Related papers: Fitting a function to time-dependent ensemble aver…
Variational data assimilation is a technique for combining measured data with dynamical models. It is a key component of Earth system state estimation and is commonly used in weather and ocean forecasting. The approach involves a…
Within the framework of weighted integrable Hamiltonian systems, we study the long-time behavior of the associated statistical ensembles. We construct an action-dependent angular conjugacy that rectifies the nonuniform angular flow into a…
Forecasting the evolution of complex systems is one of the grand challenges of modern data science. The fundamental difficulty lies in understanding the structure of the observed stochastic process. In this paper, we show that every…
In this paper, we develop a functional weighted minimum mean-squared error (WMMSE) algorithm for downlink beamforming in multiuser continuous aperture array (CAPA) systems where both the base station (BS) and users are equipped with CAPAs.…
Misspecified models often provide useful information about the true data generating distribution. For example, if $y$ is a non-linear function of $x$ the least squares estimator $\hat{\beta}$ is an estimate of $\beta$, the slope of the best…
It has previously been shown that ordinary least squares can be used to estimate the coefficients of the single-index model under only mild conditions. However, the estimator is non-robust leading to poor estimates for some models. In this…
The so-called constrained least mean-square algorithm is one of the most commonly used linear-equality-constrained adaptive filtering algorithms. Its main advantages are adaptability and relative simplicity. In order to gain analytical…
In this paper, we introduce a new adaptive data analysis method to study trend and instantaneous frequency of nonlinear and non-stationary data. This method is inspired by the Empirical Mode Decomposition method (EMD) and the recently…
Missing data is an universal problem in statistics. We develop a unified framework for estimating parameters defined by general estimating equations under a missing-at-random (MAR) mechanism, based on generalized entropy calibration…
We propose a new scalable framework for spatio-temporal data fusion with multi-fidelity Gaussian processes (MFGPs) that enables fully likelihood-based inference for both stationary and non-stationary fidelity integration. The framework is…
This paper considers generalized least squares (GLS) estimation for linear panel data models. By estimating the large error covariance matrix consistently, the proposed feasible GLS (FGLS) estimator is more efficient than the ordinary least…
We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…
Climate change detection and attribution play a central role in establishing the causal influence of human activities on global warming. The dominant framework, optimal fingerprinting, is a linear errors-in-variables model in which each…
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…
We derive a new closed-form variance-adaptive confidence sequence (CS) for estimating the average conditional mean of a sequence of bounded random variables. Empirically, it yields the tightest closed-form CS we have found for tracking…
Score matching is a vital tool for learning the distribution of data with applications across many areas including diffusion processes, energy based modelling, and graphical model estimation. Despite all these applications, little work…
Time-series forecasting has gained significant attention in machine learning due to its crucial role in various domains. However, most existing forecasting models rely heavily on point-wise loss functions like Mean Square Error, which treat…
Accurate weather forecasting holds significant importance, serving as a crucial tool for decision-making in various industrial sectors. The limitations of statistical models, assuming independence among data points, highlight the need for…
We consider fitting a bivariate spline regression model to data using a weighted least-squares cost function, with weights that sum to one to form a discrete probability distribution. By applying the principle of maximum entropy, the weight…
Functional partial least squares (FPLS) is commonly used for fitting scalar-on-function regression models. For the sake of accuracy, FPLS demands that each realization of the functional predictor is recorded as densely as possible over the…