Related papers: Minimax Optimal Conditional Density Estimation und…
In this paper, we consider the problem of estimating a conditional density in moderately large dimensions. Much more informative than regression functions, conditional densities are of main interest in recent methods, particularly in the…
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…
We investigate Bayesian nonparametric density estimation via orthogonal polynomial expansions in weighted Sobolev spaces. A core challenge is establishing minimax optimal posterior convergence rates, especially for densities on unbounded…
A scheme for locally adaptive bandwidth selection is proposed which sensitively shrinks the bandwidth of a kernel estimator at lowest density regions such as the support boundary which are unknown to the statistician. In case of a…
We propose an estimation method for the conditional mode when the conditioning variable is high-dimensional. In the proposed method, we first estimate the conditional density by solving quantile regressions multiple times. We then estimate…
Many causal estimands, such as average treatment effects under unconfoundedness, can be written as continuous linear functionals of an unknown regression function. We study a weighting estimator that sets weights by a minimax procedure:…
Bayesian density deconvolution using nonparametric prior distributions is a useful alternative to the frequentist kernel based deconvolution estimators due to its potentially wide range of applicability, straightforward uncertainty…
We consider the nonparametric estimation problem of time-dependent multivariate functions observed in a presence of additive cylindrical Gaussian white noise of a small intensity. We derive minimax lower bounds for the $L^2$-risk in the…
This paper develops a nonparametric density estimator with parametric overtones. Suppose $f(x,\theta)$ is some family of densities, indexed by a vector of parameters $\theta$. We define a local kernel smoothed likelihood function which for…
The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…
We solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…
We establish minimax optimal rates of convergence for estimation in a high dimensional additive model assuming that it is approximately sparse. Our results reveal an interesting phase transition behavior universal to this class of high…
We consider the problem of estimating the structural function in nonparametric instrumental regression, where in the presence of an instrument W a response Y is modeled in dependence of an endogenous explanatory variable Z. The proposed…
We consider the goodness-of-fit testing problem of distinguishing whether the data are drawn from a specified distribution, versus a composite alternative separated from the null in the total variation metric. In the discrete case, we…
In this paper, we derive minimax rates for estimating both parametric and nonparametric components in partially linear additive models with high dimensional sparse vectors and smooth functional components. The minimax lower bound for…
In this paper, we introduce a new estimator for the emission densities of a nonparametric hidden Markov model. It is adaptive and minimax with respect to each state's regularity--as opposed to globally minimax estimators, which adapt to the…
We consider nonparametric estimation of a mixed discrete-continuous distribution under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution. For these settings, we…
We study the multivariate nonparametric change point detection problem, where the data are a sequence of independent $p$-dimensional random vectors whose distributions are piecewise-constant with Lipschitz densities changing at unknown…
In some applications (e.g., in cosmology and economics), the regression E[Z|x] is not adequate to represent the association between a predictor x and a response Z because of multi-modality and asymmetry of f(z|x); using the full density…
We consider non-parametric estimation problems in the presence of dependent data, notably non-parametric regression with random design and non-parametric density estimation. The proposed estimation procedure is based on a dimension…