b For many models ˆ θ is consistent c The Invariance Property For many nice

# B for many models ˆ θ is consistent c the

• 6

This preview shows page 5 - 6 out of 6 pages.

by a constant. (b) For many models, ˆ θ is consistent. (c) The Invariance Property: For many nice functions g , if ˆ θ is the MLE of θ , then g ( ˆ θ ) is the MLE of g ( θ ). (d) The Asymptotic Property: For large n , ˆ θ has an approximate normal distribution with mean θ and variance 1 / B where B = nE ∂θ ln f ( X ; θ ) 2 This asymptotic property can be used to develop confidence intervals for θ .

Subscribe to view the full document.

The method of maximum likelihood works well when intuition fails and no obvious estimator can be found. When an obvious estimator exists the method of ML often will find it. The method can be applied to many statistical problems: regression analysis, analysis of variance, discriminant analysis, hypothesis testing, principal components, etc.
• Fall '13

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes