Related papers: Efficient estimation of the error distribution fun…
This study considers regression analysis of a circular response with an error-prone linear covariate. Starting with an existing estimator of the circular regression function that assumes error-free covariate, three approaches are proposed…
The main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of…
The paper deals with the nonparametric estimation problem at a given fixed point for an autoregressive model with unknown distributed noise. Kernel estimate modifications are proposed. Asymptotic minimax and efficiency properties for…
The paper deals with asymptotic properties of the adaptive procedure proposed in the author paper (2007) for estimation of unknown nonparametric regression. We prove that this procedure is asymptotically efficient for a quadratic risk. It…
Estimating linear regression using least squares and reporting robust standard errors is very common in financial economics, and indeed, much of the social sciences and elsewhere. For thick tailed predictors under heteroskedasticity this…
This study examines the optimal selections of bandwidth and semi-metric for a functional partial linear model. Our proposed method begins by estimating the unknown error density using a kernel density estimator of residuals, where the…
`Distribution regression' refers to the situation where a response Y depends on a covariate P where P is a probability distribution. The model is Y=f(P) + mu where f is an unknown regression function and mu is a random error. Typically, we…
We investigate the issue of bandwidth estimation in a nonparametric functional regression model with function-valued, continuous real-valued and discrete-valued regressors under the framework of unknown error density. Extending from the…
Benchmarking studies in computational chemistry use reference datasets to assess the accuracy of a method through error statistics. The commonly used error statistics, such as the mean signed and mean unsigned errors, do not inform…
We propose and analyze estimators for statistical functionals of one or more distributions under nonparametric assumptions. Our estimators are based on the theory of influence functions, which appear in the semiparametric statistics…
A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty. Minimizing overall prediction error often encourages models to prioritize informativeness over calibration,…
Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…
We propose a model selection approach for covariance estimation of a multi-dimensional stochastic process. Under very general assumptions, observing i.i.d replications of the process at fixed observation points, we construct an estimator of…
Triangular systems with nonadditively separable unobserved heterogeneity provide a theoretically appealing framework for the modelling of complex structural relationships. However, they are not commonly used in practice due to the need for…
This paper establishes bounds on the performance of empirical risk minimization for large-dimensional linear regression. We generalize existing results by allowing the data to be dependent and heavy-tailed. The analysis covers both the…
We study the problem of robustly estimating the mean of a $d$-dimensional distribution given $N$ examples, where most coordinates of every example may be missing and $\varepsilon N$ examples may be arbitrarily corrupted. Assuming each…
Distributional regression aims at estimating the conditional distribution of a targetvariable given explanatory co-variates. It is a crucial tool for forecasting whena precise uncertainty quantification is required. A popular methodology…
In the context of regressing a response $Y$ on a predictor $X$, we consider estimating the local modes of the distribution of $Y$ given $X=x$ when $X$ is prone to measurement error. We propose two nonparametric estimation methods, with one…
We consider an empirical likelihood inference for parameters defined by general estimating equations when some components of the random observations are subject to missingness. As the nature of the estimating equations is wide-ranging, we…
We consider the residual-based or naive bootstrap for functional autoregressions of order 1 and prove that it is asymptotically valid for, e.g., the sample mean and for empirical covariance operator estimates. As a crucial auxiliary result,…