Computer intensive methods in adaptive contexts

快速计算的出现使统计学家们能够开发出新的统计方法，这在几年前是不可想象的，因为在实践中是不可能使用的。例如，重采样方法可以用来计算复杂估计器的方差估计、近似可信区间，甚至在估计器只定义到必须确定的调整参数的情况下选择调整参数。本研究计划的主要目的是提高对这些方法的理论和实践理解，以开发健全的新统计程序。一个重要的项目如下。当研究某一现象时，收集数据是为了了解感兴趣变量的分布。通常，存在来自相关研究或前几年的其他数据。*由于不同的条件或随时间的变化，这些额外的数据通常来自相似但不同的分布。如果分布非常相似，而不是忽略这些其他数据，尝试将它们与研究中的数据相结合可能是值得的。但最大加权似然(MWL)方法恰恰尝试了这一点。通过对观测数据进行不同的加权，无论它们来自研究中的现象还是来自竞争样本之一，MWL估计器可以用一些偏差来换取更高的精度。尽管困难在于选择适当的权重。但王和Zidek(2005)建议使用交叉验证，但他们指出，当竞争样本都来自同一分布时，他们的方法不起作用。考虑到Altman和L(1997年)在调整参数选择和估计器的收敛速度方面所做的工作，这并不令人惊讶。为了缓解这个问题，将使用Bootstrap来选择权重。即使分布相同，这种方法也能起作用。这将为这个实际问题提供一个有趣的解决方案，并将为MWL方法开辟新的基础。

The advent of fast computing has allowed statisticians to develop new statistical methods which would have been unthinkable just a few years ago because it would have been impossible to use them in practice.  One example is the class of resampling methods which can be used to compute estimates of the variance of a complicated estimator, approximate confidence intervals or even choose tuning parameters in cases where an estimator is only defined up to a tuning parameter which must be determined.  The main objective of this research program is to improve the theoretical and practical understanding of these methods so as to develop sound new statistical procedures. One important project is as follows.  When studying a certain phenomenon, data are collected to learn about the distribution of the variable of interest.  Often, other data from a related study or from previous years exist.  Because of different conditions or changes over time, these additional data often come from a similar albeit different distribution.  If the distributions are quite similar, rather than ignoring these other data, it may be worthwhile to try to combine them with the data under study.  The method of maximum weighted likelihood (MWL) attempts exactly that.  By weighting differently the observations whether they come from the phenomenon under study or from one of the competing samples, the MWL estimator can trade some bias for much improved precision.  The difficulty is in choosing the appropriate weights.  Wang and Zidek (2005) have suggested using cross-validation, but noted that their method does not work when the competing samples all come from the same distribution.  This is not surprising considering the work of Altman and Léger (1997) on tuning parameter selection and the rate of convergence of estimators.  To alleviate the problem, the bootstrap will be used to choose the weights.  This method will work even when the distributions are identical.  This will provide an interesting solution to this practical problem, and will open new grounds for the method of MWL.