Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · math/0508299

Linear Latent Structure Analysis: from Foundations to Algorithms and Applications

I. Akushevich·M. Kovtun·A. I. Yashin·K. G. Manton
View original source ↗Read source document ↗Export metadata ↓

Abstract

A new statistical technique for constructing linear latent structure (LLS) models from available data, supported by well established theoretical results and an efficient algorithm, is presented. The method reduces the problem of estimating LLS model parameters to a sequence of linear algebra problems. This assures a low computational complexity and an ability to handle large scale data that involve thousands of variables. An overall computational scheme and all its components are discussed in detail. Simulation experiments demonstrate the excellent performance of the algorithm in reconstructing model parameters. Step-by-step analysis of a demographic survey is presented as an example. The technique is useful for the analysis of high-dimensional categorical data (e.g., demographic surveys, gene expression data) where the detection, evaluation, and interpretation of a underlying latent structure are required.

Explore related subjects

math.STstat.TH

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

I. Akushevich, M. Kovtun, A. I. Yashin, K. G. Manton. 2005-10-19. Linear Latent Structure Analysis: from Foundations to Algorithms and Applications. https://arxiv.org/abs/math/0508299

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Second-order PACF asymptotics and discrimination between fractional Gaussian noise and $\FARIMA(0,d,0)$

Fractional Gaussian noise and $\FARIMA(0,d,0)$ have the same long-memory pole $|θ|^{-2d}$ and hence the same leading PACF law $α(n)\sim d/n$. We show that this agreement breaks at the first non-universal order. For $0<d<1/2$, the pure fGn PACF satisfies $$ α_{\fGn}(n)=\frac d n+\frac{C_{\fGn}(d)}{n^2}+o(n^{-2}), \qquad C_{\fGn}(d)<d^2, $$ The proof uses the Bingham--Inoue--Kasahara representation, a phase-coefficient expansion for fGn, and a Hankel-operator perturbation argument. Thus the fGn spectral envelope is invisible at first order but visible in second-order finite prediction, explaining why short-memory order selection can differ when fGn data are fitted by FARIMA-type models.

math.ST↗
arXiv2026

U-centering as subset ANOVA: edge regression and higher-order theory

Unbiased squared distance covariance and the Hilbert-Schmidt independence criterion (HSIC) are fourth-order U-statistics, yet U-centering evaluates them from pairwise arrays in $O(n^2)$ operations. We show that U-centering is exactly least-squares residualization after fitting additive endpoint effects. This analysis of variance (ANOVA) interpretation explains the zero row sums and the normalization through residual degrees of freedom. The same geometry gives regression representations of dependence and two-sample statistics, exact permutation variances, and relations among pooled and regression mean squares. For arrays indexed by $r$-element subsets and $n\ge2r$, higher-order U-centering removes all lower-order subset effects and projects onto a space of dimension $\binom{n}{r}-\binom{n}{r-1}$. For fixed symmetric square-integrable kernels evaluated on independent and identically distributed (i.i.d.) paired observations, we derive the residual covariance matrix, exact mean-squared errors for estimating the highest-order Hoeffding components, unbiased positive semidefinite (PSD) covariance estimates, and moment formulas under independence and permutation. The normalized residual inner product equals a direct unbiased estimator involving up to $2r$ observations, but can be evaluated in $O(n^r)$ operations for fixed $r$. For four-argument matching kernels, three matrix products yield exactly unbiased estimators of a fourth spectral moment of kernel cross-covariance in $O(n^3)$ arithmetic and $O(n^2)$ storage. A numerical illustration distinguishes dependence structures with equal HSIC and different spectral concentration.

math.ST↗
arXiv2026

A Partial-Matching Proof of the Neyman--Pearson Lemma

Testing seeks to distinguish distributions, whereas matching seeks to identify their common mass. I show that this apparent opposition provides a direct proof of the Neyman--Pearson lemma. Maximal partial matching between the alternative distribution and a scaled null distribution separates them into a common component and two mutually singular residuals. An elementary dual problem then turns this separation into a testing rule: complementary slackness forces rejection on the alternative residual and non-rejection on the scaled-null residual, leaving freedom to randomize at the likelihood-ratio threshold. Thus the optimal test emerges from maximal matching rather than being proposed in advance. The matching profile also determines the optimal power envelope.

math.ST↗