arXiv 2 Dec 2025 · Econometrics
arXiv:2512.02970 · PDF · DOI · OpenAlex · Extracted main text
This paper develops new identification results for multidimensional continuous measurement-error models where all observed measurements are contaminated by potentially correlated errors and none provides an injective mapping of the latent distribution. Using third order cross moments, the paper constructs a three way tensor whose unique decomposition, guaranteed by Kruskal theorem, identifies the factor loading matrices. Starting with a linear structure, the paper recovers the full distribution of latent factors by constructing suitable measurements and applying scalar or multivariate versions of Kotlarski identity. As a result, the joint distribution of the latent vector and measurement errors is fully identified without requiring injective measurements, showing that multivariate latent structure can be recovered in broader settings than previously believed. Under injectivity, the paper also provides user-friendly testable conditions for identification. Finally, this paper provides general identification results for nonlinear models using a newly-defined generalized Kruskal rank - signal rank - of intergral operators. These results have wide applicability in empirical work involving noisy or indirect measurements, including factor models, survey data with reporting errors, mismeasured regressors in econometrics, and multidimensional latent-trait models in psychology and marketing, potentially enabling more robust estimation and interpretation when clean measurements are unavailable.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Kruskal, Joseph B (1977) Three-way arrays: Rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics | 0.737 | 3 | 3 | 67% |
| 2 | Allman, Elizabeth S and Matias, Catherine and Rhodes, John A (2009) Identifiability of Parameters in Latent Structure Models with Many Observed Variables | 0.737 | 3 | 2 | 100% |
| 3 | Hu, Yingyao and Schennach, Susanne (2008) Instrumental Variable Treatment of Nonclassical Measurement Error Models self | 0.737 | 3 | 2 | 100% |
| 4 | Bonhomme, Stéphane and Jochmans, Koen and Robin, Jean-Marc (2016) Nonparametric identification in finite mixtures of nonparametric product measures | 0.405 | 1 | 1 | 100% |
| 5 | Carroll, J. Douglas and Chang, Jih-Jie (1970) Analysis of Individual Differences in Multidimensional Scaling via an N-Way Generalization of “Eckart-Young” Decomposition | 0.405 | 1 | 1 | 100% |
| 6 | Harshman, Richard A (1970) Foundations of the PARAFAC procedure: Models and conditions for an “explanatory” multimodal factor analysis | 0.405 | 1 | 1 | 100% |
| 7 | Hu, Yingyao (2008) Identification of Nonparametric Measurement Error Models with Discrete Data self | 0.405 | 1 | 1 | 100% |
| 8 | Hu, Yingyao and Shiu, Ji-Liang (2022) A Simple Test of Completeness in a Class of Nonparametric Specification self | 0.405 | 1 | 1 | 100% |
| 9 | Sidiropoulos, Nicholas D. and Bro, Rasmus and Giannakis, Georgios B (2000) Parallel Factor Analysis in Sensor Array Processing | 0.405 | 1 | 1 | 100% |
| 10 | Kotlarski, Ignacy (1965) On Pairs of Independent Random Variables Whose Product Follows the Gamma Distribution | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 10 scored citations.