An Analysis of the Linear-Calibration Controversy from the Perspective of Compound Estimation

The Calibration Problem Revisited

“…Lwin and Maritz [7] mentioned that in calibration it is unwise to use data that do not support the hypothesis that ||> 0: Therefore, before estimating x it is important to test the null hypothesis H 0 : ¼ 0 against the alternative hypothesis H 1 :…”

“…where b 2 is an unbiased estimator of 2 : Properties of the classical and the inverse estimators have been examined extensively, see, Krutchkoff, [5,6] Berkson, [2] Martinelle, [8] Halperin, [3] Shukla, [14] Lwin and Maritz, [7] Oman, [11] and Srivastava. [15] However, a controversy occurred when the consistency and mean squared error properties of these two estimators were examined.…”

Linear calibration in functional regression models

“…To obtain numerical comparisons between the estimators, we write the three first order approximations to their mean squared errors as quadratic forms as considered in Lwin and Maritz (1982 and T = X/B2. After some algebraic manipulations, it can be shown that A1 > 0 if n 2 3.…”

A Note on the Conditional Approach to Interval Estimation in the Calibration Problem

“…However, the fundamental problem of the standard approach remains unsolved. In this paper, we examine a simple and natural way of handling the problem by conditioning on the nonzero slope first proposed by Graybill (1976) and later advocated by Lwin and Maritz (1982). We show that the conditional coverage rate is informative and can be computed easily.…”

“…The calibration problem usually arises when the quantity to be calibrated is harder to measure, more expensive to measure, or the value has been lost and cannot be retrieved. The point estimation problem in calibration has been widely studied (see, e.g., Lwin and Maritz, 1982;Brown, 1979;Shukla, 1972;Williams, 1969). The standard method of constructing a confidence interval is to apply Fieller's theorems (Fieller, 1954;Graybill, 1976).…”