Minimax adaptive tests for the functional linear model
نویسندگان
چکیده
منابع مشابه
Minimax adaptive tests for the Functional Linear model
. We introduce two novel procedures to test the nullity of the slope function in the functional linear model with real output. The test statistics combine multiple testing ideas and random projections of the input data through functional Principal Component Analysis. Interestingly, the procedures are completely datadriven and do not require any prior knowledge on the smoothness of the slope nor...
متن کاملMinimax and Adaptive Prediction for Functional Linear Regression
This paper considers minimax and adaptive prediction with functional predictors in the framework of functional linear model and reproducing kernel Hilbert space. Minimax rate of convergence for the excess prediction risk is established. It is shown that the optimal rate is determined jointly by the reproducing kernel and the covariance kernel. In particular, the alignment of these two kernels c...
متن کاملTests for Error Correlation in the Functional Linear Model
The paper proposes two inferential tests for error correlation in the functional linear model, which complement the available graphical goodness-of-fit checks. To construct them, finite dimensional residuals are computed in two different ways, and then their autocorrelations are suitably defined. From these autocorrelation matrices, two quadratic forms are constructed whose limiting distributio...
متن کاملDesign-adaptive Minimax Local Linear Regression for Longitudinal/clustered Data
This paper studies a weighted local linear regression smoother for longitudinal/clustered data, which takes a form similar to the classical weighted least squares estimate. As a hybrid of the methods of Chen and Jin (2005) and Wang (2003), the proposed local linear smoother maintains the advantages of both methods in computational and theoretical simplicity, variance minimization and bias reduc...
متن کاملRestricted Likelihood Ratio Tests for Functional Effects in the Functional Linear Model
The goal of our article is to provide a transparent, robust, and computationally feasible statistical approach for testing in the context of scalar-on-function linear regression models. Assuming linearity between response and predictors, we are interested in testing for the necessity of functional effects. Our methods are motivated by and applied to a large longitudinal study involving diffusio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2013
ISSN: 0090-5364
DOI: 10.1214/13-aos1093