Related papers: Smoothing splines estimators for functional linear…
In this paper, we propose a functional analysis of a set of individual space-speed profiles corresponding to speed as function of the distance traveled by the vehicle from an initial point. This functional analysis begins with a functional…
The problem tackled in this paper is the determination of sample size for a given level and power in the context of a simple linear regression model. At a technical level, the simple linear regression model is a five-parameter model. It is…
Regression splines are smooth, flexible, and parsimonious nonparametric function estimators. They are known to be sensitive to knot number and placement, but if assumptions such as monotonicity or convexity may be imposed on the regression…
The spatial random-effects model is flexible in modeling spatial covariance functions, and is computationally efficient for spatial prediction via fixed rank kriging. However, the success of this model depends on an appropriate set of basis…
We consider the problem of estimating the slope function in a functional regression with a scalar response and a functional covariate. This central problem of functional data analysis is well known to be ill-posed, thus requiring a…
We propose a functional linear model to predict a response using multiple functional and longitudinal predictors and to estimate the effect lags of predictors. The coefficient functions are written as the expansion of a basis system (e.g.…
In state space models, smoothing refers to the task of estimating a latent stochastic process given noisy measurements related to the process. We propose an unbiased estimator of smoothing expectations. The lack-of-bias property has…
This paper considers a high dimensional linear regression model with corrected variables. A variety of methods have been developed in recent years, yet it is still challenging to keep accurate estimation when there are complex correlation…
Fine stratification survey is useful in many applications as its point estimator is unbiased, but the variance estimator under the design cannot be easily obtained, particularly when the sample size per stratum is as small as one unit. One…
Surface-based data is commonly observed in diverse practical applications spanning various fields. In this paper, we introduce a novel nonparametric method to discover the underlying signals from data distributed on complex surface-based…
We propose a fast bivariate smoothing approach for symmetric surfaces that has a wide range of applications. We show how it can be applied to estimate the covariance function in longitudinal data as well as multiple additive covariances in…
We study the functional linear regression model with a scalar response and a Hilbert space-valued predictor, a canonical example of an ill-posed inverse problem. We show that the functional partial least squares (PLS) estimator attains…
Consider the problem when $X_1,X_2,..., X_n$ are distributed on a circle following an unknown distribution $F$ on $S^1$. In this article we have consider the absolute general set-up where the density can have local features such as…
We propose a multidimensional smoothing spline algorithm in the context of manifold learning. We generalize the bending energy penalty of thin-plate splines to a quadratic form on the Sobolev space of a flat manifold, based on the Frobenius…
Estimation of the mean and covariance parameters for functional data is a critical task, with local linear smoothing being a popular choice. In recent years, many scientific domains are producing multivariate functional data for which $p$,…
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…
Smoothing splines are twice differentiable by construction, so they cannot capture potential discontinuities in the underlying signal. In this work, we consider a special case of the weak rod model of Blake and Zisserman (1987) that allows…
In this paper, we study the estimation and inference of change points under a functional linear regression model with changes in the slope function. We present a novel Functional Regression Binary Segmentation (FRBS) algorithm which is…
In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution.…
Shrinkage methods are frequently used to improve the precision of least squares estimators of fixed effects. However, widely used shrinkage estimators guarantee improved precision only under strong distributional assumptions. I develop an…