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As Good as GOLD: Gram-Schmidt Orthogonalization by Another Name
1Department of Pediatrics, University of Oklahoma Health Sciences Center, Oklahoma City, OK, 73104 , USA. mhunter1@ouhsc.edu.
Psychometrika
|September 22, 2016
Summary
Generalized orthogonal linear derivative (GOLD) estimates offer advantages over generalized local linear approximation (GLLA) for noisy data interpolation. However, GLLA is superior for derivative estimation with smooth or non-noisy data.
Area of Science:
- Statistics
- Numerical Analysis
- Data Science
Background:
- Correlated estimation errors pose challenges in generalized local linear approximation (GLLA).
- Generalized orthogonal linear derivative (GOLD) estimates were developed to address these errors.
Purpose of the Study:
- To elucidate the relationship between GOLD and GLLA estimates.
- To compare the performance of GOLD and GLLA under various data conditions.
Main Methods:
- Analytical derivation of the relationship between GOLD and GLLA using Gram-Schmidt orthogonalization.
- Simulation studies to evaluate performance in approximation, smoothing, and interpolation of noisy and non-noisy data.
Main Results:
- GLLA outperforms GOLD in approximating/smoothing noisy data and in derivative estimation for non-noisy data.
- GOLD outperforms GLLA in interpolating noisy data.
- GOLD may yield biased estimates but can offer improved model estimation due to its orthogonal error structure.
Conclusions:
- GLLA is preferred for data smoothing/approximation and derivative estimation with non-noisy data.
- GOLD is preferred for interpolation of noisy data.
- GOLD is not recommended solely for derivative estimation; further research is needed for unbiased orthogonal polynomial derivative estimators.
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