Related papers: Marginal density estimation for linear processes w…
Density regression characterizes the conditional density of the response variable given the covariates, and provides much more information than the commonly used conditional mean or quantile regression. However, it is often computationally…
We investigate the discrepancy principle for choosing smoothing parameters for kernel density estimation. The method is based on the distance between the empirical and estimated distribution functions. We prove some new positive and…
Kernel Estimation provides an unbinned and non-parametric estimate of the probability density function from which a set of data is drawn. In the first section, after a brief discussion on parametric and non-parametric methods, the theory of…
We analyze four different approaches to estimate a multivariate probability density (or the log-density) and its first and second order derivatives. Two methods, local log-likelihood and local Hyv\"arinen score estimation, are in terms of…
We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…
A powerful tool for studying long-term convergence of a Markov process to its stationary distribution is a Lyapunov function. In some sense, this is a substitute for eigenfunctions. For a stochastically ordered Markov process on the…
In numerous applications data are observed at random times and an estimated graph of the spectral density may be relevant for characterizing and explaining phenomena. By using a wavelet analysis, one derives a nonparametric estimator of the…
The generalized filtered method of moments was developed in the recent papers by Alomari et al., 2020, and Ayache et al., 2022. It used functional data obtained from continuously sampled cyclic long-memory stochastic processes to…
Spectral singularities at non-zero frequencies play an important role in investigating cyclic or seasonal time series. The publication [2] introduced the generalized filtered method-of-moments approach to simultaneously estimate singularity…
This article provides convergence analysis of online stochastic gradient descent algorithms for functional linear models. Adopting the characterizations of the slope function regularity, the kernel space capacity, and the capacity of the…
This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…
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…
Polynomial convergence rate to stationarity is shown for extended Erlang -- Sevastyanov's model.
This paper addresses the estimation of locally stationary long-range dependent processes, a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency. A time-varying…
In this paper, we establish sharp two-sided estimates for the transition densities of relativistic stable processes [i.e., for the heat kernels of the operators $m-(m^{2/\alpha}-\Delta)^{\alpha/2}$] in $C^{1,1}$ open sets. Here $m>0$ and…
Estimating expected polynomials of density functions from samples is a basic problem with numerous applications in statistics and information theory. Although kernel density estimators are widely used in practice for such functional…
Long memory or long range dependency is an important phenomenon that may arise in the analysis of time series or spatial data. Most of the definitions of long memory of a stationary process $X=\{X_1, X_2,\cdots,\}$ are based on the…
In this paper we introduce randomized pivots for the means of short and long memory linear processes. We show that, under the same conditions, these pivots converge in distribution to the same limit as that of their classical non-randomized…
We introduce a novel conditional density estimation model termed the conditional density operator (CDO). It naturally captures multivariate, multimodal output densities and shows performance that is competitive with recent neural…
Bitseki and Delmas (2021) have studied recently the central limit theorem for kernel estimator of invariant density in bifurcating Markov chains models. We complete their work by proving a moderate deviation principle for this estimator.…