2000 Mathematics Subject Classification: Primary 62C99, sec-ondary 62C10, 62C20, 62J05

Yu. Golubev (1) , Th. Zimolo (1)

1 I2M - Institut de Mathématiques de Marseille

The paper deals with recovering an unknown vector β ∈ R^p based on the observations Y = Xβ + ∈ξ and Z = X + σζ, where X is an unknown n×p-matrix with n ≥ p, ξ ∈ R^p is a standard white Gaussian noise, ζ is a n × p-matrix with i.i.d. standard Gaussian entries, and ∈, σ ∈ R^+ are known noise levels. It is assumed that X has a large condition number and p is large. Therefore, in order to estimate β, the simple Tikhonov-Phillips regularization (ridge regression) with a data-driven regularization parameter is used. For this estimation method, we study the effect of noise σζ on the quality of the recovering of Xβ using concentration inequalities for the prediction error.

Mots clés: data-driven regularization; prediction mean squared error; concen-tration inequality; sec-ondary 62C10; blurred design; ridge regression; Tikhonov-Phillips method

Domaines: Statistiques [stat]

Yu. Golubev, Th. Zimolo. 2000 Mathematics Subject Classification: Primary 62C99, sec-ondary 62C10, 62C20, 62J05. Mathematical Methods of Statistics, 2016, 25 (1), pp.1-25. ⟨hal-01292382⟩