Related papers: Mixing Least-Squares Estimators when the Variance …
This study is to investigate the feasibility of least square method in fitting non-Gaussian noise data. We add different levels of the two typical non-Gaussian noises, L\'evy and stretched Gaussian noises, to exact value of the selected…
We consider the problem of reconstructing an unknown bounded function $u$ defined on a domain $X\subset \mathbb{R}^d$ from noiseless or noisy samples of $u$ at $n$ points $(x^i)_{i=1,\dots,n}$. We measure the reconstruction error in a norm…
Recent work in scalable approximate Gaussian process regression has discussed a bias-variance-computation trade-off when estimating the log marginal likelihood. We suggest a method that adaptively selects the amount of computation to use…
In this paper, we compare maximum likelihood (ML), quasi likelihood (QL) and weighted least squares (WLS) estimators for proportional error nonlinear regression models. Literature on thermoluminescence sedimentary dating revealed another…
We study the performance of estimators of a sparse nonrandom vector based on an observation which is linearly transformed and corrupted by additive white Gaussian noise. Using the reproducing kernel Hilbert space framework, we derive a new…
We perform a mathematical and statistical analysis of the Wasserstein least squares problem, a regression method for vector-valued covariates and distribution-valued responses. Our proposal contrasts with other distributional regression…
Binomial data with unknown sizes often appear in biological and medical sciences. The previous methods either use the Poisson approximation or the quasi-likelihood approach. A full likelihood approach is proposed by treating unknown sizes…
A non-Bayesian, regression-based or generalized least squares (GLS)-based approach is formally proposed to estimate a class of time-varying AR parameter models. This approach has partly been used by Ito et al. (2014, 2016a,b), and is proven…
Ridge estimator is an alternative to ordinary least square estimator when there is multicollinearity problem. There are many proposed estimators in literature. In this paper, we propose new estimators which are modifications of the…
We develop efficient algorithms for estimating low-degree moments of unknown distributions in the presence of adversarial outliers. The guarantees of our algorithms improve in many cases significantly over the best previous ones, obtained…
Consider the problem of estimating a multivariate normal mean with a known variance matrix, which is not necessarily proportional to the identity matrix. The coordinates are shrunk directly in proportion to their variances in Efron and…
In experimental design, we are given a large collection of vectors, each with a hidden response value that we assume derives from an underlying linear model, and we wish to pick a small subset of the vectors such that querying the…
We propose a Randomised Subspace Gauss-Newton (R-SGN) algorithm for solving nonlinear least-squares optimization problems, that uses a sketched Jacobian of the residual in the variable domain and solves a reduced linear least-squares on…
This paper develops a class of Bayesian non- and semiparametric methods for estimating regression curves and surfaces. The main idea is to model the regression as locally linear, and then place suitable local priors on the local parameters.…
The cumulative shrinkage process is an increasing shrinkage prior that can be employed within models in which additional terms are supposed to play a progressively negligible role. A natural application is to Gaussian factor models, where…
In the setting of entangled single-sample distributions, the goal is to estimate some common parameter shared by a family of $n$ distributions, given one single sample from each distribution. This paper studies mean estimation for entangled…
This paper considers the problem of estimating a periodic function in a continuous time regression model with an additive stationary gaussian noise having unknown correlation function. A general model selection procedure on the basis of…
In the geosciences, a recurring problem is one of estimating spatial means of a physical field using weighted averages of point observations. An important variant is when individual observations are counted with some probability less than…
In this work, we study the problem of distributed mean estimation with $1$-bit communication constraints when the variance is unknown. We focus on the specific case where each user has access to one i.i.d. sample drawn from a distribution…
Model averaging methods have become an increasingly popular tool for improving predictions and dealing with model uncertainty, especially in Bayesian settings. Recently, frequentist model averaging methods such as information theoretic and…