Bayesian Bandwidth Selection Research Articles

Sequential Bayesian bandwidth selection for multivariate kernel regression with applications

A new Bayesian bandwidth selection procedure is proposed for nonparametric kernel estimates based on the sequential Monte Carlo method. Compared with the existing Bayesian bandwidth selector of Zhang et al. (2009), this new method can enhance the convergence to the global optimum with a substantially faster computation speed. In particular, the method offers an improved out-of-sample performance as shown by simulations. The bandwidth selector is applied to the option state price density, production function, and nonparametric relationship between oil and stock index returns; results indicate that our proposed method outperforms other methods in terms of the mean square error and log-likelihood in all applications.

A New Kernel Estimator Based on Scaled Inverse Chi-Squared Density Function

In this work, a new kernel estimator based on scaled inverse chi-squared distribution is proposed to estimate densities having nonnegative support. The optimal rates of convergence for the mean squared error (MSE) and the mean integrated squared error (MISE) are obtained. Adaptive Bayesian bandwidth selection method with Lindley approximation is used for heavy tailed distributions. Simulation studies are performed to compare the performance of the average integrated square error (ISE) by using the bandwidths obtained from the global least squares cross-validation bandwidth selection method and the bandwidths obtained from adaptive Bayesian method with Lindley approximation. Finally, real data sets are presented to illustrate the findings.

Nonparametric density estimation based on beta prime kernel

In this work, we propose beta prime kernel estimator for estimation of a probability density functions defined with nonnegative support. For the proposed estimator, beta prime probability density function used as a kernel. It is free of boundary bias and nonnegative with a natural varying shape. We obtained the optimal rate of convergence for the mean squared error (MSE) and the mean integrated squared error (MISE). Also, we use adaptive Bayesian bandwidth selection method with Lindley approximation for heavy tailed distributions and compare its performance with the global least squares cross-validation bandwidth selection method. Simulation studies are performed to evaluate the average integrated squared error (ISE) of the proposed kernel estimator against some asymmetric competitors using Monte Carlo simulations. Moreover, real data sets are presented to illustrate the findings.

Bayesian bandwidth selection with two multiplicative bias correction estimators for discrete kernel

–Two classes of multiplicative bias correction (MBC) methods with discrete associated kernels are used for probability mass function estimation. The MBC estimators reduce the order of magnitude in bias, whereas the order of magnitude in variance remains unchanged. For the choice of the bandwidth, we proposed the Bayes global method against the unbiased cross-validation approach. The performance of both methods (Bayesian and cross validation methods) are evaluated under two criteria: the integrated square error criteria and the integrated square bias through simulation studies. We also present a real data application of the proposed methods. The obtained results show that the Bayes global method performs better than cross-validation one for MBC estimators.

Functional coefficient time series models with trending regressors

ABSTRACTThis paper studies a functional coefficient time series model with trending regressors, where the coefficients are unknown functions of time and random variables. We propose a local linear estimation method to estimate the unknown coefficient functions, and establish the corresponding asymptotic theory under mild conditions. We also develop a test procedure to see if the functional coefficients take particular parametric forms. For practical use, we further propose a Bayesian approach to select the bandwidths, and conduct several numerical experiments to examine the finite sample performance of our proposed local linear estimator and the test procedure. The results show that the local linear estimator works well and the proposed test has satisfactory size and power. In addition, our simulation studies show that the Bayesian bandwidth selection method performs better than the cross-validation method. Furthermore, we use the functional coefficient model to study the relationship between consumption per capita and income per capita in United States, and it was shown that the functional coefficient model with our proposed local linear estimator and Bayesian bandwidth selection method performs well in both in-sample fitting and out-of-sample forecasting.

Bayesian Bandwidth Selection for a Nonparametric Regression Model with Mixed Types of Regressors

This paper develops a sampling algorithm for bandwidth estimation in a nonparametric regression model with continuous and discrete regressors under an unknown error density. The error density is approximated by the kernel density estimator of the unobserved errors, while the regression function is estimated using the Nadaraya-Watson estimator admitting continuous and discrete regressors. We derive an approximate likelihood and posterior for bandwidth parameters, followed by a sampling algorithm. Simulation results show that the proposed approach typically leads to better accuracy of the resulting estimates than cross-validation, particularly for smaller sample sizes. This bandwidth estimation approach is applied to nonparametric regression model of the Australian All Ordinaries returns and the kernel density estimation of gross domestic product (GDP) growth rates among the organisation for economic co-operation and development (OECD) and non-OECD countries.

Comparison study to bandwidth selection in binomial kernel estimation using Bayesian approaches

Recently, several works have shown that the Bayesian approaches to global bandwidth and variable (local and adaptive) bandwidths selection in binomial kernel estimation for probability mass functions (pmfs) outperform the common classical methods, such as mean integrated squared error (MISE) and cross-validation (CV) methods. In this article, we first review the global, local, and adaptive binomial kernel estimator combined with the Bayesian approaches for selecting the bandwidths. Then we compare them by using several count data sets with different designs, in particular for small and moderate sample sizes. All the Bayesian bandwidth selection approaches are also applied to a real count data sets. In general, in terms of integrated squared error (ISE) and execution times, the local Bayesian approach outperforms the other Bayesian approaches.

Adaptive Bayesian bandwidth selection in asymmetric kernel density estimation for nonnegative heavy-tailed data

In this paper, we consider an interesting problem on adaptive Birnbaum–Saunders-power-exponential (BS-PE) kernel density estimation for nonnegative heavy-tailed (HT) data. Treating the variable bandwidths , of adaptive BS-PE kernel as parameters, we then propose a conjugate prior and estimate the 's by using the popular quadratic and entropy loss functions. Explicit formulas are obtained for the posterior and Bayes estimators. Comparison simulations with global unbiased cross-validation bandwidth selection technique were conducted under four HT distributions. Finally, two applications based on HT real data are presented and analyzed.

Bayesian Bandwidth Selection in Nonparametric Time-Varying Coefficient Models

Bandwidth plays an important role in determining the performance of local linear estimators. In this paper, we propose a Bayesian approach to bandwidth selection for local linear estimation of time-varying coefficient time series models, where the errors are assumed to follow the Gaussian kernel error density. A Markov chain Monte Carlo algorithm is presented to simultaneously estimate the bandwidths for local linear estimators in the regression function and the bandwidth for the Gaussian kernel error-density estimator. A Monte Carlo simulation study shows that: 1) our proposed Bayesian approach achieves better performance in estimating the bandwidths for local linear estimators than normal reference rule and cross-validation; 2) compared with the parametric assumption of either the Gaussian or the mixture of two Gaussians, Gaussian kernel error-density assumption is a data-driven choice and helps gain robustness in terms of different specification of the true error density. Moreover, we apply our proposed Bayesian sampling method to the estimation of bandwidth for the time-varying coefficient models that explain Okun's law and the relationship between consumption growth and income growth in the U.S. For each model, we also provide calibrated parametric form of its time-varying coefficients.