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The density weighted average derivative (DWAD) of a regression function is a canonical parameter of interest in economics. Classical first-order large sample distribution theory for kernel-based DWAD estimators relies on tuning parameter…
Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on…
We construct a density estimator and an estimator of the distribution function in the uniform deconvolution model. The estimators are based on inversion formulas and kernel estimators of the density of the observations and its derivative.…
Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature. We first show that both notions coincide, so that insights…
This paper discusses the local linear smoothing to estimate the unknown first and second infinitesimal moments in second-order jump-diffusion model based on Gamma asymmetric kernels. Under the mild conditions, we obtain the weak consistency…
Datasets from the fields of bioinformatics, chemometrics, and face recognition are typically characterized by small samples of high-dimensional data. Among the many variants of linear discriminant analysis that have been proposed in order…
Causal inference with observational studies often relies on the assumptions of unconfoundedness and overlap of covariate distributions in different treatment groups. The overlap assumption is violated when some units have propensity scores…
We consider tensor product random fields $Y_d$, $d\in\mathbb{N}$, whose covariance funtions are Gaussian kernels. The average case approximation complexity $n^{Y_d}(\varepsilon)$ is defined as the minimal number of evaluations of arbitrary…
In this short note, we prove an asymptotic expansion for the ratio of the Dirichlet density to the multivariate normal density with the same mean and covariance matrix. The expansion is then used to derive an upper bound on the total…
In this paper, we study the properties of averaged fundamental solutions of a special type for Laplace operators in the Euclidean space of an arbitrary dimension. We consider a class of kernels suitable for probabilistic averaging, and…
In this paper we study some asymptotic properties of the kernel conditional quantile estimator with randomly left-truncated data which exhibit some kind of dependence. We extend the result obtained by Lemdani, Ould-Sa\"id and Poulin [16] in…
Kernel matching is a widely used technique for estimating treatment effects, particularly valuable in observational studies where randomized controlled trials are not feasible. While kernel-matching approaches have demonstrated practical…
This paper proposes nonparametric kernel-smoothing estimation for panel data to examine the degree of heterogeneity across cross-sectional units. We first estimate the sample mean, autocovariances, and autocorrelations for each unit and…
The paper concerns the asymptotic distribution of the mixture density estimator, proposed by Oppenheim et al 2006, in the aggregation/disaggregation problem of random parameter AR(1) process. We prove that, under mild conditions on the…
Let $\alpha_n(\cdot)=P\bigl(X_{n+1}\in\cdot\mid X_1,\ldots,X_n\bigr)$ be the predictive distributions of a sequence $(X_1,X_2,\ldots)$ of $p$-dimensional random vectors. Suppose $$\alpha_n= \mathcal{N} _p (M_n,Q_n)$$ where…
This paper is devoted to parameter estimation for partially observed polynomial state space models. This class includes discretely observed affine or more generally polynomial Markov processes. The polynomial structure allows for the…
Local differential privacy has become the gold-standard of privacy literature for gathering or releasing sensitive individual data points in a privacy-preserving manner. However, locally differential data can twist the probability density…
We discuss asymptotic properties of a family of discrete probability measures which may be used to model particle configurations with a wall on a set of discrete nodes. The correlations are shown to be determinantal and are expressed in…
We consider nonparametric estimation of the derivative of a probability density function with the bounded support on $[0,\infty)$. Estimates are looked up in the class of estimates with asymmetric gamma kernel functions. The use of gamma…
For two decades, reproducing kernels and their associated discrepancies have facilitated elegant theoretical analyses in the setting of quasi Monte Carlo. These same tools are now receiving interest in statistics and related fields, as…