ESTIMATING THE PARAMETERS OF A LINEAR FUNCTION OF A RANDOM VARIABLE.
STANFORD UNIV CALIF DEPT OF STATISTICS
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Suppose we have a sample of independent observations which are values of a linear function of a random variable, and we wish to find maximum likelihood estimators for the two parameters of the linear function. If the support of the random variable is the whole real axis, the maximum likelihood estimators can be found by the usual methods in other cases restricted maximization techniques must be used. We restricted attention to the cases in which the support is an infinite interval or a lattice and the density of the random variable is non-increasing over the support. Special attention is given to the exponential and geometric distributions. If the parameter of the distribution is also unknown, its maximum likelihood estimator can also be obtained, when the support of the random variable is a lattice. Author
- Statistics and Probability