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, …, Xn with p.d.f. f (·; θ), θ ∈ Ω ⊆ ℜ, and its observed values x1, …, xn, construct a point estimate of θ, call it θ^=θ^(x1,,xn).si2_e 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 ...

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