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首页> 外文期刊>Open Journal of Statistics >Bias and Mean Square Error of Reliability Estimators under the One and Two Random Effects Models: The Effect of Non-Normality
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Bias and Mean Square Error of Reliability Estimators under the One and Two Random Effects Models: The Effect of Non-Normality

机译：一和两个随机效应模型下可靠性估计的偏差和均方误差：非正态性的影响

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摘要

The coefficient of reliability is often estimated from a sample that includes few subjects. It is therefore expected that the precision of this estimate would be low. Measures of precision such as bias and variance depend heavily on the assumption of normality, which may not be tenable in practice. Expressions for the bias and variance of the reliability coefficient in the one and two way random effects models using the multivariate Taylor’s expansion have been obtained under the assumption of normality of the score (Atenafu et al. [1]). In the present paper we derive analytic expressions for the bias and variance, hence the mean square error when the measured responses are not normal under the one-way data layout. Similar expressions are derived in the case of the two-way data layout. We assess the effect of departure from normality on the sample size requirements and on the power of Wald’s test on specified hypotheses. We analyze two data sets, and draw comparisons with results obtained via the Bootstrap methods. It was found that the estimated bias and variance based on the bootstrap method are quite close to those obtained by the first order approximation using the Taylor’s expansion. This is an indication that for the given data sets the approximations are quite adequate.
机译：可靠性系数通常是从一个样本很少的样本中估算出来的。因此，预计该估计的精度将较低。诸如偏差和方差之类的精度度量在很大程度上取决于正态性的假设，这在实践中可能难以成立。在分数为正态的假设下，已经获得了使用多元泰勒展开式的单向和双向随机效应模型中可靠性系数的偏差和方差的表达式（Atenafu等人[1]）。在本文中，我们导出了偏差和方差的解析表达式，因此，在单向数据布局下，当测量的响应不正常时，均方误差。在双向数据布局的情况下，得出类似的表达式。我们评估了偏离正态性对样本量要求以及Wald检验特定假设的能力的影响。我们分析两个数据集，并与通过Bootstrap方法获得的结果进行比较。结果发现，基于自举法的估计偏差和方差与使用泰勒展开式进行一阶近似得到的偏差和方差非常接近。这表明对于给定的数据集，近似值已足够。

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