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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…
Semiparametric regression offers a flexible framework for modeling non-linear relationships between a response and covariates. A prime example are generalized additive models where splines (say) are used to approximate non-linear functional…
We study the problem of testing whether a function f:R^n->R is linear (i.e., both additive and homogeneous) in the distribution-free property testing model, where the distance between functions is measured with respect to an unknown…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
Finite mixture distributions arise in sampling a heterogeneous population. Data drawn from such a population will exhibit extra variability relative to any single subpopulation. Statistical models based on finite mixtures can assist in the…
This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random…
Model-based trees are used to find subgroups in data which differ with respect to model parameters. In some applications it is natural to keep some parameters fixed globally for all observations while asking if and how other parameters vary…
Generalized additive models (GAMs) are flexible non-linear regression models, which can be fitted efficiently using the approximate Bayesian methods provided by the mgcv R package. While the GAM methods provided by mgcv are based on the…
Motivated by regression analysis for microbiome compositional data, this paper considers generalized linear regression analysis with compositional covariates, where a group of linear constraints on regression coefficients are imposed to…
This paper considers the problem of variable selection in regression models in the case of functional variables that may be mixed with other type of variables (scalar, multivariate, directional, etc.). Our proposal begins with a simple null…
We propose a computationally straightforward test for the linearity of a spatial interaction function. Such functions arise commonly, either as practitioner imposed specifications or due to optimizing behaviour by agents. Our conditional…
In many psychometric applications, the relationship between the mean of an outcome and a quantitative covariate is too complex to be described by simple parametric functions; instead, flexible nonlinear relationships can be incorporated…
In other FICO Technical Papers, I have shown how to fit Generalized Additive Models (GAM) with shape constraints using quadratic programming applied to B-Spline component functions. In this paper, I extend the method to Robust Least Squares…
As technology continues to advance at a rapid pace, the prevalence of multivariate functional data (MFD) has expanded across diverse disciplines, spanning biology, climatology, finance, and numerous other fields of study. Although MFD are…
We consider the functional regression model with multivariate response and functional predictors. Compared to fitting each individual response variable separately, taking advantage of the correlation between the response variables can…
This paper proposes a multivariate nonlinear function-on-function regression model, which allows both the response and the covariates can be multi-dimensional functions. The model is built upon the multivariate functional reproducing kernel…
Generalized additive models (GAMs) connecting a set of scalar covariates that map 1-1 to a response are commonly employed in ecology and beyond. However, covariates are often inherently non-scalar, taking multiple values for each…
Existing computationally efficient methods for penalized likelihood GAM fitting employ iterative smoothness selection on working linear models (or working mixed models). Such schemes fail to converge for a non-negligible proportion of…
We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), designed to handle multivariate response variables, along with a wide range of temporal and spatial…
This paper examines the problem of nonparametric testing for the no-effect of a random covariate (or predictor) on a functional response. This means testing whether the conditional expectation of the response given the covariate is almost…