Related papers: Gaussian approximation for maximum score and non-s…
We consider the problem of parameter estimation by the observations of deterministic signal in white gaussian noise. It is supposed that the signal has a singularity of cusp-type. The properties of the maximum likelihood and bayesian…
We propose and study an asymptotically optimal Monte Carlo estimator for steady-state expectations of a d-dimensional reflected Brownian motion. Our estimator is asymptotically optimal in the sense that it requires $\tilde{O}(d)$ (up to…
Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…
We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the…
In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…
To tackle massive data, subsampling is a practical approach to select the more informative data points. However, when responses are expensive to measure, developing efficient subsampling schemes is challenging, and an optimal sampling…
This paper develops distribution theory and bootstrap-based inference methods for a broad class of convex pairwise difference estimators. These estimators minimize a kernel-weighted convex-in-parameter function over observation pairs with…
We consider the problem of distributedly estimating Gaussian processes in multi-agent frameworks. Each agent collects few measurements and aims to collaboratively reconstruct a common estimate based on all data. Agents are assumed with…
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…
Several new methods have been proposed for performing valid inference after model selection. An older method is sampling splitting: use part of the data for model selection and part for inference. In this paper we revisit sample splitting…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
This study proposes a computationally efficient semiparametric distribution estimator, which is a slight modification of the naive mixture proposed by Schuster and Yakowitz (1985) and Olkin and Spiegelman (1987). The proposed method is…
This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from 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…
Empirical likelihood is an attractive inferential framework that respects natural parameter boundaries, but existing approaches typically require smoothness of the functional and miscalibrate substantially when these assumptions are…
This paper presents a practical and simple fully nonparametric multivariate smoothing procedure that adapts to the underlying smoothness of the true regression function. Our estimator is easily computed by successive application of existing…
Many probabilistic models that have an intractable normalizing constant may be extended to contain covariates. Since the evaluation of the exact likelihood is difficult or even impossible for these models, score matching was proposed to…
We consider the nonparametric regression problem with multiple predictors and an additive error, where the regression function is assumed to be coordinatewise nondecreasing. We propose a Bayesian approach to make an inference on the…
We consider the problem of statistical inference for a class of partially-observed diffusion processes, with discretely-observed data and finite-dimensional parameters. We construct unbiased estimators of the score function, i.e. the…
We consider the classical problem of estimating a vector $\bolds{\mu}=(\mu_1,...,\mu_n)$ based on independent observations $Y_i\sim N(\mu_i,1)$, $i=1,...,n$. Suppose $\mu_i$, $i=1,...,n$ are independent realizations from a completely…