摘要翻译:
本文将讨论如何将非参数密度估计推广到MLE参数估计。本文以Parzen窗理论为基础,利用量子理论中概率振幅的优点,建立了一个非线性优化问题的模型,该问题的求解即使不是不可能,也是非常困难的。研究了求解非线性规划问题的构造性方法。虽然它看起来很复杂,但本文的方法是简单而全面的。更确切地说,引理、定理及其证明是为了数学的严谨性和实际计算的目的。我们不使用高等数学的技术和术语,而是使用初等微积分的流行技术和术语。由Y.--S.的数值结果得出。蔡等人。[7]表明,完全建立了一种新的密度估计方法&超参数密度估计。严格地说,本文的工作并不局限于统计学的范畴。它可以分为非线性分析,如线性空间或流形上的优化,以及计算机科学的算法。
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英文标题:
《Application of Quantum Theory to Super-parametric Density Estimation》
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作者:
Yeong-Shyeong Tsai
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最新提交年份:
2008
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分类信息:
一级分类:Mathematics 数学
二级分类:Statistics Theory 统计理论
分类描述:Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计:例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类:Statistics 统计学
二级分类:Statistics Theory 统计理论
分类描述:stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近,贝叶斯推论,决策理论,估计,基础,推论,检验。
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英文摘要:
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, super-parametric 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.
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PDF链接:
https://arxiv.org/pdf/710.0436