Discussion of different logistic models with functional data. Application to Systemic Lupus Erythematosus

Aguilera, Ana M.; Escabias, Manuel; Valderrama, Mariano J.

doi:10.1016/j.csda.2008.07.001

Cited by 24 publications

(19 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since α [1] j (β) ≤ h sup f (· | β), then, using (3.5), we deduce from (A.21) that for a constant C 5 > 0,…”

Section: 2mentioning

confidence: 91%

“…Let T [1] j (β) denote the version of T j (β) in the special case where K ≡ 1 on [−1, 1] and K = 0 elsewhere, and write α [1] j (β) = h |u|≤1 f ( I βX j − hu | β) du, representing the corresponding version of α j (β). In this notation, N 1 = N 1 (β) equals the maximum, over j , of the values of T [1] j (β) for j ∈ J (β). The argument leading to (A.10) now gives…”

Section: 2mentioning

confidence: 99%

“…The analogue of (A.12) in this setting is, assuming that (A.11) holds: [1] j (β) for all j and all β ∈ B 1 → 1. (A.21)…”

Section: 2mentioning

confidence: 99%

“…Advances in this direction include those made in [1,9,10,14] and [17], where both parametric and nonparametric link functions were introduced in order to connect the response to a linear functional model in the explanatory variables. However, the flexibility of available link-function models is still rather limited.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Single and multiple index functional regression models with nonparametric link

Chen¹,

Hall²,

Müller³

2011

Ann. Statist.

143

View full text Add to dashboard Cite

Fully nonparametric methods for regression from functional data have poor accuracy from a statistical viewpoint, reflecting the fact that their convergence rates are slower than nonparametric rates for the estimation of highdimensional functions. This difficulty has led to an emphasis on the so-called functional linear model, which is much more flexible than common linear models in finite dimension, but nevertheless imposes structural constraints on the relationship between predictors and responses. Recent advances have extended the linear approach by using it in conjunction with link functions, and by considering multiple indices, but the flexibility of this technique is still limited. For example, the link may be modeled parametrically or on a grid only, or may be constrained by an assumption such as monotonicity; multiple indices have been modeled by making finite-dimensional assumptions. In this paper we introduce a new technique for estimating the link function nonparametrically, and we suggest an approach to multi-index modeling using adaptively defined linear projections of functional data. We show that our methods enable prediction with polynomial convergence rates. The finite sample performance of our methods is studied in simulations, and is illustrated by an application to a functional regression problem.

show abstract

“…Since α [1] j (β) ≤ h sup f (· | β), then, using (3.5), we deduce from (A.21) that for a constant C 5 > 0,…”

Section: 2mentioning

confidence: 91%

Section: 2mentioning

confidence: 99%

“…The analogue of (A.12) in this setting is, assuming that (A.11) holds: [1] j (β) for all j and all β ∈ B 1 → 1. (A.21)…”

Section: 2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Single and multiple index functional regression models with nonparametric link

Chen¹,

Hall²,

Müller³

2011

Ann. Statist.

143

View full text Add to dashboard Cite

show abstract

“…As we have seen in previous chapters, PCA offers the possibility of uncovering modes of variation that are more complex. As in Section III , we work with the density functions p;(z) for log-shifted reaction times z defined in (5).…”

Section: Analysis With Pcamentioning

confidence: 99%

Classifying scatterbrains by their reaction based on method of functional data

Chen

2010

2010 International Conference on Future Information Technology and Management Engineering

View full text Add to dashboard Cite

In this paper, we present a nonparametric statistical method for functional data analysis. We actually work with the functions obtained by taking logarithms of the densities and differentiating, one aspect of this transformation is that it makes a normal density into a straight line. We work with the probability density function, describing the reaction-time distributions. By studying a density function, we explore the use of functional principal components analysis to get a sense of how the density functions vary from student to student. The result of this paper is giving some help for computational classifying of human's attention with the aid of their reaction-time. Keywords-junctional data; distribution, density, estimation 978-1-4244-9088-211 0/$26.00 ©20 I 0 IEEE

show abstract