Related papers: Optimal Global Test for Functional Regression
Empirical likelihood is an attractive inferential framework that respects natural parameter boundaries, but existing approaches typically require smoothness of the functional and miscalibrate substantially when these assumptions are…
Considering a regression model, we address the question of testing the nullity of the regression function. The testing procedure is available when the variance of the observations is unknown and does not depend on any prior information on…
Lack-of-fit testing of a regression model with Berkson measurement error has not been discussed in the literature to date. To fill this void, we propose a class of tests based on minimized integrated square distances between a nonparametric…
We propose a family of tests to assess the goodness-of-fit of a high-dimensional generalized linear model. Our framework is flexible and may be used to construct an omnibus test or directed against testing specific non-linearities and…
Regression models with a response variable taking values in a Hilbert space and hybrid covariates are considered. This means two sets of regressors are allowed, one of finite dimension and a second one functional with values in a Hilbert…
Scalar-on-function linear models are commonly used to regress functional predictors on a scalar response. However, functional models are more difficult to estimate and interpret than traditional linear models, and may be unnecessarily…
We consider the problem of estimating the slope parameter in circular functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of 1-periodic, second order stationary random functions X1,...,Xn. We consider an…
A formal likelihood ratio hypothesis test for the validity of a parametric regression function is proposed, using a large-dimensional, nonparametric double cone alternative. For example, the test against a constant function uses the…
We study the error landscape of deep linear and nonlinear neural networks with the squared error loss. Minimizing the loss of a deep linear neural network is a nonconvex problem, and despite recent progress, our understanding of this loss…
We propose an active-learning method for nonlinear minimax regression. Given a nonlinear function that can be arbitrarily evaluated over a compact set, we fit a surrogate model, such as a feedforward neural network, by minimizing the…
Global optimization of black-box functions from noisy samples is a fundamental challenge in machine learning and scientific computing. Traditional methods such as Bayesian Optimization often converge to local minima on multi-modal…
We consider the problem of comparing probability densities between two groups. A new probabilistic tensor product smoothing spline framework is developed to model the joint density of two variables. Under such a framework, the probability…
A simple test is proposed for examining the correctness of a given completely specified response function against unspecified general alternatives in the context of univariate regression. The usual diagnostic tools based on residuals plots…
Finding the global minimum of non-convex functions is one of the main and most difficult problems in modern optimization. In the first part of the paper, we consider a certain class of "good" non-convex functions that can be bounded above…
Testing the significance of a variable or group of variables $X$ for predicting a response $Y$, given additional covariates $Z$, is a ubiquitous task in statistics. A simple but common approach is to specify a linear model, and then test…
In this paper, we address stochastic optimization problems involving a composition of a non-smooth outer function and a smooth inner function, a formulation frequently encountered in machine learning and operations research. To deal with…
We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…
The functional generalized additive model (FGAM) provides a more flexible nonlinear functional regression model than the well-studied functional linear regression model. This paper restricts attention to the FGAM with identity link and…
Logistic regression is widely used to model the propensity score in the analysis of nonignorable missing data. However, goodness-of-fit testing for this propensity score model has received limited attention in the literature. In this paper,…
Function-on-function linear regression is important for understanding the relationship between the response and the predictor that are both functions. In this article, we propose a reproducing kernel Hilbert space approach to…