Estimating Optimal Weights for Instrumental Variable Methods

✍ Scribed by Petre Stoica; Magnus Jansson

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 187 KB
• Volume: 11
• Category: Article
• ISSN: 1051-2004
• DOI: 10.1006/dspr.2001.0385

✦ Synopsis

The accuracy of the instrumental variable approach to parameter estimation (also called correlation analysis) can be significantly improved by optimally weighting the estimating equations. However, the optimal weight in general depends on unknown quantities and hence must be itself estimated before its use becomes possible. The optimal weighting matrix encountered in a typical parameter estimation problem is equal to the DC power of a certain vector sequence and usually it has to be consistently estimated in a nonparametric manner. Consistent nonparametric estimation of power (at any frequency, zero or not) is not an easy task and typically it cannot be achieved by using "natural" estimators (such as the periodogram). Surprisingly, it turns out that in the case considered in this paper there is a natural consistent estimator of the DC power matrix that represents the desired optimal weight. This result will promote the use of optimally weighted parameter estimation methods of instrumental variable or related types; it may also have some interesting consequences for nonparametric spectral analysis which though are not explored herein.