Application of Smoothing Measures in Nonparametric Kernel Classifiers with Usage of Normal Approximation of Probabilities

2015 ◽  
Vol 47 (10) ◽  
pp. 60-68
Author(s):  
Alexander A. Galkin
Keyword(s):  
Normal Approximation ◽  
Nonparametric Kernel

A Note on the Accuracy of Normal Approximation of Random Quantities

2021 ◽  
Vol 73 (1) ◽  
pp. 62-67
Author(s):  
Ibrahim A. Ahmad ◽  
A. R. Mugdadi
Keyword(s):  
Sample Size ◽  
Order Statistic ◽  
Normal Approximation ◽  
Order Approximation ◽  
Random Variables ◽  
Random Variable ◽  
Limiting Distribution ◽  
Exact Order ◽  
Fixed Sample ◽  
Independent Identically Distributed

For a sequence of independent, identically distributed random variable (iid rv's) [Formula: see text] and a sequence of integer-valued random variables [Formula: see text], define the random quantiles as [Formula: see text], where [Formula: see text] denote the largest integer less than or equal to [Formula: see text], and [Formula: see text] the [Formula: see text]th order statistic in a sample [Formula: see text] and [Formula: see text]. In this note, the limiting distribution and its exact order approximation are obtained for [Formula: see text]. The limiting distribution result we obtain extends the work of several including Wretman[Formula: see text]. The exact order of normal approximation generalizes the fixed sample size results of Reiss[Formula: see text]. AMS 2000 subject classification: 60F12; 60F05; 62G30.

scholarly journals The limits of normal approximation for adult height

2021 ◽  
Author(s):  
Sergei A. Slavskii ◽  
Ivan A. Kuznetsov ◽  
Tatiana I. Shashkova ◽  
Georgii A. Bazykin ◽  
Tatiana I. Axenovich ◽  
...  
Keyword(s):  
Complex Traits ◽  
Adult Height ◽  
Normal Approximation ◽  
Classical Model ◽  
Model Complexity ◽  
Test Case ◽  
Genetic Studies ◽  
Quantitative Genetic ◽  
Profound Influence ◽  
Log Normal

AbstractAdult height inspired the first biometrical and quantitative genetic studies and is a test-case trait for understanding heritability. The studies of height led to formulation of the classical polygenic model, that has a profound influence on the way we view and analyse complex traits. An essential part of the classical model is an assumption of additivity of effects and normality of the distribution of the residuals. However, it may be expected that the normal approximation will become insufficient in bigger studies. Here, we demonstrate that when the height of hundreds of thousands of individuals is analysed, the model complexity needs to be increased to include non-additive interactions between sex, environment and genes. Alternatively, the use of log-normal approximation allowed us to still use the additive effects model. These findings are important for future genetic and methodologic studies that make use of adult height as an exemplar trait.

Imitation of Demonstrations Using Bayesian Filtering With Nonparametric Data-Driven Models

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Nurali Virani ◽  
Devesh K. Jha ◽  
Zhenyuan Yuan ◽  
Ishana Shekhawat ◽  
Asok Ray
Keyword(s):  
Particle Filtering ◽  
Dynamic Models ◽  
Training Data ◽  
Data Driven ◽  
Conditional Density ◽  
Bayesian Filtering ◽  
State Dependent ◽  
State Evolution ◽  
And Control ◽  
Nonparametric Kernel

This paper addresses the problem of learning dynamic models of hybrid systems from demonstrations and then the problem of imitation of those demonstrations by using Bayesian filtering. A linear programming-based approach is used to develop nonparametric kernel-based conditional density estimation technique to infer accurate and concise dynamic models of system evolution from data. The training data for these models have been acquired from demonstrations by teleoperation. The trained data-driven models for mode-dependent state evolution and state-dependent mode evolution are then used online for imitation of demonstrated tasks via particle filtering. The results of simulation and experimental validation with a hexapod robot are reported to establish generalization of the proposed learning and control algorithms.

scholarly journals Fast pixel-based optical proximity correction based on nonparametric kernel regression

2014 ◽  
Vol 13 (4) ◽  
pp. 043007 ◽  
Author(s):  
Xu Ma ◽  
Bingliang Wu ◽  
Zhiyang Song ◽  
Shangliang Jiang ◽  
Yanqiu Li
Keyword(s):  
Kernel Regression ◽  
Optical Proximity Correction ◽  
Nonparametric Kernel ◽  
Nonparametric Kernel Regression
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