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studies by Huang, Caines and Malhame ́ (2003), and that by Lasry and Lions (2006a, b and 2007). In this paper, we provide a compre-hensive study of a general class of mean field games in the linear quadratic framework. We adopt the adjoint equation approach to investigate the existence and uniqueness

This note revisits the delightfully subtle interconnections between three ideas: differentiability, in an L 2 sense, of the square-root of a probability density; local asymptotic normality; and contiguity. 99.1 A mystery The traditional regularity conditions for maximum likelihood theory involve existence of two or three derivatives of the density functions, together with domination assumptions to justify differentiation under integral signs. Le Cam (1970) noted that such conditions are unnecessarily stringent. He commented: Even if one is not interested in the maximum economy of assumptions one cannot escape practical statistical problems in which apparently "slight" violations of the assumptions occur. For instance the derivatives fail to exist at one point x which may depend on `, or the distributions may not be mutually absolutely continuous or a variety of other difficulties may occur. The existing literature is rather unclear about what may happen in these circumstances. Note...

Dedicated to the memory of Prof. N. Obreshkoff Abstract. A Schoenberg conjecture connecting quadratic mean radii of a polynomial and its derivative is verified for some kinds of polynomials, including fourth degree ones. 1. Introduction. Let Pn(z) = zn +a2z n−2 + · · ·+an, (n> 2) be a

Abstract. This paper deals with the study of the Bayes estimator’s asymptotic properties on Differentiable in Quadratic Mean (DQM) models in the case of independent and identically distributed observations. The investigation is led in order to define weak assumptions on the model under which

errors, in which approach the induction process is biased towards the majority class for skewed data. To overcome this drawback, we propose a quadratic mean based learning framework (QMLearn) that is robust and insensitive to class skewness. We will note that minimizing the quadratic mean is a convex

We propose and evaluate explicit tests of the null hypothesis of no difference in the accuracy of two competing forecasts. In contrast to previously developed tests, a wide variety of accuracy measures can be used (in particular, the loss function need not be quadratic, and need not even

Abstract. Nowadays, mobile robot tracking is the one of application in wireless sensor networks (WSNs). A one of promising localization algorithm in range-free algorithm is the weighted centroid localization (WCL) algorithm. This work proposed the improved WCL algorithm with quadratic means based

SeDuMi is an add-on for MATLAB, that lets you solve optimization problems with linear, quadratic and semidefiniteness constraints. It is possible to have complex valued data and variables in SeDuMi. Moreover, large scale optimization problems are solved efficiently, by exploiting sparsity

surfaces are found by solving a linearly constrained quadratic programming problem. This optimization problem is challenging because the quadratic form is completely dense and the memory requirements grow with the square of the number of data points. We present a decomposition algorithm that guarantees