Theory and Methods of Statistics

6.11 Sequential Probability Ratio Test

Traditional statistical inference deals with analysis of a set of data $\left(X_1,\dots ,X_n\right)$ to draw some conclusion about a parameter θ involved in the joint pdf (or pmf) $f_n\left(x_1,\dots ,x_n;\theta \right)$. The observations X₁, …, X_n are often iid with individual pdf f(x;θ) (although they need not be so), in which case, $f_n(x_1,\dots ,x_n;\theta )={\prod }_{i=1}^{n}f\left(x_i;\theta \right)$. But the main thing is that n is fixed and the functional form f_n is fixed (ie, the sample size and ...