Some Problems in Interval Estimation

Abstract

Summary The object of this paper is to propose for discussion the following topic: b1, b2, … are unbiased estimates of β1, β2, …, distributed normally with variances and covariances jointly estimated, with / degrees of freedom and independently of b1, b2, …, as v11, v12, v22, …, and the functions Fr(α) do not involve the parameters βr. What can we say about the roots of the equation in F(β,α)=β1F1(α)+β2 F2(α)+…=0? Numerical examples are discussed in detail to illustrate the problems of determining the fiducial distributions of (i)the root of a simple equation (i.e., a ratio),(i)the roots of a quadratic equation with variable coefficients. The solutions proposed are based on a consideration of the region of the (α, t2) plane lying above the curve {F(b,α)}2=t2 V{F(b,α)}=t2∑vijFi(α)Fj(α).