Related papers: Sharp adaptive nonparametric testing for Sobolev e…
In this paper, we investigate optimal linear approximations ($n$-approximation numbers ) of the embeddings from the Sobolev spaces $H^r\ (r>0)$ for various equivalent norms and the Gevrey type spaces $G^{\alpha,\beta}\ (\alpha,\beta>0)$ on…
This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong…
This paper addresses the problem of deriving the asymptotic performance of adaptive Low Rank (LR) filters used in target detection embedded in a disturbance composed of a LR Gaussian noise plus a white Gaussian noise. In this context, we…
We consider tests of hypotheses when the parameters are not identifiable under the null in semiparametric models, where regularity conditions for profile likelihood theory fail. Exponential average tests based on integrated profile…
This paper investigates asymptotic minimaxity properties of Bayesian multiple testing rules in the sparse Gaussian sequence model using a broad class of global-local scale mixtures of normals as priors for the means. Minimaxity is studied…
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…
The solvability in Sobolev spaces $W^{1,2}_p$ is proved for nondivergence form second order parabolic equations for $p>2$ close to 2. The leading coefficients are assumed to be measurable in the time variable and two coordinates of space…
Arbitrary matrices $M \in \mathbb{R}^{m \times n}$, randomly perturbed in an additive manner using a random matrix $R \in \mathbb{R}^{m \times n}$, are shown to asymptotically almost surely satisfy the so-called {\sl robust null space…
Consider the noisy underdetermined system of linear equations: y=Ax0 + z0, with n x N measurement matrix A, n < N, and Gaussian white noise z0 ~ N(0,\sigma^2 I). Both y and A are known, both x0 and z0 are unknown, and we seek an…
Consider estimating a structured signal $\mathbf{x}_0$ from linear, underdetermined and noisy measurements $\mathbf{y}=\mathbf{A}\mathbf{x}_0+\mathbf{z}$, via solving a variant of the lasso algorithm: $\hat{\mathbf{x}}=\arg\min_\mathbf{x}\{…
Regularized linear regression under the $\ell_1$ penalty, such as the Lasso, has been shown to be effective in variable selection and sparse modeling. The sampling distribution of an $\ell_1$-penalized estimator $\hat{\beta}$ is hard to…
We consider unbiased estimation of a sparse nonrandom vector corrupted by additive white Gaussian noise. We show that while there are infinitely many unbiased estimators for this problem, none of them has uniformly minimum variance.…
Misspecified models often provide useful information about the true data generating distribution. For example, if $y$ is a non-linear function of $x$ the least squares estimator $\hat{\beta}$ is an estimate of $\beta$, the slope of the best…
We consider spherical data $X_i$ noised by a random rotation $\varepsilon_i\in$ SO(3) so that only the sample $Z_i=\varepsilon_iX_i$, $i=1,\dots, N$ is observed. We define a nonparametric test procedure to distinguish $H_0:$ ''the density…
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…
This paper considers the problem of robust adaptive efficient estimating of a periodic function in a continuous time regression model with the dependent noises given by a general square integrable semimartingale with a conditionally…
The paper deals with asymptotic properties of the adaptive procedure proposed in the author paper (2007) for estimation of unknown nonparametric regression. We prove that this procedure is asymptotically efficient for a quadratic risk. It…
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…
This work considers the problem of finding a first-order stationary point of a non-convex function with potentially unbounded smoothness constant using a stochastic gradient oracle. We focus on the class of $(L_0,L_1)$-smooth functions…
Wasserstein distributionally robust optimization (WDRO) strengthens statistical learning under model uncertainty by minimizing the local worst-case risk within a prescribed ambiguity set. Although WDRO has been extensively studied in…