Related papers: Asymptotics of constrained $M$-estimation under co…
We establish asymptotic properties of $M$-estimators, defined in terms of a contrast function and observations from a continuous-time locally stationary process. Using the stationary approximation of the sequence, $\theta$-weak dependence,…
This paper revisits a fundamental problem in statistical inference from a non-asymptotic theoretical viewpoint $\unicode{x2013}$ the construction of confidence sets. We establish a finite-sample bound for the estimator, characterizing its…
In this paper, we consider asymptotics of the optimal value and the optimal solutions of parametric minimax estimation problems. Specifically, we consider estimators of the optimal value and the optimal solutions in a sample minimax problem…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…
The recent empirical work of Amaya et al. (2015) has pointed out that the realized skewness, which is the sample skewness of intraday high-frequency returns of a financial asset, serves as forecasting future returns in the cross-section.…
We derive a new representation for $U$- and $V$-statistics. Using this representation, the asymptotic distribution of $U$- and $V$-statistics can be derived by a direct application of the Continuous Mapping theorem. That novel approach not…
Causal inference with observational studies often relies on the assumptions of unconfoundedness and overlap of covariate distributions in different treatment groups. The overlap assumption is violated when some units have propensity scores…
We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…
Contemporary machine learning applications often involve classification tasks with many classes. Despite their extensive use, a precise understanding of the statistical properties and behavior of classification algorithms is still missing,…
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…
In this paper we address the convergence of stochastic approximation when the functions to be minimized are not convex and nonsmooth. We show that the "mean-limit" approach to the convergence which leads, for smooth problems, to the ODE…
Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical techniques based on maximum likelihood and related methods. Recently Ghosh et al. (2013) proposed a general class…
For the zone of moderate deviation probabilities the local asymptotic minimax lower bound of asymptotic efficiency of estimators is established. The estimation parameter is multidimensional. The lower bound admits the interpretation as the…
This paper presents a general asymptotic theory of sequential Bayesian estimation giving results for the strongest, almost sure convergence. We show that under certain smoothness conditions on the probability model, the greedy information…
We present a new finite-sample analysis of M-estimators of locations in $\mathbb{R}^d$ using the tool of the influence function. In particular, we show that the deviations of an M-estimator can be controlled thanks to its influence function…
The classical asymptotic theory for parametric $M$-estimators guarantees that, in the limit of infinite sample size, the excess risk has a chi-square type distribution, even in the misspecified case. We demonstrate how self-concordance of…
Modern statistical inference tasks often require iterative optimization methods to compute the solution. Convergence analysis from an optimization viewpoint only informs us how well the solution is approximated numerically but overlooks the…
When a parameter of interest is nondifferentiable in the probability, the existing theory of semiparametric efficient estimation is not applicable, as it does not have an influence function. Song (2014) recently developed a local asymptotic…
This paper studies high-dimensional M-estimation in the proportional asymptotic regime (p/n -> gamma > 0) when the noise distribution has infinite variance. For noise with regularly-varying tails of index alpha in (1,2), we establish that…