An Overview of the Frequentist Approach to Estimation
The frequentist will often make the assumption that the available data is a random sample of i.i.d. variables. DeGroot (1988) articulates the view that the i.i.d. assumption is logically untenable. Are i.i.d. observations really possible? Are the conditions under which we toss a coin several times ever truly identical? Of course the answer is no. In general, identical trials are physically impossible. If repeated trials were truly identical, wouldn’t we necessarily obtain the same result in each trial? These criticisms notwithstanding, experience suggests that the i.i.d. assumption is often an excellent approximation to reality, and, in many statistical contexts, making this assumption is relatively harmless. While one might take issue with the i.i.d. assumption in modeling the available data, this is not a central issue in the disagreements between frequentists and Bayesians. Both schools will often make this assumption when describing the data available for study. In this section, we will make the assumption, for the sake of simplicity and clarity, that the available experimental data satisfies an i.i.d. assumption and may thus be represented as the random sample X1;X2; : : : ;Xn ~ FӨ.
KeywordsMean Square Error Maximum Likelihood Estimator Risk Function Unbiased Estimator Exponential Family
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