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On The Density Estimation By SuperParametric Method
, 709
"... The superparametric density estimators and its related algorism were suggested by Y. –S. Tsai et al [7]. The number of parameters is unlimited in the super parametric estimators and it is a general theory in sense of unifying or connecting nonparametric and parametric estimators. Before applying t ..."
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The superparametric density estimators and its related algorism were suggested by Y. –S. Tsai et al [7]. The number of parameters is unlimited in the super parametric estimators and it is a general theory in sense of unifying or connecting nonparametric and parametric estimators. Before applying to numerical examples, we can not give any comment of the estimators. In this paper, we will focus on the implementation, the computer programming, of the algorism and strategies of choosing window functions. Bsplines, Bezier splines and covering windows are studied as well. According to the criterion of the convergence conditions for Parzen window, the number of the window functions shall be, roughly, proportional to the number of samples and so is the number of the variables. Since the algorism is designed for solving the optimization of likelihood function, there will be a set of nonlinear equations with a large number of variables. The results show that algorism suggested by Y. –S. Tsai is very powerful and effective in the sense of mathematics, that is, the iteration procedures converge and the rates of convergence are very fast. Also, the numerical results of different window functions show that the approach of superparametric density estimators has ushered a new era of statistic.
stochastic simulation of web users
 In Procs. of the 2010 IEEE / WIC / ACM International Conference
, 2010
"... Abstract—A biologically inspired cognitive model is presented for human decision making and applied to the simulation of the web user. The model is based on the Neurophysiology description of multiple decision process; this is a well proven psychological theory. The model simulates the behaviour of ..."
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Abstract—A biologically inspired cognitive model is presented for human decision making and applied to the simulation of the web user. The model is based on the Neurophysiology description of multiple decision process; this is a well proven psychological theory. The model simulates the behaviour of a real user on a website and it was observed that the distribution of artificial web users in sessions successfully simulates a genuine user’s web mode of behaviour. On the hypothesis that the adjusted artificial web user behaves statistically similar to the human web users, a system was created for the improvement of the structure of a web site based on stochastic simulations as a Proof of Concept. Since simulation recover observed statistical behaviour, changes on a web site are used to predict changes on navigational patterns.
FORMULATION AND SOLUTION STRATEGIES FOR NONPARAMETRIC NONLINEAR STOCHASTIC PROGRAMS, WITH AN APPLICATION IN FINANCE
, 2007
"... nonparametric nonlinear stochastic programs, with an application in finance. ..."
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nonparametric nonlinear stochastic programs, with an application in finance.
Application of Quantum Theory to Superparametric Density Estimation
, 710
"... In this paper, we will discuss how to generalize nonparametric density estimators to MLE parametric estimators. Basing on the Parzen window theory and using the advantages of probability amplitude of quantum theory, we model a nonlinear optimization problem and it is very difficult, if not impossibl ..."
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In this paper, we will discuss how to generalize nonparametric density estimators to MLE parametric estimators. Basing on the Parzen window theory and using the advantages of probability amplitude of quantum theory, we model a nonlinear optimization problem and it is very difficult, if not impossible, to solve the problem. A constructive procedure for solving the nonlinear programming problem is studied. Though it seems to be very complicated, the approach of this paper is simple and comprehensive. More precisely, the lemmas, the theorems and their proofs serve the purpose for mathematical rigor and practical computation. Instead of using techniques and terminologies of advanced mathematics, we use the popular techniques and terminologies of elementary calculus. From the numerical results of the paper by Y. –S. Tsai et al. [7], it shows that a new approach of density estimation, superparametric density estimation, is established completely. Strictly speaking, the work of the paper is not confined in the category of statistics. It could be classified into nonlinear analysis such as optimization on linear space, or manifold, and the algorithm of computer science.
New Tools for Consistency in Bayesian Nonparametrics
"... Posterior consistency and the parallel behaviour of consistency of maximum likelihood estimators is analyzed in nonparametric statistical problems. The framework is the hypoStrong Law of Large Numbers, a form of “onesided ” Uniform Law of Large Numbers. Keywords: ..."
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Posterior consistency and the parallel behaviour of consistency of maximum likelihood estimators is analyzed in nonparametric statistical problems. The framework is the hypoStrong Law of Large Numbers, a form of “onesided ” Uniform Law of Large Numbers. Keywords:
Nonparametric Maximum Likelihood Estimation of Probability Measures: Existence
, 2004
"... This paper formulates the nonparametric maximum likelihood estimation of probability measures and generalizes the consistency result on the maximum likelihood estimator (MLE). We drop the independence assumption on the underlying stochastic process and replace it with the assumption that the stoch ..."
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This paper formulates the nonparametric maximum likelihood estimation of probability measures and generalizes the consistency result on the maximum likelihood estimator (MLE). We drop the independence assumption on the underlying stochastic process and replace it with the assumption that the stochastic process is stationary and ergodic. The present proof employs Birkhoff’s ergodic theorem and the martingale convergence theorem. The main result is applied to the parametric and nonparametric maximum likelihood estimation of density functions.
UNIVERSIDAD DE CHILE Web User Behavior Analysis
, 2011
"... “Scientia vincere tenebras” ..."
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