Nonparametric statistics

Nonparametric statistics is the type of statistics that is not restricted by assumptions concerning the nature of the population from which a sample is drawn. This is opposed to parametric statistics, for which a problem is restricted a priori by assumptions concerning the specific distribution of the population (such as the normal distribution) and parameters (such the mean or variance). Nonparametric statistics is based on either not assuming a particular distribution or having a distribution specified but with the distribution's parameters not specified in advance (though a parameter may be generated by the data, such as the median). Nonparametric statistics can be used for descriptive statistics or statistical inference. Nonparametric tests are often used when the assumptions of parametric tests are evidently violated. Definitions The term "nonparametric statistics" has been defined imprecisely in the following two ways, among others: Applications and purpose

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Unsupervised Robust Nonparametric Learning Of Hidden Community Properties

Akhilesh Deepak Gotmare, Martin Jaggi, Mikhail Langovoy

We consider learning of fundamental properties of communities in large noisy networks, in the prototypical situation where the nodes or users are split into two classes according to a binary property, e.g., according to their opinions or preferences on a topic. For learning these properties, we propose a nonparametric, unsupervised, and scalable graph scan procedure that is, in addition, robust against a class of powerful adversaries. In our setup, one of the communities can fall under the influence of a knowledgeable adversarial leader, who knows the full network structure, has unlimited computational resources and can completely foresee our planned actions on the network. We prove strong consistency of our results in this setup with minimal assumptions. In particular, the learning procedure estimates the baseline activity of normal users asymptotically correctly with probability 1; the only assumption being the existence of a single implicit community of asymptotically negligible logarithmic size. We provide experiments on real and synthetic data to illustrate the performance of our method, including examples with adversaries.

2019

Study on the Performances of AlScN based SAW/BAW Hybrid Resonators A Parametric Analysis of Acoustic Wave Resonators with Large Figure of Merit

Guilain Lionel Germain Lang, Luis Guillermo Villanueva Torrijo, Soumya Yandrapalli

In this study, we analyze a 3rd type of FBAR's fundamental mode by finite element method. We show the importance of the substrate's wave velocity and conductivity on the electromechanical coupling efficiency. Then we demonstrate that etching traditional SAW sensors in between its electrodes is an effective solution to increase its performances. Finally, the finite device simulations of optimized geometries demonstrate the full potential of AlSc(0.4)N based SAW/BAW hybrid resonators: an impedance response free of spurious modes and large figure of merit (k(t)(FD, 1.35GHz)(2) = 2.48%).

IEEE2021

Spline- and Wavelet-based Models of Neural Activity in Response to Natural Visual Stimulation

Joao Emanuel Felipe Gerhard, Luca Szegletes

We present a comparative study of the performance of different basis functions for the nonparametric modeling of neural activity in response to natural stimuli. Based on naturalistic video sequences, a generative model of neural activity was created using a stochastic linear-nonlinear-spiking cascade. The temporal dynamics of the spiking response is well captured with cubic splines with equidistant knot spacings. Whereas a sym4-wavelet decomposition performs competitively or only slightly worse than the spline basis, Haar wavelets (or histogram-based models) seem unsuitable for faithfully describing the temporal dynamics of the sensory neurons. This tendency was confirmed with an application to a real data set of spike trains recorded from visual cortex of the awake monkey.

Ieee2012