STAT231 Lecture Notes - Lecture 8: Maximum Likelihood Estimation, Data Set, Random Variable
15 Jan 2018
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Interval estimation: likelihood function -> likelihood intervals, sampling distribution -> confidence intervals. Problem: theta = unknown population attribute of interest; {y1, ,yn} -> sample drawn from the population; based on the sample, theta hat(y1, ,yn) which is our estimate for theta. Method of maximum likelihood: identify the distribution from which the data is drawn (modelling, construct the likelihood function, calculate the log likelihood function, take derivatives to find the maximum likelihood estimate. Alternative method - method of least squares (more practical, do not care about distribution. only care about how accurate the prediction is): choose mu hat such that the sum of squared errors is minimized. 2 sigma(yi-mu)(-1) = 0 sigma(yi-mu) = 0 mu = y average. For the normal problem, mle and ls estimate for mu are the same. We want to estimate the random interval [a, B] which would contain theta with a high probability (that is pre-specified/defined)
