUM) charts using RSS, and the CUSUM, CCUSUM, SCUSUM and SCCUSUM charts using ORSS. Moreover, fast initial response features are also attached with these CUSUM charts to improve their sensitivities for an initial out-of-control situation. Monte Carlo simulations are used to compute the run length characteristics of the proposed CUSUM charts. Upon comparing the run length performances of the CUSUM charts, it turns out that the proposed CUSUM charts are more sensitive than their existing counterparts. A real dataset is used to explain the implementation of the proposed CUSUM charts.     

Topp–Leone normal distribution with application to increasing failure rate data

In this article, we proposed a new three-parameter probability distribution, called Topp–Leone normal, for modelling increasing failure rate data. The distribution is obtained by using Topp–Leone-X family of distributions with normal as a baseline model. The basic properties including moments, quantile function, stochastic ordering and order statistics are derived here. The estimation of unknown parameters is approached by the method of maximum likelihood, least squares, weighted least squares and maximum product spacings. An extensive simulation study is carried out to compare the long-run performance of the estimators. Applicability of the distribution is illustrated by means of three real data analyses over existing distributions.     

Two-stage Liu estimator in a simultaneous equations model

Two-stage least squares estimation in a simultaneous equations model has several desirable properties under the problem of multicollinearity. So, various kinds of improved estimation techniques can be developed to deal with the problem of multicollinearity. One of them is ridge regression estimation that can be applied at both stages and defined in Vinod and Ullah [Recent advances in regression methods. New York: Marcel Dekker; 1981]. We propose three different kinds of Liu estimators that are named by their implementation stages. Mean square errors are derived to compare the performances of the mentioned estimators and two different choices of the biasing parameter are offered. Moreover, a numerical example is given with a data analysis based on the Klein Model I and a Monte Carlo experiment is conducted.     

股票技术分析模型的自动辨识研究

基于非参数的kernel回归引入了一种股票技术模型辨识算法.通过对几种技术分析模型进行定量化定义,实现了文中引入的模型辨识算法,从而能够通过历史价格进行自动化模型辨认.利用沪市大盘指数的历史价格进行了实证研究,得出了对这种算法具有一定支持性的结论.     

Effect of adding regressors on the equality of the BLUEs under two linear models

In this paper we consider the estimation of regression coefficients in two partitioned linear models, shortly denoted as , and , which differ only in their covariance matrices. We call and full models, and correspondingly, and small models. We give a necessary and sufficient condition for the equality between the best linear unbiased estimators (BLUEs) of X₁β₁ under and . In particular, we consider the equality of the BLUEs under the full models assuming that they are equal under the small models.     

Asymptotic normality of kernel type regression estimators for random fields

The asymptotic normality of the Nadaraya–Watson regression estimator is studied for α-mixing$\alpha \text{-}\mathrm{mixing}$ random fields. The infill-increasing setting is considered, that is when the locations of observations become dense in an increasing sequence of domains. This setting fills the gap between continuous and discrete models. In the infill-increasing case the asymptotic normality of the Nadaraya–Watson estimator holds, but with an unusual asymptotic covariance structure. It turns out that this covariance structure is a combination of the covariance structures that we observe in the discrete and in the continuous case.