Related papers: Minimax wavelet estimation for multisample heteros…
Let $i=1,\ldots,N$ index a simple random sample of units drawn from some large population. For each unit we observe the vector of regressors $X_{i}$ and, for each of the $N\left(N-1\right)$ ordered pairs of units, an outcome $Y_{ij}$. The…
This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior…
We consider constructing model selection criteria for evaluating nonlinear mixed effects models via basis expansions. Mean functions and random functions in the mixed effects model are expressed by basis expansions, then they are estimated…
We consider nonparametric estimation of a regression function for a situation where precisely measured predictors are used to estimate the regression curve for coarsened, that is, less precise or contaminated predictors. Specifically, while…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
We consider nonparametric regression under covariate shift, where we observe samples from both the target distribution and a related but distinct source distribution. We introduce a novel object, the transfer function, and show that…
We develop and apply an approach for analyzing multi-curve data where each curve is driven by a latent state process. The state at any particular point determines a smooth function, forcing the individual curve to switch from one function…
In the nonparametric regression setting, we construct an estimator which is a continuous function interpolating the data points with high probability, while attaining minimax optimal rates under mean squared risk on the scale of H\"older…
This paper studies the problem of parameter estimation in resonant, acoustic fluid-structure interaction problems over a wide frequency range. Problems with multiple resonances are known to be subjected to local minima, which represents a…
This work presents a new approach, called MISFIT, for fitting generalized functional linear regression models with sparsely and irregularly sampled data. Current methods do not allow for consistent estimation unless one assumes that the…
In this paper, we study parametric nonlinear regression under the Harris recurrent Markov chain framework. We first consider the nonlinear least squares estimators of the parameters in the homoskedastic case, and establish asymptotic theory…
We develop a minimax theory for operator learning, where the goal is to estimate an unknown operator between separable Hilbert spaces from finitely many noisy input-output samples. For uniformly bounded Lipschitz operators, we prove…
We study nonparametric covariance function estimation for functional data observed with noise at discrete locations on a $d$-dimensional domain. Estimating the covariance function from discretely observed data is a challenging nonparametric…
We consider the estimation of a regression function with random design and heteroscedastic noise in a nonparametric setting. More precisely, we address the problem of characterizing the optimal penalty when the regression function is…
We consider the regression model with errors-in-variables where we observe $n$ i.i.d. copies of $(Y,Z)$ satisfying $Y=f(X)+\xi, Z=X+\sigma\epsilon$, involving independent and unobserved random variables $X,\xi,\epsilon$. The density $g$ of…
We study the nonparametric estimation of the jump density of a compound Poisson process from the discrete observation of one trajectory over $[0,T]$. We consider the microscopic regime when the sampling rate $\Delta=\Delta_T\rightarrow0$ as…
We consider the problem of nonparametric regression under shape constraints. The main examples include isotonic regression (with respect to any partial order), unimodal/convex regression, additive shape-restricted regression, and…
Event datasets are sequences of events of various types occurring irregularly over the time-line, and they are increasingly prevalent in numerous domains. Existing work for modeling events using conditional intensities rely on either using…
A fundamental problem of causal discovery is cause-effect inference, learning the correct causal direction between two random variables. Significant progress has been made through modelling the effect as a function of its cause and a noise…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…