The multivariate linear errors-in-variables model when the regressors are missing at random in the sense of Rubin （1976） is considered in this paper. A constrained empirical likelihood confidence region for a parame...The multivariate linear errors-in-variables model when the regressors are missing at random in the sense of Rubin （1976） is considered in this paper. A constrained empirical likelihood confidence region for a parameter β0 in this model is proposed, which is constructed by combining the score function corresponding to the weighted squared orthogonal distance based on inverse probability with a constrained region of β0. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. Simulations show that the coverage rate of the proposed confidence region is closer to the nominal level and the length of confidence interval is narrower than those of the normal approximation of inverse probability weighted adjusted least square estimator in most cases. A real example is studied and the result supports the theory and simulation＇s conclusion.展开更多
目的：探讨配对二项资料两组率差置信区间的估计方法,并从中进行优选推荐。方法：按照方差估计反推（method of variance of estimates recovery,MOVER）原理,将两配对组率的关联Ф系数与单组率的置信区间进行组合,构建两组率差的置信...目的：探讨配对二项资料两组率差置信区间的估计方法,并从中进行优选推荐。方法：按照方差估计反推（method of variance of estimates recovery,MOVER）原理,将两配对组率的关联Ф系数与单组率的置信区间进行组合,构建两组率差的置信区间估计方法。其中,单组率置信区间估计分别采用Wilson计分法、Agresti-Coull法（AC法）、Jeffreys法和Clopper-Pearson精确法（CP法）。借助Monte Carlo模拟实验比较不同方法的统计学性能,在不同参数设定下进行I类错误率和把握度的模拟实验：（1）设定两组率关联Ф系数为0、0.2、0.4、0.6,样本量为20、60、100,分别模拟不同率水平下各方法的I类错误率,判定其模拟I类错误率是否接近事先定义的检验水平。（2）设定关联Ф系数为0.3,两组率差为10%,分别模拟不同率水平下各方法不同样本含量下的把握度（power）变化趋势。结果：在基于单组置信区间组合估计的几种MOVER方法中,MOVER Wilson计分法、MOVER Jeffreys法的I类错误率更接近事先设定的水平,尤其是在靠近0和100%两端时,MOVER Jeffreys法的I类错误率更优;除MOVER CP法,其他3种方法的把握度接近。结论：对于配对二项资料两组率差的置信区间估计,一般情况下（两组率在20%~80%范围内）,可选择MOVER Wilson计分法或MOVER Jeffreys法;当两组率靠近两端时,推荐使用MOVER Jeffreys法。展开更多
Nitrogen rate trials are often performed to determine the economically optimum N application rate. For this purpose, the yield is modeled as a function of the N application. The regression analysis provides an estimat...Nitrogen rate trials are often performed to determine the economically optimum N application rate. For this purpose, the yield is modeled as a function of the N application. The regression analysis provides an estimate of the modeled function and thus also an estimate of the economic optimum, Nopt. Obtaining the accuracy of such estimates by confidence intervals for Nopt is subject to the model assumptions. The dependence of these assumptions is a further source of inaccuracy. The Nopt estimate also strongly depends on the N level design, i.e., the area on which the model is fitted. A small area around the supposed Nopt diminishes the dependence of the model assumptions, but prolongs the confidence interval. The investigations of the impact of the mentioned sources on the inaccuracy of the Nopt estimate rely on N rate trials on the experimental field Sieblerfeld (Bavaria). The models applied are the quadratic and the linear-plus-plateau yield regression model.展开更多
基金supported by the Natural Science Foundation of China under Grant Nos.10771017 and 11071022Key Project of MOE,PRC under Grant No.309007
文摘The multivariate linear errors-in-variables model when the regressors are missing at random in the sense of Rubin （1976） is considered in this paper. A constrained empirical likelihood confidence region for a parameter β0 in this model is proposed, which is constructed by combining the score function corresponding to the weighted squared orthogonal distance based on inverse probability with a constrained region of β0. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. Simulations show that the coverage rate of the proposed confidence region is closer to the nominal level and the length of confidence interval is narrower than those of the normal approximation of inverse probability weighted adjusted least square estimator in most cases. A real example is studied and the result supports the theory and simulation＇s conclusion.
文摘Nitrogen rate trials are often performed to determine the economically optimum N application rate. For this purpose, the yield is modeled as a function of the N application. The regression analysis provides an estimate of the modeled function and thus also an estimate of the economic optimum, Nopt. Obtaining the accuracy of such estimates by confidence intervals for Nopt is subject to the model assumptions. The dependence of these assumptions is a further source of inaccuracy. The Nopt estimate also strongly depends on the N level design, i.e., the area on which the model is fitted. A small area around the supposed Nopt diminishes the dependence of the model assumptions, but prolongs the confidence interval. The investigations of the impact of the mentioned sources on the inaccuracy of the Nopt estimate rely on N rate trials on the experimental field Sieblerfeld (Bavaria). The models applied are the quadratic and the linear-plus-plateau yield regression model.
