Related papers: Laplace deconvolution with noisy observations
We consider the problem of estimating the unknown response function in the multichannel deconvolution model with long-range dependent Gaussian errors. We do not limit our consideration to a specific type of long-range dependence rather we…
Nonparametric regression problems with qualitative constraints such as monotonicity or convexity are ubiquitous in applications. For example, in predicting the yield of a factory in terms of the number of labor hours, the monotonicity of…
We consider the nonparametric estimation of the intensity function of a Poisson point process in a circular model from indirect observations $N_1,\ldots,N_n$. These observations emerge from hidden point process realizations with the target…
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…
Estimation and prediction problems for dense signals are often framed in terms of minimax problems over highly symmetric parameter spaces. In this paper, we study minimax problems over l2-balls for high-dimensional linear models with…
Given data generated by an observable stochastic process, we study how to construct statistically optimal decisions for general stochastic optimization problems. Our setting encompasses non-standard data structures, including data…
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 work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…
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 study the problem of finding the index of the minimum value of a vector from noisy observations. This problem is relevant in population/policy comparison, discrete maximum likelihood, and model selection. We develop an asymptotically…
Sequential data collection has emerged as a widely adopted technique for enhancing the efficiency of data gathering processes. Despite its advantages, such data collection mechanism often introduces complexities to the statistical inference…
We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an…
This paper deals with the parametric inference for integrated signals embedded in an additive Gaussian noise and observed at deterministic discrete instants which are not necessarily equidistant. The unknown parameter is multidimensional…
Given a differentially private unbiased estimate $\tilde{q}=q(D) +\nu$ of a statistic $q(D)$, we wish to obtain unbiased estimates of functions of $q(D)$, such as $1/q(D)$, solely through post-processing of $\tilde{q}$, with no further…
The density deconvolution problem involves recovering a target density g from a sample that has been corrupted by noise. From the perspective of Le Cam's local asymptotic normality theory, we show that non-parametric density deconvolution…
In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…
We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…
New upper bounds are developed for the $L_2$ distance between $\xi/\text{Var}[\xi]^{1/2}$ and linear and quadratic functions of $z\sim N(0,I_n)$ for random variables of the form $\xi=bz^\top f(z) - \text{div} f(z)$. The linear approximation…
We study the reknown deconvolution problem of recovering a distribution function from independent replicates (signal) additively contaminated with random errors (noise), whose distribution is known. We investigate whether a Bayesian…
We analyze the performance of a data-assimilation algorithm based on a linear feedback control when used with observational data that contains measurement errors. Our model problem consists of dynamics governed by the two-dimension…