A note on equivalent Thurstone models

Rockwell, Christina; Yellott, John I.

doi:10.1016/0022-2496(79)90006-3

Cited by 4 publications

(1 citation statement)

References 2 publications

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“…Thus whenever f is uniquely determined by its moments, it is also uniquely determined up to translation by its triple correlation. The problem of characterizing classes of functions that are uniquely determined by their moments has a large literature that we will not attempt to summarize; Shohat and Tamarkin' 7 and Akhiezer' 8 provide reviews. Instead we describe a single condition involving moments that is sufficient to guarantee that an image is determined by its triple correlation.…”

Section: Uniqueness Theorems For Special Classes Of Infinitementioning

confidence: 99%

Uniqueness properties of higher-order autocorrelation functions

Yellott

Iverson

1992

J. Opt. Soc. Am. A

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The kth-order autocorrelation function of an image is formed by integrating the product of the image and k independently shifted copies of itself: The case k = 1 is the ordinary autocorrelation; k = 2 is the triple correlation. Bartelt et al. [Appl. Opt. 23, 3121 (1984)] have shown that every image of finite size is uniquely determined up to translation by its triple-correlation function. We point out that this is not true in general for images of infinite size, e.g., frequency-band-limited images. Examples are given of pairs of simple bandlimited periodic images and pairs of band-limited aperiodic images that are not translations of each other but that have identical triple correlations. Further examples show that for every k there are distinct band-limited images that have identical kth-order autocorrelation functions. However, certain natural subclasses of infinite images are uniquely determined up to translation by their triple correlations. We develop two general types of criterion for the triple correlation to have an inverse image that is unique up to translation, one based on the zeros of the image spectrum and the other based on image moments. Examples of images satisfying such criteria include diffraction-limited optical images of finite objects and finite images blurred by Gaussian point spreads.

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Section: Uniqueness Theorems For Special Classes Of Infinitementioning

confidence: 99%

Uniqueness properties of higher-order autocorrelation functions

Yellott

Iverson

1992

J. Opt. Soc. Am. A

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Generalized thurstone models for ranking: Equivalence and reversibility

Yellott

1980

Journal of Mathematical Psychology

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Previous work has determined the conditions under which generalized versions of Thurstone's theory of comparative judgment are formally equivalent (i.e., empirically indistinguishable) for choice experiments. This note solves the analogous problem for ranking experiments: It is shown that if two "Generalized Thurstone Models" are equivalent for choice experiments with n alternatives they are also equivalent for ranking experiments with n alternatives, despite the fact that ranking generates many more preference probabilities. This result in turn allows one to determine which Generalized Thurstone Models are "reversible," i.e., satisfy the requirement that regardless of whether the subject ranks from best to worst or from worst to best, rankings that express the same preference order will occur with the same probability.

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