Bayesian expectile regression with asymmetric normal distribution

In this paper, we adopt the Bayesian approach to expectile regression employing a likelihood function that is based on an asymmetric normal distribution. We demonstrate that improper uniform priors for the unknown model parameters yield a proper joint posterior. Three simulated data sets were generated to evaluate the proposed method which show that Bayesian expectile regression performs well and has different characteristics comparing with Bayesian quantile regression. We also apply this approach into two real data analysis.     

Identification-robust moment-based tests for Markov switching in autoregressive models

ABSTRACT

This paper develops tests of the null hypothesis of linearity in the context of autoregressive models with Markov-switching means and variances. These tests are robust to the identification failures that plague conventional likelihood-based inference methods. The approach exploits the moments of normal mixtures implied by the regime-switching process and uses Monte Carlo test techniques to deal with the presence of an autoregressive component in the model specification. The proposed tests have very respectable power in comparison with the optimal tests for Markov-switching parameters of Carrasco et al. (2014 Carrasco, M., Hu, L., Ploberger, W. (2014). Optimal test for Markov switching parameters. Econometrica 82(2):765–784.[Crossref], [Web of Science ®] , [Google Scholar]), and they are also quite attractive owing to their computational simplicity. The new tests are illustrated with an empirical application to an autoregressive model of USA output growth.     

Estimation for Birnbaum–Saunders Distribution in Simple Step Stress–accelerated Life Test with Type-II Censoring

This paper develops the Bayesian estimation for the Birnbaum–Saunders distribution based on Type-II censoring in the simple step stress–accelerated life test with power law accelerated form. Maximum likelihood estimates are obtained and Gibbs sampling procedure is used to get the Bayesian estimates for shape parameter of Birnbaum–Saunders distribution and parameters of power law–accelerated model. Asymptotic normality method and Markov Chain Monte Carlo method are employed to construct the corresponding confidence interval and highest posterior density interval at different confidence level, respectively. At last, the results are compared by using Monte Carlo simulations, and a numerical example is analyzed for illustration.     

A framework for the comparison of maximum pseudo-likelihood and maximum likelihood estimation of exponential family random graph models

The statistical modeling of social network data is difficult due to the complex dependence structure of the tie variables. Statistical exponential families of distributions provide a flexible way to model such dependence. They enable the statistical characteristics of the network to be encapsulated within an exponential family random graph (ERG) model. For a long time, however, likelihood-based estimation was only feasible for ERG models assuming dyad independence. For more realistic and complex models inference has been based on the pseudo-likelihood. Recent advances in computational methods have made likelihood-based inference practical, and comparison of the different estimators possible.     

Goodness-of-fit test for exponentiality based on spacings for general progressive Type-II censored data

There have been numerous tests proposed to determine whether or not the exponential model is suitable for a given data set. In this article, we propose a new test statistic based on spacings to test whether the general progressive Type-II censored samples are from exponential distribution. The null distribution of the test statistic is discussed and it could be approximated by the standard normal distribution. Meanwhile, we propose an approximate method for calculating the expectation and variance of samples under null hypothesis and corresponding power function is also given. Then, a simulation study is conducted. We calculate the approximation of the power based on normality and compare the results with those obtained by Monte Carlo simulation under different alternatives with distinct types of hazard function. Results of simulation study disclose that the power properties of this statistic by using Monte Carlo simulation are better for the alternatives with monotone increasing hazard function, and otherwise, normal approximation simulation results are relatively better. Finally, two illustrative examples are presented.     

Estimation of parameters of inverse Weibull distribution and application to multi-component stress-strength model

The problem of estimation of the parameters of two-parameter inverse Weibull distributions has been considered. We establish existence and uniqueness of the maximum likelihood estimators of the scale and shape parameters. We derive Bayes estimators of the parameters under the entropy loss function. Hierarchical Bayes estimator, equivariant estimator and a class of minimax estimators are derived when shape parameter is known. Ordered Bayes estimators using information about second population are also derived. We investigate the reliability of multi-component stress-strength model using classical and Bayesian approaches. Risk comparison of the classical and Bayes estimators is done using Monte Carlo simulations. Applications of the proposed estimators are shown using real data sets.     

On the Flexibility of Metropolis–Hastings Acceptance Probabilities in Auxiliary Variable Proposal Generation

Abstract. Use of auxiliary variables for generating proposal variables within a Metropolis–Hastings setting has been suggested in many different settings. This has in particular been of interest for simulation from complex distributions such as multimodal distributions or in transdimensional approaches. For many of these approaches, the acceptance probabilities that are used turn up somewhat magic and different proofs for their validity have been given in each case. In this article, we will present a general framework for construction of acceptance probabilities in auxiliary variable proposal generation. In addition to showing the similarities between many of the proposed algorithms in the literature, the framework also demonstrates that there is a great flexibility in how to construct acceptance probabilities. With this flexibility, alternative acceptance probabilities are suggested. Some numerical experiments are also reported.     

Bayes Inference in Constant Partially Accelerated Life Tests for the Generalized Exponential Distribution with Progressive Censoring

In this paper, the problem of constant partially accelerated life tests when the lifetime follows the generalized exponential distribution is considered. Based on progressive type-II censoring scheme, the maximum likelihood and Bayes methods of estimation are used for estimating the distribution parameters and acceleration factor. A Monte Carlo simulation study is carried out to examine the performance of the obtained estimates.     

A Bayesian approach to non-parametric monotone function estimation

Summary.  The paper proposes two Bayesian approaches to non-parametric monotone function estimation. The first approach uses a hierarchical Bayes framework and a characterization of smooth monotone functions given by Ramsay that allows unconstrained estimation. The second approach uses a Bayesian regression spline model of Smith and Kohn with a mixture distribution of constrained normal distributions as the prior for the regression coefficients to ensure the monotonicity of the resulting function estimate. The small sample properties of the two function estimators across a range of functions are provided via simulation and compared with existing methods. Asymptotic results are also given that show that Bayesian methods provide consistent function estimators for a large class of smooth functions. An example is provided involving economic demand functions that illustrates the application of the constrained regression spline estimator in the context of a multiple-regression model where two functions are constrained to be monotone.