The Finite Sample Performance of Modified Adaptive Kernel Estimators for Probability Density Function

2016 ◽  
Vol 11 (5) ◽  
pp. 1-9
Author(s):  
Serpil Cula ◽  
Serdar Demir ◽  
Oniz Toktamis
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Kernel Estimators ◽  
Finite Sample ◽  
Adaptive Kernel

scholarly journals Manifold-adaptive dimension estimation revisited

2022 ◽  
Vol 8 ◽  
pp. e790
Author(s):  
Zsigmond Benkő ◽  
Marcell Stippinger ◽  
Roberta Rehus ◽  
Attila Bencze ◽  
Dániel Fabó ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Nearest Neighbor ◽  
Epileptic Seizures ◽  
Percentage Error ◽  
Finite Sample ◽  
Asymptotically Unbiased Estimator ◽  
Intrinsic Dimensionality

Data dimensionality informs us about data complexity and sets limit on the structure of successful signal processing pipelines. In this work we revisit and improve the manifold adaptive Farahmand-Szepesvári-Audibert (FSA) dimension estimator, making it one of the best nearest neighbor-based dimension estimators available. We compute the probability density function of local FSA estimates, if the local manifold density is uniform. Based on the probability density function, we propose to use the median of local estimates as a basic global measure of intrinsic dimensionality, and we demonstrate the advantages of this asymptotically unbiased estimator over the previously proposed statistics: the mode and the mean. Additionally, from the probability density function, we derive the maximum likelihood formula for global intrinsic dimensionality, if i.i.d. holds. We tackle edge and finite-sample effects with an exponential correction formula, calibrated on hypercube datasets. We compare the performance of the corrected median-FSA estimator with kNN estimators: maximum likelihood (Levina-Bickel), the 2NN and two implementations of DANCo (R and MATLAB). We show that corrected median-FSA estimator beats the maximum likelihood estimator and it is on equal footing with DANCo for standard synthetic benchmarks according to mean percentage error and error rate metrics. With the median-FSA algorithm, we reveal diverse changes in the neural dynamics while resting state and during epileptic seizures. We identify brain areas with lower-dimensional dynamics that are possible causal sources and candidates for being seizure onset zones.

scholarly journals Joint Behaviour of Semirecursive Kernel Estimators of the Location and of the Size of the Mode of a Probability Density Function

2011 ◽  
Vol 2011 ◽  
pp. 1-27
Author(s):  
Abdelkader Mokkadem ◽  
Mariane Pelletier ◽  
Baba Thiam
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Convergence Rates ◽  
Confidence Regions ◽  
Kernel Estimators ◽  
Computational Advantage ◽  
Joint Behaviour

Let and denote the location and the size of the mode of a probability density. We study the joint convergence rates of semirecursive kernel estimators of and . We show how the estimation of the size of the mode allows measuring the relevance of the estimation of its location. We also enlighten that, beyond their computational advantage on nonrecursive estimators, the semirecursive estimators are preferable to use for the construction of confidence regions.

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