Related papers: A Partially Linear Framework for Massive Heterogen…
In this paper we propose a new method of joint nonparametric estimation of probability density and its support. As is well known, nonparametric kernel density estimator has "boundary bias problem" when the support of the population density…
We incorporate a version of a spike and slab prior, comprising a pointmass at zero ("spike") and a Normal distribution around zero ("slab") into a dynamic panel data framework to model coefficient heterogeneity. In addition to homogeneity…
Persistent homology is a powerful tool for characterizing the topology of a data set at various geometric scales. When applied to the description of molecular structures, persistent homology can capture the multiscale geometric features and…
This paper concerns the estimation of the regression function at a given point in nonparametric heteroscedastic models with Gaussian noise or with noise having unknown distribution. In the two cases an asymptotically efficient kernel…
Finite mixture distributions arise in sampling a heterogeneous population. Data drawn from such a population will exhibit extra variability relative to any single subpopulation. Statistical models based on finite mixtures can assist in the…
This paper proposes a linear categorical random coefficient model, in which the random coefficients follow parametric categorical distributions. The distributional parameters are identified based on a linear recurrence structure of moments…
The ultimate goal of any numerical scheme for partial differential equations (PDEs) is to compute an approximation of user-prescribed accuracy at quasi-minimal computational time. To this end, algorithmically, the standard adaptive finite…
The estimation of categorical distributions under marginal constraints summarizing some sample from a population in the most-generalizable way is key for many machine-learning and data-driven approaches. We provide a parameter-agnostic…
Handling incomplete and heterogeneous data remains a central challenge in real-world machine learning, where missing values may follow complex mechanisms (MCAR, MAR, MNAR) and features can be of mixed types (numerical and categorical).…
Databases in domains such as healthcare are routinely released to the public in aggregated form. Unfortunately, naive modeling with aggregated data may significantly diminish the accuracy of inferences at the individual level. This paper…
We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…
This paper proposes a regularized pairwise difference approach for estimating the linear component coefficient in a partially linear model, with consistency and exact rates of convergence obtained in high dimensions under mild scaling…
In this paper, we introduce a family of robust estimates for the parametric and nonparametric components under a generalized partially linear model, where the data are modeled by $y_i|(\mathbf{x}_i,t_i)\sim F(\cdot,\mu_i)$ with…
Coresets have emerged as a powerful tool to summarize data by selecting a small subset of the original observations while retaining most of its information. This approach has led to significant computational speedups but the performance of…
This paper introduces unit-specific heterogeneity in panel data threshold regression. We develop the asymptotic theory for models with heterogeneous thresholds, heterogeneous slope coefficients, and interactive fixed effects. The estimation…
In this paper, we derive minimax rates for estimating both parametric and nonparametric components in partially linear additive models with high dimensional sparse vectors and smooth functional components. The minimax lower bound for…
The present paper provides a generalized model of network, namely, Hybrid Layered Network (HLN). We proved that the sets of all homogeneous, heterogeneous and multi-layered networks are subsets of the set of all HLNs depicting the model's…
When predicting scalar responses in the situation where the explanatory variables are functions, it is sometimes the case that some functional variables are related to responses linearly while other variables have more complicated…
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…
We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…