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Shrinkage Regression:

ridge, BLUP, Bayes, spline & Stein

Left-click on a link below to view or download the PDF file for one of my papers or a Chapter from my E-book-in-progress.

Unfortunately, some of the math / symbol fonts used in these rather old PDF files cannot be embedded into them. However, once downloaded to your computer, fonts installed on you system will be substituted for these missing fonts. Try it, and See!

Chapter 00: Preface and Table-of-Contents [382K]

Chapter 01: Introduction [388K]

Chapter 02: Basic Linear Model Concepts[498K]

Chapter 03: Shrinkage Regression Fundamentals[281K]

Chapter 04: The Risk of Shrinkage[271K]

Chapter 05: Normal-Theory Maximum Likelihood: BLUEs and BLUPs [272K]

Chapter 06: MSE Risk Estimation and Simulation [308K]

Chapter 07: Random Coefficient Formulations [0k]

Chapter 08: Bayesian Formulations [225K]

Chapter 09: Errors-In-Variables and Resampling Methods [208K]

Chapter 10: Historical Topics, Heuristic Arguments & Common Misconceptions [133K]

Chapter 11: TRACE Displays: The Psychology of Perception [0k]

Maximum Likelihood Shrinkage in Regression


The above link displays my 26 page manuscript, MLSIR.PDF.  Here, I derive a closed-form expression for the shrinkage estimator within the 2-parameter Goldstein-Smith generalized ridge family that is most likely (under normal-distribution-theory) to attain minimum MSE risk. Some simulated risk profiles for uniform shrinkage are also displayed and discussed.

Influential Observations in Ridge Regression


The above link is for my 31 page manuscript, INFLUIRR.PDF  This is an introduction to linked "Visual Re-Regression" and "Leverage-Outlier" plots, including a Cook-like "overall influence" hyperbola.