David Ruppert

David Ruppert
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David Ruppert

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Statistics - Methodology (11)
Statistics - Theory (6)
Mathematics - Statistics (6)
Statistics - Computation (3)
Statistics - Applications (2)
Instrumentation and Methods for Astrophysics (2)
High Energy Astrophysical Phenomena (2)
Astrophysics of Galaxies (1)

Publications Authored By David Ruppert

This paper studies a \textit{partial functional partially linear single-index model} that consists of a functional linear component as well as a linear single-index component. This model generalizes many well-known existing models and is suitable for more complicated data structures. However, its estimation inherits the difficulties and complexities from both components and makes it a challenging problem, which calls for new methodology. Read More

We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology based on a novel combination of spline bases with an eigenbasis to represent the trivariate kernel function. We discuss prediction of a new response trajectory, propose an inference procedure that accounts for total variability in the predicted response curves, and construct pointwise prediction intervals. Read More

We develop a hierarchical Gaussian process model for forecasting and inference of functional time series data. Unlike existing methods, our approach is especially suited for sparsely or irregularly sampled curves and for curves sampled with non-negligible measurement error. The latent process is dynamically modeled as a functional autoregression (FAR) with Gaussian process innovations. Read More

Independent component analysis (ICA) is popular in many applications, including cognitive neuroscience and signal processing. Due to computational constraints, principal component analysis is used for dimension reduction prior to ICA (PCA+ICA), which could remove important information. The problem is that interesting independent components (ICs) could be mixed in several principal components that are discarded and then these ICs cannot be recovered. Read More

We present a method to simultaneously model the dust far-infrared spectral energy distribution (SED) and the total infrared $-$ carbon monoxide (CO) integrated intensity $(S_{\rm IR}-I_{\rm CO})$ relationship. The modelling employs a hierarchical Bayesian (HB) technique to estimate the dust surface density, temperature ($T_{\rm eff}$), and spectral index at each pixel from the observed far-infrared (FIR) maps. Additionally, given the corresponding CO map, the method simultaneously estimates the slope and intercept between the FIR and CO intensities, which are global properties of the observed source. Read More

We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic linear models for multivariate time series to the functional data setting. We also develop Bayesian spline theory in a more general constrained optimization framework. Read More

In high dimensions, the classical Hotelling's $T^2$ test tends to have low power or becomes undefined due to singularity of the sample covariance matrix. In this paper, this problem is overcome by projecting the data matrix onto lower dimensional subspaces through multiplication by random matrices. We propose RAPTT (RAndom Projection T-Test), an exact test for equality of means of two normal populations based on projected lower dimensional data. Read More

We propose a procedure for testing the linearity of a scalar-on-function regression relationship. To do so, we use the functional generalized additive model (FGAM), a recently developed extension of the functional linear model. For a functional covariate X(t), the FGAM models the mean response as the integral with respect to t of F{X(t),t} where F is an unknown bivariate function. Read More

For smoothing covariance functions, we propose two fast algorithms that scale linearly with the number of observations per function. Most available methods and software cannot smooth covariance matrices of dimension $J \times J$ with $J>500$; the recently introduced sandwich smoother is an exception, but it is not adapted to smooth covariance matrices of large dimensions such as $J \ge 10,000$. Covariance matrices of order $J=10,000$, and even $J=100,000$, are becoming increasingly common, e. Read More

The functional generalized additive model (FGAM) was recently proposed in McLean et al. (2012) as a more flexible alternative to the common functional linear model (FLM) for regressing a scalar on functional covariates. In this paper, we develop a Bayesian version of FGAM for the case of Gaussian errors with identity link function. Read More

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 additive errors, which we will call the additive functional model, a generalization of the functional linear model. This paper studies the minimax rate of convergence of predictions from the additive functional model in the framework of reproducing kernel Hilbert space. Read More

Ultra-high energy cosmic rays (UHECRs) are atomic nuclei with energies over ten million times energies accessible to human-made particle accelerators. Evidence suggests that they originate from relatively nearby extragalactic sources, but the nature of the sources is unknown. We develop a multilevel Bayesian framework for assessing association of UHECRs and candidate source populations, and Markov chain Monte Carlo algorithms for estimating model parameters and comparing models by computing, via Chib's method, marginal likelihoods and Bayes factors. Read More

The Earth is continuously showered by charged cosmic ray particles, naturally produced atomic nuclei moving with velocity close to the speed of light. Among these are ultra high energy cosmic ray particles with energy exceeding 5x10^19 eV, which is ten million times more energetic than the most energetic particles produced at the Large Hadron Collider. Astrophysical questions include: what phenomenon accelerates particles to such high energies, and what sort of nuclei are energized? Also, the magnetic deflection of the trajectories of the cosmic rays makes them potential probes of galactic and intergalactic magnetic fields. Read More

This report studies local asymptotics of P-splines with $p$th degree B-splines and a $m$th order difference penalty. Earlier work with $p$ and $m$ restricted is extended to the general case. Asymptotically, penalized splines are kernel estimators with equivalent kernels depending on $m$, but not on $p$. Read More

We propose a fast penalized spline method for bivariate smoothing. Univariate P-spline smoothers (Eilers and Marx, 1996) are applied simultaneously along both coordinates. The new smoother has a sandwich form which suggested the name "sandwich smoother" to a referee. Read More

This paper addresses asymptotic properties of general penalized spline estimators with an arbitrary B-spline degree and an arbitrary order difference penalty. The estimator is approximated by a solution of a linear differential equation subject to suitable boundary conditions. It is shown that, in certain sense, the penalized smoothing corresponds approximately to smoothing by the kernel method. Read More