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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2007 • Question 8

Question

Math 6010 • Linear Models Fall 2007 • Question 8

Let \((X_1,\ldots ,X_m)\) be a multinomial random vector with parameters \(N\) and \(p_1,p_2,\ldots ,p_m\). Note that \(N=X_1+\cdots +X_m\) and \(p_1+p_2+\cdots +p_m=1\). Find the maximum likelihood estimators for \(p_1,p_2,\ldots ,p_m\). (7 points)

Raw LaTeX

Let \((X_1,\ldots,X_m)\) be a multinomial random vector with
parameters \(N\) and \(p_1,p_2,\ldots,p_m\). Note that
\(N=X_1+\cdots+X_m\) and \(p_1+p_2+\cdots+p_m=1\). Find the maximum likelihood
estimators for \(p_1,p_2,\ldots,p_m\). (7 points)

Topic Tags

Estimator Distributions Likelihood Ratio Tests Maximum Likelihood Estimation Uniform Integrability and Truncation Methods