Related papers: Optimal Designs for Regression on Lie Groups
This paper studies optimal designs for linear regression models with correlated effects for single responses. We introduce the concept of rhombic design to reduce the computational complexity and find a semi-algebraic description for the…
Hierarchical random effect models are used for different purposes in clinical research and other areas. In general, the main focus is on population parameters related to the expected treatment effects or group differences among all units of…
The determination of an optimal design for a given regression problem is an intricate optimization problem, especially for models with multivariate predictors. Design admissibility and invariance are main tools to reduce the complexity of…
In the common linear regression model the problem of determining optimal designs for least squares estimation is considered in the case where the observations are correlated. A necessary condition for the optimality of a given design is…
The celebrated de la Garza phenomenon states that for a polynomial regression model of degree $p-1$ any optimal design can be based on at most $p$ design points. In a remarkable paper, Yang [Ann. Statist. 38 (2010) 2499--2524] showed that…
We consider the optimal design problem for a comparison of two regression curves, which is used to establish the similarity between the dose response relationships of two groups. An optimal pair of designs minimizes the width of the…
In discrete choice experiments, the information matrix depends on the model parameters. Therefore designing optimally informative experiments for arbitrary initial parameters often yields highly nonlinear optimization problems and makes…
In this article, we obtain new results for Fourier restriction type problems on compact Lie groups. We first provide a sharp form of $L^p$ estimates of irreducible characters in terms of their Laplace-Beltrami eigenvalue and as a…
The paper extends the result of Harman and Pronzato [Stat. & Prob. Lett., 77:90--94, 2007], which corresponds to $p=0$, to all strictly concave criteria in Kiefer's $\phi_p$-class. Let $\xi$ be any design on a compact set…
In this paper we study the statistical properties of Principal Components Regression with Laplacian Eigenmaps (PCR-LE), a method for nonparametric regression based on Laplacian Eigenmaps (LE). PCR-LE works by projecting a vector of observed…
We provide a general expression of the Haar measure $-$ that is, the essentially unique translation-invariant measure $-$ on a $p$-adic Lie group. We then argue that this measure can be regarded as the measure naturally induced by the…
We present a new optimization method for the group selection problem in linear regression. In this problem, predictors are assumed to have a natural group structure and the goal is to select a small set of groups that best fits the…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
Two-phase designs measure variables of interest on a subcohort where the outcome and covariates are readily available or cheap to collect on all individuals in the cohort. Given limited resource availability, it is of interest to find an…
In this paper an additive regression model for a symmetric positive-definite matrix valued response and multiple scalar predictors is proposed. The model exploits the abelian group structure inherited from either the Log-Cholesky metric or…
We investigate the possibility of extending some results of Pazman and Pronzato (2014) to a larger set of optimality criteria. Namely, in a linear regression model the problem of computing D-, A-, E_k-optimal designs, of combining these…
High-dimensional regression often suffers from heavy-tailed noise and outliers, which can severely undermine the reliability of least-squares based methods. To improve robustness, we adopt a non-smooth Wilcoxon score based rank objective…
We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach uses an…
In this article, we investigate the robust optimal design problem for the prediction of response when the fitted regression models are only approximately specified, and observations might be missing completely at random. The intuitive idea…
This paper investigates the effect of the design matrix on the ability (or inability) to estimate a sparse parameter in linear regression. More specifically, we characterize the optimal rate of estimation when the smallest singular value of…