Related papers: Estimating the conditional density by histogram ty…
The paper considers probability distribution, density, conditional distribution and density and conditional moments as well as their kernel estimators in spaces of generalized functions. This approach does not require restrictions on…
Estimation frameworks for statistical inference are preferred to hypothesis testing when quantifying uncertainty and precise estimation are more valuable than binary decisions about statistical significance. Study design for…
We present a novel framework for performing statistical sampling, expectation estimation, and partition function approximation using \emph{arbitrary} heuristic stochastic processes defined over discrete state spaces. Using a highly parallel…
For discrete-time survival data, conditional likelihood inference in Cox's hazard odds model is theoretically desirable but exact calculation is numerical intractable with a moderate to large number of tied events. Unconditional maximum…
Conditional density estimation (CDE) is the task of estimating the probability of an event conditioned on some inputs. A neural network (NN) can also be used to compute the output distribution for continuous-domain, which can be viewed as…
We consider the problem of model selection type aggregation in the context of density estimation. We first show that empirical risk minimization is sub-optimal for this problem and it shares this property with the exponential weights…
Mathematical models for complex systems under random fluctuations often certain uncertain parameters. However, quantifying model uncertainty for a stochastic differential equation with an $\alpha$-stable L\'evy process is still lacking.…
Divergence estimators based on direct approximation of density-ratios without going through separate approximation of numerator and denominator densities have been successfully applied to machine learning tasks that involve distribution…
Nonparametric mixture models based on the Pitman-Yor process represent a flexible tool for density estimation and clustering. Natural generalization of the popular class of Dirichlet process mixture models, they allow for more robust…
Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…
Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges…
Compromise estimation entails using a weighted average of outputs from several candidate models, and is a viable alternative to model selection when the choice of model is not obvious. As such, it is a tool used by both frequentists and…
Algorithms for jointly obtaining projection estimates of the density and distribution function of a random variable using Legendre polynomials are proposed. For these algorithms, a problem of the conditional optimization is solved. Such…
There are several estimators of conditional probability from observed frequencies of features. In this paper, we propose using the lower limit of confidence interval on posterior distribution determined by the observed frequencies to…
Model selection consistency in the high-dimensional regression setting can be achieved only if strong assumptions are fulfilled. We therefore suggest to pursue a different goal, which we call a minimal class of models. The minimal class of…
We tackle the natural question of whether it is possible to estimate conditional distributions via Sklar's theorem by separately estimating the conditional distributions of the underlying copula and the marginals. Working with so-called…
If the probability distribution model aims to approximate the hidden mother distribution, it is imperative to establish a useful criterion for the resemblance between the mother and the model distributions. This study proposes a criterion…
In this paper we introduce new estimators of the coefficient functions in the varying coefficient regression model. The proposed estimators are obtained by projecting the vector of the full-dimensional kernel-weighted local polynomial…
We present a new non-parametric estimator of the conditional density of the kernel type. It is based on an efficient transformation of the data by quantile transform. By use of the copula representation, it turns out to have a remarkable…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…