Related papers: Additive Regression Model for Continuous Time Proc…
In multivariate regression estimation, the rate of convergence depends on the dimension of the regressor. This fact, known as the curse of the dimensionality, motivated several works. The additive model, introduced by Stone (10), offers an…
We establish some uniform limit results in the setting of additive regression model estimation. Our results allow to give an asymptotic 100% confidence bands for these components. These results are stated in the framework of i.i.d random…
Additive regression models have a long history in multivariate nonparametric regression. They provide a model in which each regression function depends only on a single explanatory variable allowing to obtain estimators at the optimal…
Big data is ubiquitous in practices, and it has also led to heavy computation burden. To reduce the calculation cost and ensure the effectiveness of parameter estimators, an optimal subset sampling method is proposed to estimate the…
This paper is about optimal estimation of the additive components of a nonparametric, additive isotone regression model. It is shown that asymptotically up to first order, each additive component can be estimated as well as it could be by a…
When training predictive models on data with missing entries, the most widely used and versatile approach is a pipeline technique where we first impute missing entries and then compute predictions. In this paper, we view prediction with…
Autoregressive neural networks within the temporal point process (TPP) framework have become the standard for modeling continuous-time event data. Even though these models can expressively capture event sequences in a one-step-ahead…
We establish minimax optimal rates of convergence for estimation in a high dimensional additive model assuming that it is approximately sparse. Our results reveal an interesting phase transition behavior universal to this class of high…
A $d$-dimensional nonparametric additive regression model with dependent observations is considered. Using the marginal integration technique and wavelets methodology, we develop a new adaptive estimator for a component of the additive…
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…
As with classic statistics, functional regression models are invaluable in the analysis of functional data. While there are now extensive tools with accompanying theory available for linear models, there is still a great deal of work to be…
We study mixed models with a single grouping factor, where inference about unknown parameters requires optimizing a marginal likelihood defined by an intractable integral. Low-dimensional numerical integration techniques are regularly used…
This paper develops a new framework, called modular regression, to utilize auxiliary information -- such as variables other than the original features or additional data sets -- in the training process of linear models. At a high level, our…
We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the…
This paper proposes an algorithm to estimate the parameters, including time delay, of continuous time systems based on instrumental variable identification methods. To overcome the multiple local minima of the cost function associated with…
We consider data-adaptive wavelet estimation of a trend function in a time series model with strongly dependent Gaussian residuals. Asymptotic expressions for the optimal mean integrated squared error and corresponding optimal smoothing and…
Many applications in mechanical, acoustic, and electronic engineering require estimating complex dynamical models, often represented as additive multi-input multi-output (MIMO) transfer functions with structural constraints. This paper…
We consider the problem of estimating an additive regression function in an inverse regres- sion model with a convolution type operator. A smooth backfitting procedure is developed and asymptotic normality of the resulting estimator is…
We present algorithms for nonparametric regression in settings where the data are obtained sequentially. While traditional estimators select bandwidths that depend upon the sample size, for sequential data the effective sample size is…
This paper develops asymptotic theory for estimation of parameters in regression models for binomial response time series where serial dependence is present through a latent process. Use of generalized linear model (GLM) estimating…