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Modern problems in statistics tend to include estimators of high computational complexity and with complicated distributions. Statistical inference on such estimators usually relies on asymptotic normality assumptions, however, such…
Conformal prediction is a distribution-free and model-agnostic uncertainty-quantification method that provides finite-sample prediction intervals with guaranteed coverage. In this work, for the first time, we apply conformal-prediction to…
Conformal prediction provides a distribution-free framework for uncertainty quantification. This study explores the application of conformal prediction in scenarios where covariates are missing, which introduces significant challenges for…
Consider the semiparametric transformation model $\Lambda_{\theta_o}(Y)=m(X)+\epsilon$, where $\theta_o$ is an unknown finite dimensional parameter, the functions $\Lambda_{\theta_o}$ and $m$ are smooth, $\epsilon$ is independent of $X$,…
Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…
We estimate on a compact interval densities with isolated irregularities, such as discontinuities or discontinuities in some derivatives. From independent and identically distributed observations we construct a kernel estimator with…
This paper presents a computationally feasible method to compute rigorous bounds on the interval-generalisation of regression analysis to account for epistemic uncertainty in the output variables. The new iterative method uses machine…
We propose estimators based on kernel ridge regression for nonparametric causal functions such as dose, heterogeneous, and incremental response curves. Treatment and covariates may be discrete or continuous in general spaces. Due to a…
A class of estimating functions is introduced for the regression parameter of the Cox proportional hazards model to allow unknown failure statuses on some study subjects. The consistency and asymptotic normality of the resulting estimators…
Kernel-based modal statistical methods include mode estimation, regression, and clustering. Estimation accuracy of these methods depends on the kernel used as well as the bandwidth. We study effect of the selection of the kernel function to…
Nonparametric regression problems with qualitative constraints such as monotonicity or convexity are ubiquitous in applications. For example, in predicting the yield of a factory in terms of the number of labor hours, the monotonicity of…
This paper develops inferential methods for a very general class of ill-posed models in econometrics encompassing the nonparametric instrumental variable regression, various functional regressions, and the density deconvolution. We focus on…
We explore a novel methodology for constructing confidence regions for parameters of linear models, using predictions from any arbitrary predictor. Our framework requires minimal assumptions on the noise and can be extended to functions…
In this paper we study the asymptotic normality in high-dimensional linear regression. We focus on the case where the covariance matrix of the regression variables has a KMS structure, in asymptotic settings where the number of predictors,…
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 problem of error density estimation for a functional single index model with dependent errors is studied. A Bayesian method is utilized to simultaneously estimate the bandwidths in the kernel-form error density and regression function,…
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…
Depth measures are powerful tools for defining level sets in emerging, non--standard, and complex random objects such as high-dimensional multivariate data, functional data, and random graphs. Despite their favorable theoretical properties,…
In this paper we investigate the problem of estimating the regression function in models with correlated observations. The data is obtained from several experimental units each of them forms a time series. We propose a new estimator based…
We introduce a novel approach to estimation problems in settings with missing data. Our proposal -- the Correlation-Assisted Missing data (CAM) estimator -- works by exploiting the relationship between the observations with missing features…