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.

On the Use of a Modified Intersection of Confidence Intervals (MICIH) Kernel Density Estimation Approach

2021 ◽  
Vol 8 (4) ◽  
pp. 309-332
Author(s):  
Efosa Michael Ogbeide ◽  
Joseph Erunmwosa Osemwenkhae
Keyword(s):  
Confidence Intervals ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Mean Squared Error ◽  
Kernel Density ◽  
Window Size ◽  
National Bureau ◽  
Squared Error ◽  
Data Density ◽  
Adaptive Kernel

Density estimation is an important aspect of statistics. Statistical inference often requires the knowledge of observed data density. A common method of density estimation is the kernel density estimation (KDE). It is a nonparametric estimation approach which requires a kernel function and a window size (smoothing parameter H). It aids density estimation and pattern recognition. So, this work focuses on the use of a modified intersection of confidence intervals (MICIH) approach in estimating density. The Nigerian crime rate data reported to the Police as reported by the National Bureau of Statistics was used to demonstrate this new approach. This approach in the multivariate kernel density estimation is based on the data. The main way to improve density estimation is to obtain a reduced mean squared error (MSE), the errors for this approach was evaluated. Some improvements were seen. The aim is to achieve adaptive kernel density estimation. This was achieved under a sufficiently smoothing technique. This adaptive approach was based on the bandwidths selection. The quality of the estimates obtained of the MICIH approach when applied, showed some improvements over the existing methods. The MICIH approach has reduced mean squared error and relative faster rate of convergence compared to some other approaches. The approach of MICIH has reduced points of discontinuities in the graphical densities the datasets. This will help to correct points of discontinuities and display adaptive density. Keywords: approach, bandwidth, estimate, error, kernel density

scholarly journals Log-Transform Kernel Density Estimation of Income Distribution

2016 ◽  
Vol 91 (1-2) ◽  
pp. 141-159 ◽  
Author(s):  
Arthur Charpentier ◽  
Emmanuel Flachaire
Keyword(s):  
Income Distribution ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Estimation Methods ◽  
Density Functions ◽  
Income Distributions ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Positive Support

Standard kernel density estimation methods are very often used in practice to estimate density functions. It works well in numerous cases. However, it is known not to work so well with skewed, multimodal and heavy-tailed distributions. Such features are usual with income distributions, defined over the positive support. In this paper, we show that a preliminary logarithmic transformation of the data, combined with standard kernel density estimation methods, can provide a much better fit of the density estimation.

scholarly journals Benchmarks for detecting ‘breakthroughs’ in clinical trials: empirical assessment of the probability of large treatment effects using kernel density estimation

BMJ Open ◽  
2014 ◽  
Vol 4 (10) ◽  
pp. e005249 ◽  
Author(s):  
Branko Miladinovic ◽  
Ambuj Kumar ◽  
Rahul Mhaskar ◽  
Benjamin Djulbegovic
Keyword(s):  
Clinical Trials ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Treatment Effects ◽  
Kernel Density ◽  
Data Sources ◽  
Cooperative Groups ◽  
Publicly Funded ◽  
Adaptive Kernel ◽  
Improve Health

ObjectiveTo understand how often ‘breakthroughs,’ that is, treatments that significantly improve health outcomes, can be developed.DesignWe applied weighted adaptive kernel density estimation to construct the probability density function for observed treatment effects from five publicly funded cohorts and one privately funded group.Data Sources820 trials involving 1064 comparisons and enrolling 331 004 patients were conducted by five publicly funded cooperative groups. 40 cancer trials involving 50 comparisons and enrolling a total of 19 889 patients were conducted by GlaxoSmithKline.ResultsWe calculated that the probability of detecting treatment with large effects is 10% (5–25%), and that the probability of detecting treatment with very large treatment effects is 2% (0.3–10%). Researchers themselves judged that they discovered a new, breakthrough intervention in 16% of trials.ConclusionsWe propose these figures as the benchmarks against which future development of ‘breakthrough’ treatments should be measured.

scholarly journals Identifying Outliers in Response Quality Assessment by Using Multivariate Control Charts Based on Kernel Density Estimation

2021 ◽  
Vol 37 (1) ◽  
pp. 97-119
Author(s):  
Jiayun Jin ◽  
Geert Loosveldt
Keyword(s):  
Density Estimation ◽  
Kernel Density Estimation ◽  
Control Charts ◽  
Kernel Density ◽  
Item Nonresponse ◽  
Minimum Covariance Determinant ◽  
Control Data ◽  
Statistical Process ◽  
Data Set ◽  
Response Quality

Abstract When monitoring industrial processes, a Statistical Process Control tool, such as a multivariate Hotelling T 2 chart is frequently used to evaluate multiple quality characteristics. However, research into the use of T 2 charts for survey fieldwork–essentially a production process in which data sets collected by means of interviews are produced–has been scant to date. In this study, using data from the eighth round of the European Social Survey in Belgium, we present a procedure for simultaneously monitoring six response quality indicators and identifying outliers: interviews with anomalous results. The procedure integrates Kernel Density Estimation (KDE) with a T 2 chart, so that historical “in-control” data or reference to the assumption of a parametric distribution of the indicators is not required. In total, 75 outliers (4.25%) are iteratively removed, resulting in an in-control data set containing 1,691 interviews. The outliers are mainly characterized by having longer sequences of identical answers, a greater number of extreme answers, and against expectation, a lower item nonresponse rate. The procedure is validated by means of ten-fold cross-validation and comparison with the minimum covariance determinant algorithm as the criterion. By providing a method of obtaining in-control data, the present findings go some way toward a way to monitor response quality, identify problems, and provide rapid feedbacks during survey fieldwork.

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