Banner for LabNotes
From Lab Notes
Contact Information
Forest Products Laboratory
One Gifford Pinchot Drive
Madison, WI 53726-2398
Phone: (608) 231-9200
Fax: (608) 231-9592
Email

 

You are here: FPL Home  / Information Products & Services  / Publications

Requested Product

Title: Rate of convergence of k-step Newton estimators to efficient likelihood estimators

Source: Statistics & probability letters. Vol. 77 (2007): Pages 1371-1376.

Author(s)Verrill, Steve

Publication Year: 2007  View PDF »

Category: Journal Articles

Abstract: We make use of Cramer conditions together with the well-known local quadratic convergence of Newton's method to establish the asymptotic closeness of k-step Newton estimators to efficient likelihood estimators. In Verrill and Johnson [2007. Confidence bounds and hypothesis tests for normal distribution coefficients of variation. USDA Forest Products Laboratory Research Paper FPL-RP-638], we use this result to establish that estimators based on Newton steps from [square root]n- consistent estimators may be used in place of efficient solutions of the likelihood equations in likelihood ratio, Wald, and Rao tests. Taking a quadratic mean differentiability approach rather than our Crame´r condition approach, Lehmann and Romano [2005. Testing Statistical Hypotheses, third ed. Springer, New York] have outlined proofs of similar results. However, their Newton step estimator results actually rely on unstated assumptions about Cramer conditions. Here we make our Cramer condition assumptions and their use explicit.

Keywords: Cramer conditions, quadratic mean differentiability, likelihood ratio, Wald tests, Rao tests, asymptotics, confidence intervals, mathematical statistics, equations, quadratic differentials, statistical hypothesis testing, asymptotic efficiences, statistics, efficient likelihood estimators, Cramer conditions, Newton estimators, coefficients of variation, statistical analysis, asymptotic relative efficiency

File size: 147 kb(s)

This publication is also viewable on Treesearch:  view
RITS Product ID: 28580
Current FPL Scientist associated with this product
Verrill, Steve P.
Mathematical Statistician
  

Additional items that might interest you
View the video celebrating FPL's 100 years of public service in 2010, from the producers of the Greatest Good....view

Research Highlights from FPL....view

Termite Eradication: A search for the Holy Grail.... view

Moisture Management in Residential Construction Series videos...view

Wood Floor Systems in Residential Construction Series videos....view
- FPL's Mission and Strategic Plan -

FPL's mission is to identify and conduct innovative wood and fiber utilization research that contributes to conservation and productivity of the forest resource, thereby sustaining forests, the economy, and quality of life. ... ..more »

- FPL Research Emphasis Areas -
Advanced Composites

As an integral part of the FPL mission, we improve the long-term sustainability of our Nation's forests by creating valuable composite products from biobased materials ... ..more »


Advanced Structures

The FPL has been in the forefront of wood-frame housing research since 1910 and has long been recognized as a world leader in such housing-related areas as engineered wood ... ..more »


Forest Biorefinery

We all know the compelling reasons that the United States needs to reduce its dependence on fossil fuels. Historically, the greatest increases in energy demand have been for transportation fuels ... ..more »


Nanotechnology

A leader in wood products research for over a century, the FPL is positioning itself to become the lead Federal research facility for the application of nanotechnology in forest products ... more »


Woody Biomass Utilization

Forests in the United States contain a substantial amount of small-diameter, overstocked, and underutilized material.FPL research projects are exploring the potential of the small-diameter ... ..more »