Studies of Possibilities and Limits of Statistical Prediction

这个项目的目的是研究统计预测在实际问题中的可能性和局限性。在统计预测中有两种情况。一种是插值法，另一种是外推法。前者的典型概念是内插法，它是一种回归理论，即非线性、半参数和非参数回归。此外，还介绍了几种提取合理有用信息的建模技术。在这些方法上，我们得到了很好的结果，如“基于分层个体内设计矩阵的增长曲线模型”、“基于遥感数据的人口与土地覆盖格局关系的梯形分析”、“一种用于分层逆回归模型的投影寻踪算法”、“删失数据的Kullback-Leibler信息一致性估计器”等。另一方面，后一种概念，外推，对于天气、商业或股票价格预测来说是熟悉的。典型的方法是时间序列分析。尽管仍然存在许多困难，但在本项目中，我们取得了许多有益的成果，特别是在状态空间建模、误差分布松弛和几种用于降噪的滤波理论方面。例如“非线性非高斯预测和过滤公式的计算实现”、“一种使用概率神经网络的组合预测方法”、“预测状态空间模型中的结构变化”、“收缩法扩展MDL准则”等。

The aim of this project was to study out the possibilities and limits of statistical prediction in the practical problems. There are two situations in the statistical prediction. One is an interpolation and the other is an extrapolation. The typical concept of the former, interpolation, is a theory of regression, namely, the nonlinear, semi-parametric and nonparametric regression. Moreover, the several modeling techniques by which the reasonable and useful information are extracted have been included. On these methods, we get excellent results, for instance, "growth curve model with hierarchcal within-individual design matrices", "echelon analysis of the relationship between population and land cover patterns based on remote sensing data", "an algorithm with projection pursuit for sliced inverse regression model", "Kullback-Leibler information consistent estimator for censored data" and so on. On the other hand, the latter concept, extrapolation, is familiar to weather or a business or a stock price forecasting. The typical method is a time series analysis. Although, there still remain many dfficulties, in this project, many useful results are proposed, especially on the state space modeling a relaxation of error distribution and several filtering theory for the noise reduction. For example, "computational implementations of nonlinear non-Gaussian prediction and filtering formulas", "a combining forecast method using a probabilistic neural network", "forecasting structural changes in a state-space model", "extension of the MDL criterion by shrinkage method" and so on.