scholarly journals Speaking Stata: Density Probability Plots

2005 ◽  
Vol 5 (2) ◽  
pp. 259-273 ◽  
Author(s):  
Nicholas J. Cox
Keyword(s):  
Order Statistics ◽  
Density Function ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Real Data ◽  
Continuous Variable ◽  
Quantile Plots ◽  
Probability Plots ◽  
Parameter Values

Density probability plots show two guesses at the density function of a continuous variable, given a data sample. The first guess is the density function of a specified distribution (e.g., normal, exponential, gamma, etc.) with appropriate parameter values plugged in. The second guess is the same density function evaluated at quantiles corresponding to plotting positions associated with the sample's order statistics. If the specified distribution fits well, the two guesses will be close. Such plots, suggested by Jones and Daly in 1995, are explained and discussed with examples from simulated and real data. Comparisons are made with histograms, kernel density estimation, and quantile–quantile plots.

scholarly journals One Value of Smoothing Parameter vs Interval of Smoothing Parameter Values in Kernel Density Estimation

2018 ◽  
Vol 6 (332) ◽  
pp. 73-86
Author(s):  
Aleksandra Katarzyna Baszczyńska
Keyword(s):  
Density Function ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Ad Hoc ◽  
Kernel Density ◽  
Kernel Estimator ◽  
Smoothing Parameter ◽  
Smoothing Parameter Selection ◽  
Starting Point ◽  
Parameter Values

Ad hoc methods in the choice of smoothing parameter in kernel density estimation, al­though often used in practice due to their simplicity and hence the calculated efficiency, are char­acterized by quite big error. The value of the smoothing parameter chosen by Silverman method is close to optimal value only when the density function in population is the normal one. Therefore, this method is mainly used at the initial stage of determining a kernel estimator and can be used only as a starting point for further exploration of the smoothing parameter value. This paper pre­sents ad hoc methods for determining the smoothing parameter. Moreover, the interval of smooth­ing parameter values is proposed in the estimation of kernel density function. Basing on the results of simulation studies, the properties of smoothing parameter selection methods are discussed.

Body tail adaptive kernel density estimation for nonnegative heavy-tailed data

2021 ◽  
Vol 27 (1) ◽  
pp. 57-69
Author(s):  
Yasmina Ziane ◽  
Nabil Zougab ◽  
Smail Adjabi
Keyword(s):  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Kernel Estimator ◽  
Real Data ◽  
Density Region ◽  
Data Set ◽  
Bandwidth Parameter ◽  
Adaptive Kernel ◽  
Heavy Tailed

Abstract In this paper, we consider the procedure for deriving variable bandwidth in univariate kernel density estimation for nonnegative heavy-tailed (HT) data. These procedures consider the Birnbaum–Saunders power-exponential (BS-PE) kernel estimator and the bayesian approach that treats the adaptive bandwidths. We adapt an algorithm that subdivides the HT data set into two regions, high density region (HDR) and low-density region (LDR), and we assign a bandwidth parameter for each region. They are derived by using a Monte Carlo Markov chain (MCMC) sampling algorithm. A series of simulation studies and real data are realized for evaluating the performance of a procedure proposed.

scholarly journals Kernel Density Estimation: Theory and Application in Discriminant Analysis

2016 ◽  
Vol 33 (3) ◽  
pp. 267-279 ◽  
Author(s):  
Thomas Ledl
Keyword(s):  
Discriminant Analysis ◽  
Density Function ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Random Variable ◽  
Kernel Density Estimator ◽  
Density Estimator ◽  
Quadratic Discriminant Analysis ◽  
Bandwidth Parameter

Nowadays, one can find a huge set of methods to estimate the density function of a random variable nonparametrically. Since the first version of the most elementary nonparametric density estimator (the histogram) researchers produced a vast amount of ideas especially corresponding to the issue of choosing the bandwidth parameter in a kernel density estimator model. To focus not only on a descriptive application, the model seems to be quite suitable for application in discriminant analysis, where (multivariate) class densities are the basis for the assignment of a vector to a given class. Thisarticle gives insight to most popular bandwidth parameter selectors as well as to the performance of the kernel density estimator as a classification method compared to the classical linear and quadratic discriminant analysis, respectively. Both a direct estimation in a multivariate space as well as an application of the concept to marginal normalizations of the single variables will be taken into consideration. From this report the gap between theory and application is going to be pointed out.

BIAS CORRECTION AT END POINTS IN KERNEL DENSITY ESTIMATION

2021 ◽  
Vol 10 (12) ◽  
pp. 3515-3531
Author(s):  
H. Bouredji ◽  
A. Sayah
Keyword(s):  
Monte Carlo ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Bias Correction ◽  
Kernel Density ◽  
Real Data ◽  
Boundary Region ◽  
Finite Sample ◽  
New Approach ◽  
The Right

In this paper, we propose a new approach of boundary correction for kernel density estimation with the support $[0,1]$, in particular at the right endpoints and we derive the theoretical properties of this new estimator and show that it asymptotically reduce the order of bias at the boundary region, whereas the order of variance remains unchanged. Our Monte Carlo simulations demonstrate the good finite sample performance of our proposed estimator. Two examples with real data are provided.

scholarly journals Author Correction: An extended Weight Kernel Density Estimation model forecasts COVID-19 onset risk and identifies spatiotemporal variations of lockdown effects in China

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Wenzhong Shi ◽  
Chengzhuo Tong ◽  
Anshu Zhang ◽  
Bin Wang ◽  
Zhicheng Shi ◽  
...  
Keyword(s):  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Spatiotemporal Variations ◽  
Estimation Model

A Correction to this paper has been published: https://doi.org/10.1038/s42003-021-01924-6

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