相关论文: The minimum mean square estimator for a sublinear …
This article introduces operator on operator regression in quantum probability. Here in the regression model, the response and the independent variables are certain operator valued observables, and they are linearly associated with unknown…
Estimating linear regression using least squares and reporting robust standard errors is very common in financial economics, and indeed, much of the social sciences and elsewhere. For thick tailed predictors under heteroskedasticity this…
Assume one observes independent categorical variables or, equivalently, one observes the corresponding multinomial variables. Estimating the distribution of the observed sequence amounts to estimating the expectation of the multinomial…
This is a brief tutorial on the least square estimation technique that is straightforward yet effective for parameter estimation. The tutorial is focused on the linear LSEs instead of nonlinear versions, since most nonlinear LSEs can be…
In continuous-time system identification, the intersample behavior of the input signal is known to play a crucial role in the performance of estimation methods. One common input behavior assumption is that the spectrum of the input is…
In this paper, we consider the problem of finding the Least Squares estimators of two isotonic regression curves $g^\circ_1$ and $g^\circ_2$ under the additional constraint that they are ordered; e.g., $g^\circ_1 \le g^\circ_2$. Given two…
This paper investigates a mean-field linear-quadratic optimal control problem where the state dynamics and cost functional incorporate both expectation and conditional expectation terms. We explicitly derive the pre-committed, na\"{\i}ve,…
We develop an approach for estimating models described via conditional moment restrictions, with a prototypical application being non-parametric instrumental variable regression. We introduce a min-max criterion function, under which the…
We provide a unified approach to MM-estimation with auxiliary scale for balanced linear models with structured covariance matrices. This approach leads to estimators that are highly robust against outliers and highly efficient for normal…
We study admissibility of a subclass of generalized Bayes estimators of a multivariate normal vector when the variance is unknown, under scaled quadratic loss. Minimaxity is also established for certain of these estimators.
We propose two least-squares estimators of a discrete probability under the constraint of k-monotony and study their statistical properties. We give a characterization of these estimators based on the decomposition on a spline basis of…
This work presents a new variation of the commonly used Least Mean Squares Algorithm (LMS) for the identification of sparse signals with an a-priori known sparsity using a hard threshold operator in every iteration. It examines some useful…
Let $X$ be a random variable with unknown mean and finite variance. We present a new estimator of the mean of $X$ that is robust with respect to the possible presence of outliers in the sample, provides tight sub-Gaussian deviation…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…
In this paper we obtain minimal support properties of solutions of Schr\"odinger equations. We improve previously known conditions on the potential for which the measure of the support of solutions cannot be too small. We also use these…
We propose an adversarial evaluation framework for sensitive feature inference based on minimum mean-squared error (MMSE) estimation with a finite sample size and linear predictive models. Our approach establishes theoretical lower bounds…
We study estimation and prediction in linear models where the response and the regressor variable both take values in some Hilbert space. Our main objective is to obtain consistency of a principal components based estimator for the…
Linear minimum mean square error (MMSE) detector has been shown to alleviate the noise amplification problem, resulting in the conventional zero-forcing (ZF) detector. In this paper, we analyze the performance improvement by the MMSE…
In this paper we study the subdifferential set of an operator. We give possible relation of the subdifferential set of an operator to that of its value, at a point where the operator attains its norm.
This paper deals with a projection least squares estimator of the drift function of a jump diffusion process $X$ computed from multiple independent copies of $X$ observed on $[0,T]$. Risk bounds are established on this estimator and on an…