In this video, the question of measuring and quantifying the performance
of an estimator is discussed. The video focusses on the concepts and
definitions of bias and variance of the probability density function
(pdf) of the estimator, and highlights the bias-variance trade-off;
namely, that by introducing a small amount of bias in an estimator, the
variance can be reduced. The normalised bias and normalised variance are
also defined. Assuming the observations are independent, then the bias
of the sample mean is calculated and shown to be unbiased. Similarly,
the variance of the sample mean is calculated, using two similar but
PGEE11164 Probability, Estimation Theory, and Random Signals Lectures -- School of Engineering, University of Edinburgh. Copyright James R. Hopgood and University of Edinburgh, Scotland, United Kingdom (UK). 2020.
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