Related papers: Confidence Intervals for Low-Dimensional Parameter…
We study confidence interval construction for linear regression under Huber's contamination model, where an unknown fraction of noise variables is arbitrarily corrupted. While robust point estimation in this setting is well understood,…
Estimating the conditional mean function is a central task in statistical learning. In this paper, we consider estimation and inference for a nonparametric class of real-valued cadlag functions with bounded sectional variation (Gill et al.,…
For data segmentation in high-dimensional linear regression settings, the regression parameters are often assumed to be sparse segment-wise, which enables many existing methods to estimate the parameters locally via $\ell_1$-regularised…
We study the problem of parameter estimation for time-series possessing two, widely separated, characteristic time scales. The aim is to understand situations where it is desirable to fit a homogenized singlescale model to such multiscale…
Linear mixed models (LMMs) are used extensively to model dependecies of observations in linear regression and are used extensively in many application areas. Parameter estimation for LMMs can be computationally prohibitive on big data.…
This paper studies nonparametric series estimation and inference for the effect of a single variable of interest x on an outcome y in the presence of potentially high-dimensional conditioning variables z. The context is an additively…
Consider a high-dimensional linear regression problem, where the number of covariates is larger than the number of observations and the interest is in estimating the conditional variance of the response variable given the covariates. A…
High-dimensional multivariate time series are challenging due to the dependent and high-dimensional nature of the data, but in many applications there is additional structure that can be exploited to reduce computing time along with…
We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1…
We develop adaptive estimation and inference methods for high-dimensional Gaussian copula regression that achieve the same performance without the knowledge of the marginal transformations as that for high-dimensional linear regression.…
A prediction interval covers a future observation from a random process in repeated sampling, and is typically constructed by identifying a pivotal quantity that is also an ancillary statistic. Analogously, a tolerance interval covers a…
This paper proposes a new method for estimating high-dimensional binary choice models. We consider a semiparametric model that places no distributional assumptions on the error term, allows for heteroskedastic errors, and permits endogenous…
This paper studies inference in the high-dimensional linear regression model with outliers. Sparsity constraints are imposed on the vector of coefficients of the covariates. The number of outliers can grow with the sample size while their…
Experimental designs based on the classical D-optimal criterion minimize the volume of the linear-approximation inference regions for the parameters using local sensitivity coefficients. For nonlinear models, these designs can be unreliable…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
In functional linear regression, the parameters estimation involves solving a non necessarily well-posed problem and it has points of contact with a range of methodologies, including statistical smoothing, deconvolution and projection on…
High-dimensional group inference is an essential part of statistical methods for analysing complex data sets, including hierarchical testing, tests of interaction, detection of heterogeneous treatment effects and inference for local…
This paper considers the generation of prediction intervals (PIs) by neural networks for quantifying uncertainty in regression tasks. It is axiomatic that high-quality PIs should be as narrow as possible, whilst capturing a specified…
Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…
Constructing valid inferential methods for constrained parameters in normal and Poisson distributions represents two fundamental and important problems in applied statistics, for which there is currently no unified framework for statistical…