Dissertation > Excellent graduate degree dissertation topics show

Further Exploration on the Linear Regression Model Parameters Biased Estimate

Author: LiBing
Tutor: ZhuNing
School: Guilin University of Electronic Science and Technology
Course: Applied Mathematics
Keywords: Biased Estimator The Combining Generalized Ridge and Principal Components Estimate Pitman Measure Admissible Estimate Cook Distance Principal Component Diagnose Multicollinearity
CLC: O212.1
Type: Master's thesis
Year: 2008
Downloads: 208
Quote: 2
Read: Download Dissertation

Abstract


Linear Statistical models mainly include Linear Regression model, variance and analysis model,Covariance and analysis model etc..This paper mainly discuss GeneralizedLinear regression model,accordingly,In term of the unknown parameterβ,it is necessary to study the estimation ofβand its linear function.when the design matrix X ill-conditions,we find the least squares estimator can be not a good estimate, In order to study parameterβestimation which base on the least squares and biased estimator especially the combining generalized Ridge and principal Components estimate. This paper discusses its superiority of the optimal and classical predictors based on the shrunken dimension biased estimate. In order to judge Multicellularity-Influential cases we raised two methods and examples of verification.This paper makes some research on the above mentioned question,the main result include the following.First, when the design matrix X ill-conditions We research some properties of The Combining Generalized Ridge and Principal Components Estimate ,Defined a relative efficiency .It was proved The Combining Generalized Ridge and Principal Components Estimate is better than least squares estimate under the MSE and GMSE principal, also better than Ridge estimate,Combining Ridge and Principal Components Estimate, Principal Components Estimate under the Pitman measure. It also proved the Combining Generalized Ridge and Principal Components Estimate is more efficiency than LS,Principal Components Estimate,The Combining Ridge and Principal ComponentsEstimate We proved the Combining Generalized Ridge and Principal Components Estimate was an admissible estimate.Secondly, Basing on the The Combining Generalized Ridge and Principal Components Estimation.We Consider the generalized linear regression model Y = Xβ+ε,ε-N(0,σ~2∑), A necessary and sufficient condition of comparison of its superiority of the optimal and classical predictors. An new method is proposed for the further research of superiority two predictors based on the shrunken dimension biased estimate.Thirdly , Basing on the Principal Components Estimate ,we discuss the Cook distance’s perturbation analysis.We prove the equivalency of means-shift models and case-deletion models firstly.Deletion is employed and the exact deletion formula for Cook distance is gained,which not only simplifies the computation but also proposes a diagnostic for identifying influential observations.At last,we propose a principal component diagnose criterion for the multicollinearity- influential cases,whenη_i > 1.2,the cases are high multicollinearity-influential,so we have two methods for judging the multicollinearity-influential.

Related Dissertations

  1. Some Researches on the Ridge Estimator,O212.1
  2. The Application for the Partial Least-Squares Regression (PLS) in the Short-term Climate Forecast,P456.8
  3. Study on the Modeling Methods of the In-output Statistical Models in Agriculture,F224
  4. Study on Diagnostic Methods of Multicollinearity in Logistic Regression,R195
  5. Ridge estimate linear model with constraints impact analysis,O212.1
  6. CIR model of statistical diagnostics,F830
  7. Statistical Diagnosis diffusion process,O211.67
  8. Influence Analysis of Regression Parameter in Linear Model,O212.1
  9. Randomly censored linear model statistical diagnostics,O212.1
  10. Reexamination of Service Quality Scale,F719
  11. Study on Estimation Method and Application of Regression Model in Forestry,F307.2
  12. The Decision and Simulation of the Indoor Air Temperature in Sunlight Greenhouse,TP311.11
  13. A Case-control Study on the Motor Vehicle Driver’s Risk Factors for the Road Traffic Injury in 5 Zhejiang Districts,R181.3
  14. Design and Study of the Model about the Number of College Enrollment,G647
  15. The Impact Analysis and Local Influence Analysis of LIU Estimate in Linear Model,O212.1
  16. Local Influence in Semi-parametric Nonlinear Reproductive Dispersion Models,O212.1
  17. Ridge-type Estimation of the Direction in Generalized Single-index Models,O211.67
  18. Research on Application of Economic System Based on PLS Regression Nonlinear Methods,F124
  19. Statistical Diagnostics for the Log-normal Distribution Regression Model,O212.1
  20. Some Studies about Partial Least Squares Regression,O212.1
  21. Research on a Number of Issues Related to Partial Least Squares Regression Analysis,O212.1

CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Mathematical Statistics > General mathematical statistics
© 2012 www.DissertationTopic.Net  Mobile