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LinearQuadratic Mean Field Games
"... As an organic combination of mean field theory in statistical physics and (nonzero sum) stochastic differential games, Mean Field Games (MFGs) has become a very popular research topic in the fields ranging from physical and social sciences to engineering applications, see for example the earlier s ..."
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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 comprehensive 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
Another Look At Differentiability in Quadratic Mean
, 1995
"... This note revisits the delightfully subtle interconnections between three ideas: differentiability, in an L 2 sense, of the squareroot of a probability density; local asymptotic normality; and contiguity. 99.1 A mystery The traditional regularity conditions for maximum likelihood theory involve ..."
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Cited by 6 (0 self)
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This note revisits the delightfully subtle interconnections between three ideas: differentiability, in an L 2 sense, of the squareroot 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...
QUADRATIC MEAN RADIUS OF A POLYNOMIAL IN C(Z)
"... 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 polynomia ..."
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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
ASYMPTOTIC OPTIMALITY OF THE BAYES ESTIMATOR ON DIFFERENTIABLE IN QUADRATIC MEAN MODELS
"... 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 this es ..."
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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
A Quadratic Mean based Supervised Learning Model for Managing Data Skewness
"... In this paper, we study the problem of data skewness. A data set is skewed/imbalanced if its dependent variable is asymmetrically distributed. Dealing with skewed data sets has been identified as one of the ten most challenging problems in data mining research. We address the problem of class skewne ..."
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Cited by 3 (1 self)
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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
Comparing Predictive Accuracy
 JOURNAL OF BUSINESS AND ECONOMIC STATISTICS, 13, 253265
, 1995
"... 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 be symmetri ..."
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Cited by 1309 (26 self)
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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
Improved Weighted Centroid Localization with Quadratic Means for Indoor Mobile Robot Tracking
"... Abstract. Nowadays, mobile robot tracking is the one of application in wireless sensor networks (WSNs). A one of promising localization algorithm in rangefree algorithm is the weighted centroid localization (WCL) algorithm. This work proposed the improved WCL algorithm with quadratic means based on ..."
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Abstract. Nowadays, mobile robot tracking is the one of application in wireless sensor networks (WSNs). A one of promising localization algorithm in rangefree algorithm is the weighted centroid localization (WCL) algorithm. This work proposed the improved WCL algorithm with quadratic means based
Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
, 1998
"... SeDuMi is an addon 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. This pape ..."
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Cited by 1334 (4 self)
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SeDuMi is an addon 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
Training Support Vector Machines: an Application to Face Detection
, 1997
"... We investigate the application of Support Vector Machines (SVMs) in computer vision. SVM is a learning technique developed by V. Vapnik and his team (AT&T Bell Labs.) that can be seen as a new method for training polynomial, neural network, or Radial Basis Functions classifiers. The decision sur ..."
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Cited by 728 (1 self)
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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
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