Further Study On Pitman Criterion And The Incomplete Data Mining

The outlier mining is an important topic of data mining, the incomplete data mining has practice meanings. The incomplete data has been involved with many field issues, such as expert system, artificial intelligence, stocks in stock-market and the forecast of the securities. There are three main methods to deal with these data: Gibbs sampling, Variation method and EM algorithm. Gibbs sampling is a MCMC algorithm which is the most simple and been extensive applied. Variation method is an approximation algorithm based upon learning to the incomplete data in graph models. EM algorithm is an improved iterative algorithm based on the MLE in point estimation.The estimator of regression parameters is very important in estimation theory and practical applications of linear statistical models. Among of the estimators, the least squares estimator stands out because of its excellent characters. But when the design matrix X has the problem of multi-collinearity, the ordinary least squares estimation shows apparently disadvantage, the linear biased estimation is the most direct method in ameliorating the ordinary least squares estimation. Then, Statisticians proposed many kinds of linear biased estimation, like Ridge Estimation, Principal Components Estimation, Liu Estimation and so on, and the United Biased Estimation includes the biased estimation which we common used. The goal of the biased estimator is reducing the variance by increasing skewness. The biased estimator departure its actual value after all, so some statistician proposed the almost unbiased estimator.The MSE criterion and Pitman criterion are two common criterions for comparing the estimator's superiority. Pitman criterion proposed by E.Pitman in 1937 is a criterion to appraise the superiority of regression parameter estimation. In recent years, the researches on Pitman make it become hot topic in the theoretical research of statistical parameter estimation.The main contents of this dissertation are as follows:â‘ We summarize the results on incomplete data.â‘¡For preparing discuss the Pitman superiority of the incomplete data estimator, we research the Pitman superiority of the Restricted Ridge Estimator, the Almost Unbiased Unified Biased Estimator and the Restricted Almost Unbiased Unified Biased Estimator. Respectively, we give out the ellipsoidal areas in which the Restricted Ridge estimator is superior to the least squares estimator, the Almost Unbiased Unified Biased Estimator is superior to the least squares estimator and the Restricted Almost Unbiased Unified Biased Estimator is superior to the restricted least squares estimator.â‘¢To solve the forecast of financial time series data, the time series model is applied to simulation. Then, we modify the model by the methods of handling missing data to increasing the accuracy of forecast. The practical examples are also given out.