A Bayesian procedure for bandwidth selection in circular kernel density estimation

2020 ◽  
Vol 26 (1) ◽  
pp. 69-82
Author(s):  
Kahina Bedouhene ◽  
Nabil Zougab
Keyword(s):  
Density Estimation ◽  
Cross Validation ◽  
Bandwidth Selection ◽  
Kernel Density ◽  
Real Data ◽  
Loss Functions ◽  
Data Sets ◽  
Bayesian Procedure ◽  
Bayes Estimates ◽  
Mcmc Sampling

AbstractA Bayesian procedure for bandwidth selection in kernel circular density estimation is investigated, when the Markov chain Monte Carlo (MCMC) sampling algorithm is utilized for Bayes estimates. Under the quadratic and entropy loss functions, the proposed method is evaluated through a simulation study and real data sets, which were already discussed in the literature. The proposed Bayesian approach is very competitive in comparison with the existing classical global methods, namely plug-in and cross-validation techniques.

scholarly journals Bayesian inference on reliability in a multicomponent stress-strength bathtub-shaped model based on record values

2019 ◽  
pp. 431-444 ◽  
Author(s):  
Abbas Pak ◽  
Nayereh Bagheri Khoolenjani ◽  
Manoj Kumar Rastogi
Keyword(s):  
Real Data ◽  
Record Values ◽  
Loss Functions ◽  
Data Sets ◽  
Simulation Studies ◽  
Reliability Parameter ◽  
Bayes Estimates ◽  
Squared Error ◽  
Current Value ◽  
Strength Models

In the literature, there are a well-developed estimation techniques for the reliability assessment in multicomponent stress-strength models when the information about all the experimental units are available. However, in real applications, only observations that exceed (or fall below) the current value may be recorded. In this paper, assuming that the components of the system follow bathtub-shaped distribution, we investigate Bayesian estimation of the reliability of a multicomponent stress-strength system when the available data are reported in terms of record values. Considering squared error, linex and entropy loss functions, various Bayes estimates of the reliability are derived. Because there are not closed forms for the Bayes estimates, we will use Lindley’s method to calculate the approximate Bayes estimates. Further, for comparison purposes, the maximum likelihood estimate of the reliability parameter is obtained. Finally, simulation studies are conducted in order to evaluate the performances of the proposed procedures and analysis of real data sets is provided.

scholarly journals Exploring the Use of Variable Bandwidth Kernel Density Estimators

2003 ◽  
Vol 3 (2) ◽  
pp. 133-147 ◽  
Author(s):  
Isaías H. Salgado-Ugarte ◽  
Marco A. Pérez-Hernández
Keyword(s):  
Cross Validation ◽  
Computational Cost ◽  
Bandwidth Selection ◽  
Kernel Density ◽  
Kernel Estimator ◽  
Safe Procedure ◽  
Kernel Density Estimators ◽  
Window Width ◽  
Variable Bandwidth ◽  
Density Estimators

Variable bandwidth kernel density estimators increase the window width at low densities and decrease it where data concentrate. This represents an improvement over the fixed bandwidth kernel density estimators. In this article, we explore the use of one implementation of a variable kernel estimator in conjunction with several rules and procedures for bandwidth selection applied to several real datasets. The considered examples permit us to state that when working with tens or a few hundreds of data observations, least-squares cross-validation bandwidth rarely produces useful estimates; with thousands of observations, this problem can be surpassed. Optimal bandwidth and biased cross-validation (BCV), in general, oversmooth multimodal densities. The Sheather–Jones plug-in rule pro-duced bandwidths that behave slightly better in this respect. The Silverman test is considered as a very sophisticated and safe procedure to estimate the number of modes in univariate distributions; however, similar results could be obtained with the Sheather–Jones rule, but at a much lower computational cost. As expected, the variable bandwidth kernel density estimates showed fewer modes than those chosen by the Silverman test, especially those distributions in which multimodality was caused by several noisy minor modes. More research on the subject is needed.

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