Related papers: Robust Kernel Density Estimation with Median-of-Me…
Frequent significant deviations of the observed magnitude distribution of anthropogenic seismicity from the Gutenberg-Richter relation require alternative estimation methods for probabilistic seismic hazard assessments. We evaluate five…
In this paper, we will discuss how to generalize nonparametric density estimators to MLE parametric estimators. Basing on the Parzen window theory and using the advantages of probability amplitude of quantum theory, we model a nonlinear…
The discrete kernel method was developed to estimate count data distributions, distinguishing discrete associated kernels based on their asymptotic behaviour. This study investigates the class of discrete asymmetric kernels and their…
Kernel-based nonparametric hazard rate estimation is considered with a special class of infinite-order kernels that achieves favorable bias and mean square error properties. A fully automatic and adaptive implementation of a density and…
Machine-Learned Likelihoods (MLL) combines machine-learning classification techniques with likelihood-based inference tests to estimate the experimental sensitivity of high-dimensional data sets. We extend the MLL method by including Kernel…
In this paper we prove large and moderate deviations principles for the recursive kernel estimator of a probability density function and its partial derivatives. Unlike the density estimator, the derivatives estimators exhibit a quadratic…
In this paper, we study the strong consistency of a bias reduced kernel density estimator and derive a strongly con- sistent Kullback-Leibler divergence (KLD) estimator. As application, we formulate a goodness-of-fit test and an…
Stochastic processes are random variables with values in some space of paths. However, reducing a stochastic process to a path-valued random variable ignores its filtration, i.e. the flow of information carried by the process through time.…
Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate…
Importance sampling with data-driven proposal distributions is widely used in practice. A common workflow first generates an auxiliary sample of size $N$ from an approximation of the target distribution, constructs a density estimate $\hat…
The standard definition of pedestrian density produces scattered values, hence, many approaches have been developed to improve the features of the estimated density. This paper provides a review of generally applied methods and presents a…
We consider the problem of estimation of a bivariate density function with support $\Re\times[0,\infty)$, where a classical bivariate kernel estimator causes boundary bias due to the non-negative variable. To overcome this problem, we…
Given $M \geq 2$ distributions defined on a general measurable space, we introduce a nonparametric (kernel) measure of multi-sample dissimilarity (KMD) -- a parameter that quantifies the difference between the $M$ distributions. The…
Dyadic data is often encountered when quantities of interest are associated with the edges of a network. As such it plays an important role in statistics, econometrics and many other data science disciplines. We consider the problem of…
Goodness-of-fit testing is often criticized for its lack of practical relevance: since ``all models are wrong'', the null hypothesis that the data conform to our model is ultimately always rejected as the sample size grows. Despite this,…
We study the problem of space and time efficient evaluation of a nonparametric estimator that approximates an unknown density. In the regime where consistent estimation is possible, we use a piecewise multivariate polynomial interpolation…
In this work, we generalize the Cram\'er-von Mises statistic via projection-averaging to obtain a robust test for the multivariate two-sample problem. The proposed test is consistent against all fixed alternatives, robust to heavy-tailed…
In this paper, we consider the problem of estimating the marginal density in some nonlinear autoregressive time series models for which the conditional mean and variance have a parametric specification. Under some regularity conditions, we…
We study the density estimation problem with observations generated by certain dynamical systems that admit a unique underlying invariant Lebesgue density. Observations drawn from dynamical systems are not independent and moreover, usual…
Kernel density estimation and kernel regression are powerful but computationally expensive techniques: a direct evaluation of kernel density estimates at $M$ evaluation points given $N$ input sample points requires a quadratic…