Related papers: Fractional order statistic approximation for nonpa…

In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that noisy information about the gradients of the objective function is available via a stochastic first-order oracle (SFO). We…

Conformal prediction provides prediction sets with coverage guarantees. The informativeness of conformal prediction depends on its efficiency, typically quantified by the expected size of the prediction set. Prior work on the efficiency of…

We obtain an asymptotic expansion for the null distribution function of thegradient statistic for testing composite null hypotheses in the presence of nuisance parameters. The expansion is derived using a Bayesian route based on the…

We consider the problem of state estimation in general state-space models using variational inference. For a generic variational family defined using the same backward decomposition as the actual joint smoothing distribution, we establish…

This paper develops a novel nonparametric significance test based on a tailored nonparametric-type projected weighting function that exhibits appealing theoretical and numerical properties. We derive the asymptotic properties of the…

It can be argued that optimal prediction should take into account all available data. Therefore, to evaluate a prediction interval's performance one should employ conditional coverage probability, conditioning on all available observations.…

In this paper we discuss the estimation of a nonparametric component $f_1$ of a nonparametric additive model $Y=f_1(X_1) + ...+ f_q(X_q) + \epsilon$. We allow the number $q$ of additive components to grow to infinity and we make sparsity…

Incomplete U-statistics have been proposed to accelerate computation. They use only a subset of the subsamples required for kernel evaluations by complete U-statistics. This paper gives a finite sample bound in the style of Bernstein's…

We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction…

We introduce uncertainty regions to perform inference on partial correlations when data are missing not at random. These uncertainty regions are shown to have a desired asymptotic coverage. Their finite sample performance is illustrated via…

The traditional kernel density estimator of an unknown density is by construction completely nonparametric, in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of…

This paper studies inference in predictive quantile regressions when the predictive regressor has a near-unit root. We derive asymptotic distributions for the quantile regression estimator and its heteroskedasticity and autocorrelation…

In this paper, we derive the improved uniform error bounds for the long-time dynamics of the $d$-dimensional $(d=2,3)$ nonlinear space fractional sine-Gordon equation (NSFSGE). The nonlinearity strength of the NSFSGE is characterized by…

We consider the problem of providing nonparametric confidence guarantees for undirected graphs under weak assumptions. In particular, we do not assume sparsity, incoherence or Normality. We allow the dimension $D$ to increase with the…

Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may…

We focus on the construction of confidence corridors for multivariate nonparametric generalized quantile regression functions. This construction is based on asymptotic results for the maximal deviation between a suitable nonparametric…

This paper clarifies a fundamental difference between causal inference and traditional statistical inference by formalizing a mathematical distinction between their respective parameters. We connect two major approaches to causal inference,…

Data analysis in science, e.g., high-energy particle physics, is often subject to an intractable likelihood if the observables and observations span a high-dimensional input space. Typically the problem is solved by reducing the…

We present a new method for generating confidence sets within the split conformal prediction framework. Our method performs a trainable transformation of any given conformity score to improve conditional coverage while ensuring exact…

We consider four prototypes of variational problems and prove the existence of fractal minimizers through the direct method in the calculus of variations. By design these minimizers are H\"older curves or H\"older parametrizations of…