An Introduction to Probability and Statistical Inference, 2nd Edition

Chapter 10

Confidence intervals and confidence regions

In Section 8.2, the basic concepts about confidence intervals, etc. were introduced; the detailed discussion was deferred to the present chapter. The point estimation problem, in its simplest form, discussed extensively in the previous chapter, is as follows: On the basis of a random sample X₁, …, X_n with p.d.f. f (·; θ), θ ∈ Ω ⊆ ℜ, and its observed values x₁, …, x_n, construct a point estimate of θ, call it $\widehat{\theta }=\widehat{\theta }\left(x_1,\dots ,x_n\right).$ Thus, for example, in the N(θ, 1) case, we are invited to pinpoint a value of θ ∈ ℜ as the (unknown to us but) true value of θ. Such estimates were, actually, constructed ...