摘要翻译:
我们考虑了在加性色噪声场中观测到的二维正弦信号的数目和参数的联合估计问题。我们首先阐述了当假设的正弦数目不正确时,二维正弦信号的最小二乘估计。在正弦信号个数被低估的情况下,我们证明了最小二乘估计对主导正弦信号参数的几乎肯定收敛性。在这个数字被高估的情况下,由最小二乘估计器获得的估计参数向量包含几乎肯定收敛到正弦的正确参数的子向量。基于这些结果,我们证明了一个新的模型顺序选择规则的强相合性。
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英文标题:
《Strongly Consistent Model Order Selection for Estimating 2-D Sinusoids
in Colored Noise》
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作者:
Mark Kliger and Joseph M. Francos
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最新提交年份:
2008
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分类信息:
一级分类:Statistics 统计学
二级分类:Methodology 方法论
分类描述:Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计,调查,模型选择,多重检验,多元方法,信号和图像处理,时间序列,平滑,空间统计,生存分析,非参数和半参数方法
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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:
We consider the problem of jointly estimating the number as well as the parameters of two-dimensional sinusoidal signals, observed in the presence of an additive colored noise field. We begin by elaborating on the least squares estimation of 2-D sinusoidal signals, when the assumed number of sinusoids is incorrect. In the case where the number of sinusoidal signals is under-estimated we show the almost sure convergence of the least squares estimates to the parameters of the dominant sinusoids. In the case where this number is over-estimated, the estimated parameter vector obtained by the least squares estimator contains a sub-vector that converges almost surely to the correct parameters of the sinusoids. Based on these results, we prove the strong consistency of a new model order selection rule.
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PDF链接:
https://arxiv.org/pdf/801.279