Related papers: HAL-MLE Log-Splines Density Estimation (Part I: Un…
In variable selection, most existing screening methods focus on marginal effects and ignore dependence between covariates. To improve the performance of selection, we incorporate pairwise effects in covariates for screening and…
We estimate on a compact interval densities with isolated irregularities, such as discontinuities or discontinuities in some derivatives. From independent and identically distributed observations we construct a kernel estimator with…
Maximum likelihood (ML) estimation is widely used in statistics. The h-likelihood has been proposed as an extension of Fisher's likelihood to statistical models including unobserved latent variables of recent interest. Its advantage is that…
We consider the Lame system of linear elasticity with periodically distributed inclusions whose elastic parameters have high contrast compared to the background media. We develop a unified method based on layer potential techniques to…
Suppose that $\m{U} = (U_1, \ldots , U_d) $ has a Uniform$([0,1]^d)$ distribution, that $\m{Y} = (Y_1 , \ldots , Y_d) $ has the distribution $G$ on $\RR_+^d$, and let $\m{X} = (X_1 , \ldots , X_d) = (U_1 Y_1 , \ldots , U_d Y_d )$. The…
Consider the nonparametric logistic regression problem. In the logistic regression, we usually consider the maximum likelihood estimator, and the excess risk is the expectation of the Kullback-Leibler (KL) divergence between the true and…
Adaptive experimental designs have gained popularity in clinical trials and online experiments. Unlike traditional, fixed experimental designs, adaptive designs can dynamically adjust treatment randomization probabilities and other design…
Targeted maximum likelihood estimators (TMLEs) are asymptotically optimal among regular, asymptotically linear estimators. In small samples, however, we may be far from "asymptopia" and not reap the benefits of optimality. Here we propose a…
In this paper, we tackle for the first time the problem of maximum likelihood (ML) estimation of the signal-to-noise ratio (SNR) parameter over time-varying single-input multiple-output (SIMO) channels. Both the data-aided (DA) and the…
This paper proposes a new method for finding the highest predictive density set or region, within the heteroscedastic regression framework. This framework enjoys the property that any highest predictive density set is a translation of some…
Estimating the clutter-plus-noise covariance matrix in high-dimensional STAP is challenging in the presence of Internal Clutter Motion (ICM) and a high noise floor. The problem becomes more difficult in low-sample regimes, where the Sample…
We formulate an optimization problem to estimate probability densities in the context of multidimensional problems that are sampled with uneven probability. It considers detector sensitivity as an heterogeneous density and takes advantage…
Sequential change-point detection in non-Gaussian stochastic processes is challenging because the underlying densities are rarely known in real time. Classical parametric procedures such as CUSUM lose optimality under distributional…
We describe $k$-MLE, a fast and efficient local search algorithm for learning finite statistical mixtures of exponential families such as Gaussian mixture models. Mixture models are traditionally learned using the expectation-maximization…
In this paper, a nonparametric maximum likelihood (ML) estimator for band-limited (BL) probability density functions (pdfs) is proposed. The BLML estimator is consistent and computationally efficient. To compute the BLML estimator, three…
Quantile regression has become a valuable tool to analyze heterogeneous covaraite-response associations that are often encountered in practice. The development of quantile regression methodology for high-dimensional covariates primarily…
This paper addresses the problem of estimating a convex regression function under both the sup-norm risk and the pointwise risk using B-splines. The presence of the convex constraint complicates various issues in asymptotic analysis,…
Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observations where the variances are unknown and may vary arbitrarily…
This paper presents a general theoretical framework of penalized quasi-maximum likelihood (PQML) estimation in stationary multiple time series models when the number of parameters possibly diverges. We show the oracle property of the PQML…
Deconvolution is the important problem of estimating the distribution of a quantity of interest from a sample with additive measurement error. Nearly all methods in the literature are based on Fourier transformation because it is…