Related papers: Influence Function: Local Robustness and Efficienc…
In the last few years, many works have tried to explain the predictions of deep learning models. Few methods, however, have been proposed to verify the accuracy or faithfulness of these explanations. Recently, influence functions, which is…
The functional delta-method provides a convenient tool for deriving the asymptotic distribution of a plug-in estimator of a statistical functional from the asymptotic distribution of the respective empirical process. Moreover, it provides a…
Robust M-estimation uses loss functions, such as least absolute deviation (LAD), quantile loss and Huber's loss, to construct its objective function, in order to for example eschew the impact of outliers, whereas the difficulty in analysing…
The paper discusses inference techniques for semiparametric models based on suitable versions of inference functions. The text contains two parts. In the first part, we review the optimality theory for non-parametric models based on the…
In this study, we focus on a generalized nonparametric scalar-on-function regression model for heterogeneously distributed and strongly mixing data. We provide almost complete convergence rates for the local linear estimator of the…
We introduce a double/debiased machine learning estimator for the impulse response function in settings where a time series of interest is subjected to multiple discrete treatments, assigned over time, which can have a causal effect on…
Many causal parameters are linear functionals of an underlying regression. The Riesz representer is a key component in the asymptotic variance of a semiparametrically estimated linear functional. We propose an adversarial framework to…
Study samples often differ from the target populations of inference and policy decisions in non-random ways. Researchers typically believe that such departures from random sampling -- due to changes in the population over time and space, or…
Function-on-function regression has been a topic of substantial interest due to its broad applicability, where the relation between functional predictor and response is concerned. In this article, we propose a new framework for modeling the…
Motivated by applications in emergency response and experimental design, we consider smooth stochastic optimization problems over probability measures supported on compact subsets of the Euclidean space. With the influence function as the…
The transformation of the path integral measure under the reduction procedure in the dynamical systems with a symmetry is considered. The investigation is carried out in the case of the Wiener--type path integrals that are used for…
We develop a novel and general framework for reduced-bias $M$-estimation from asymptotically unbiased estimating functions. The framework relies on an empirical approximation of the bias by a function of derivatives of estimating function…
Influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations. For high-dimensional data, it is particularly so, as the increased dimensionality and complexity…
This article considers nonparametric regression models with multivariate covariates and with responses missing at random. We estimate the regression function with a local polynomial smoother. The residual-based empirical distribution…
We show that any smooth bi-Lipschitz $h$ can be represented exactly as a composition $h_m \circ ... \circ h_1$ of functions $h_1,...,h_m$ that are close to the identity in the sense that each $\left(h_i-\mathrm{Id}\right)$ is Lipschitz, and…
We study a method for calculating the utility function from a candidate of a demand function that is not differentiable, but is locally Lipschitz. Using this method, we obtain two new necessary and sufficient conditions for a candidate of a…
We consider the estimation of the value of a linear functional of the slope parameter in functional linear regression, where scalar responses are modeled in dependence of random functions. The theory in this paper covers in particular…
Influence functions estimate the effect of removing a training point on a model without the need to retrain. They are based on a first-order Taylor approximation that is guaranteed to be accurate for sufficiently small changes to the model,…
We present a new finite-sample analysis of M-estimators of locations in $\mathbb{R}^d$ using the tool of the influence function. In particular, we show that the deviations of an M-estimator can be controlled thanks to its influence function…
The semivarying coefficient models are widely used in the application of finance, economics, medical science and many other areas. The functional coefficients are commonly estimated by local smoothing methods, e.g. local linear estimator.…