Research On Sample Effect-Based Regression Method

Regression analysis is one of the most common prediction methods,and it has gained many successful applied results in many fields.And the reliability of the regression model rigorously depends on the reliability of sample data.But it is worth noting that it is unable to get the perfect samples in real prediction process.Meanwhile,it is inevitable to subjectively choose or process the sample data.Once there exists some defects,even a small one,between the samples and processing methods,it will badly affect the results of regression analysis results.That is the reliability of samples-based regression model will be lose validity.So far,there are much research on the modification and improvement of regression model.But most assume the samples are completely reliable and obey to the strict assumptions of the regression model.Obviously,these research neglect the impact for result of the regression analysis causing by different reliable sample data.However,samples with different reliabilities is a common form in real decision process.Therefore,research on regression prediction model,considering the imperfection of samples,has important theoretical significance and applied value under the case of the sample data with different reliabilities.In the paper,considering the losing sight of the samples' reliability of current regression model and the severe application prerequisite of the regression test models,we mainly do the following work.For establishing an efficient regression model: 1)We first add an auxiliary index describing the satisfaction degree of samples in current descriptive system.Then we propose a basic effect function that reflects the decision makers' sample decision consciousness and establish a regression model based on synthesizing effect(denoted as BSE-RM).Further we note that the descriptive system of classical regression result descriptive system lacks of index evaluating functions' reliability.So we construct a regression credible evaluating index called synthesizing effect-based regression credibility.We apply it into a concrete example,and analyze its effectiveness.2)For the hypothesis condition of the regression model is not related to the nature of the least square method which is used to fit regression model.But it is closely related to the test of regression model.In this case,the regression models which do not satisfy the hypothesis,cannot be verified its reliability by the current test models.For this shortcoming,we establish a volatility statistic based on the random sampling theory and its characteristics are analyzed.Then we establish a regression test model based on the volatility statistics(denoted by VR-TM).Theoretical analysis and practice show that VR-TM can verify the regression models,whether or not meeting the assumptions,with a quantitative description.BSE-RM and VR-TM both enrich the existing regression models theory and can be widely applied to the complex system optimization,portfolio analysis,capital market risk measurement,financial risk management etc.