Related papers: Efficient Estimation in Single Index Models throug…
In this paper, we propose a robust profile estimation method for the parametric and nonparametric components of a single index model when the errors have a strongly unimodal density with unknown nuisance parameter. Under regularity…
Ordinary differential equations (ODEs) are commonly used to model dynamic behavior of a system. Because many parameters are unknown and have to be estimated from the observed data, there is growing interest in statistics to develop…
This paper studies the asymptotic behavior of penalized spline estimates of derivatives. In particular, we show that simply differentiating the penalized spline estimator of the mean regression function itself to estimate the corresponding…
We present an estimation procedure for nonlinear mixed-effects models in which the population trajectory is represented by penalized splines and adapted to individuals via subject-specific transformation parameters. By exploiting the mixed…
We consider a linear regression model with a spatially correlated error term on a lattice. When estimating coefficients in the linear regression model, the generalized least squares estimator (GLSE) is used if the covariance structures are…
In some real world applications, such as spectrometry, functional models achieve better predictive performances if they work on the derivatives of order m of their inputs rather than on the original functions. As a consequence, the use of…
Within the framework of smoothing spline ANOVA, we propose a plug-in kernel ridge regression estimator to estimate the derivatives of the underlying multivariate regression function. We first establish an $L_\infty$ convergence rate of the…
We consider functional data where an underlying smooth curve is composed not just with errors, but also with irregular spikes. We propose an approach that, combining regularized spline smoothing and an Expectation-Maximization algorithm,…
The problem of statistical inference for regression coefficients in a high-dimensional single-index model is considered. Under elliptical symmetry, the single index model can be reformulated as a proxy linear model whose regression…
We construct estimators for the parameters of a parabolic SPDE with one spatial dimension based on discrete observations of a solution in time and space on a bounded domain. We establish central limit theorems for a high-frequency…
Regression with a spherical response is challenging due to the absence of linear structure, making standard regression models inadequate. Existing methods, mainly parametric, lack the flexibility to capture the complex relationship induced…
This paper deals with the drift estimation in linear stochastic evolution equations (with emphasis on linear SPDEs) with additive fractional noise (with Hurst index ranging from 0 to 1) via least-squares procedure. Since the least-squares…
We consider the problem of approximating smoothing spline estimators in a nonparametric regression model. When applied to a sample of size $n$, the smoothing spline estimator can be expressed as a linear combination of $n$ basis functions,…
We consider a general multivariate model where univariate marginal distributions are known up to a parameter vector and we are interested in estimating that parameter vector without specifying the joint distribution, except for the…
The estimation of regression parameters in one dimensional broken stick models is a research area of statistics with an extensive literature. We are interested in extending such models by aiming to recover two or more intersecting…
Observational data are often accompanied by natural structural indices, such as time stamps or geographic locations, which are meaningful to prediction tasks but are often discarded. We leverage semantically meaningful indexing data while…
Penalized spline regression is a popular method for scatterplot smoothing, but there has long been a debate on how to construct confidence intervals for penalized spline fits. Due to the penalty, the fitted smooth curve is a biased estimate…
We consider estimation of a functional parameter of a realistically modeled data distribution based on observing independent and identically distributed observations. We define an $m$-th order Spline Highly Adaptive Lasso Minimum Loss…
A new statistical procedure, based on a modified spline basis, is proposed to identify the linear components in the panel data model with fixed effects. Under some mild assumptions, the proposed procedure is shown to consistently estimate…
Mixed-effect models are widely used for the analysis of correlated data such as longitudinal data and repeated measures. In this article, we study an approach to the nonparametric estimation of mixed-effect models. We consider models with…