Squared Linear Models
Abstract
Abstract. We study statistical models that are parametrized by squares of linear forms. All critical points of the likelihood function are real and positive. There is one critical point in each region of the projective hyperplane arrangement defined by the linear forms. We examine the ideal and singular locus of the model, and we give a determinantal presentation for its likelihood correspondence. We characterize tropical degenerations of the maximum likelihood estimation (MLE), we describe the log-normal polytopes, and we explore connections to determinantal point processes.
Fields of Study & Subjects
Polynomial and algebraic computation
Numerical Methods and Algorithms
Matrix Theory and Algorithms
Publication details
- Journal / source
- SIAM Journal on Applied Algebra and Geometry
- Volume
- 10
- Issue
- 2
- Pages
- 153–173
- Publication date
- 7 April 2026
- Language
- EN