Related papers: Sequential Multiple Testing: A Second-Order Asympt…
We propose a new approach to sequential testing which is an adaptive (on-line) extension of the (off-line) framework developed in [10]. It relies upon testing of pairs of hypotheses in the case where each hypothesis states that the vector…
We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster…
We consider exact asymptotics of the minimax risk for global testing against sparse alternatives in the context of high dimensional linear regression. Our results characterize the leading order behavior of this minimax risk in several…
A distributed binary hypothesis testing problem, in which multiple observers transmit their observations to a detector over noisy channels, is studied. Given its own side information, the goal of the detector is to decide between two…
In this paper, we consider sequential testing over a single-sensor, a single-decision center setup. At each time instant $t$, the sensor gets $k$ samples $(k>0)$ and describes the observed sequence until time $t$ to the decision center over…
The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function,…
We treat the statistical inference problems in which one needs to detect and estimate simultaneously using as small number of samples as possible. Conventional methods treat the detection and estimation subproblems separately, ignoring the…
We assume the direct sum <A> o <B> for the signal subspace. As a result of post- measurement, a number of operational contexts presuppose the a priori knowledge of the LB -dimensional "interfering" subspace <B> and the goal is to estimate…
This paper considers the asymptotic theory of a semiparametric M-estimator that is generally applicable to models that satisfy a monotonicity condition in one or several parametric indexes. We call the estimator two-stage maximum score…
The paper is devoted to deriving novel second-order necessary and sufficient optimality conditions for local minimizers in rather general classes of nonsmooth unconstrained and constrained optimization problems in finite-dimensional spaces.…
In this paper, we introduce a new method for testing the stationarity of time series, where the test statistic is obtained from measuring and maximising the difference in the second-order structure over pairs of randomly drawn intervals.…
We analyze the asymptotic performance of a generalized multiuser diversity scheme for an interference-limited secondary multiuser network of underlay cognitive radio systems. Assuming a large number of secondary users and that the noise at…
Consider a situation of analyzing high-dimensional count data containing an excess of near-zero counts with a small number of moderate or large counts. Assuming that the observations are modeled by a Poisson distribution, we are interested…
We propose a new approach to compute an interval over-approximation of the finite time reachable set for a large class of nonlinear systems. This approach relies on the notions of sensitivity matrices, which are the partial derivatives…
First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored…
In this work, we study Bayesian quantum parameter estimation given a finite number of uses of the process encoding one or more unknown physical quantities. For multiple uses, it is conventional to classify quantum metrological protocols as…
The problem of searching for $L$ anomalous processes among $M$ processes is considered. At each time, the decision maker can observe a subset of $K$ processes (i.e., multiple plays). The measurement drawn when observing a process follows…
In this article we investigate consistency and asymptotic normality of the maximum likelihood and the posterior distribution of the parameters in the context of state space stochastic differential equations (SDEs). We then extend our…
Recent advances in noiseless non-adaptive group testing have led to a precise asymptotic characterization of the number of tests required for high-probability recovery in the sublinear regime $k = n^{\theta}$ (with $\theta \in (0,1)$), with…
In this paper, we consider the nonasymptotic sequential estimation of means of random variables bounded in between zero and one. We have rigorously demonstrated that, in order to guarantee prescribed relative precision and confidence level,…