STATS 426 Lecture Notes - Lecture 12: Bias Of An Estimator, Multivariate Random Variable, Exponential Family
Document Summary
We saw in the above section that for a variety of di erent models one could di erentiate the log likelihood function with respect to the parameter and set this equal to 0 to obtain the mle of . In these examples, the log likelihood as a function of looks like an inverted bowl and hence solving for the stationary point gives us the unique maximizer of the log likelihood. We start this section by introducing some notation. Let l(x, ) = log f (x, ). Also let l(x, ) = / l(x, ). As before, x denots the vector (x1, x2, . , xn) and x denotes a particular value (x1, x2, . , xn) assumed by the random vector x. We denote by pn(x, ) the value of the density of x at the point x. Thus pn(x, ) = n i=1 f (xi, ).
