BAYES EMPIRICAL BAYES APPROACH TO ESTIMATION OF THE FAILURE RATE IN EXPONENTIAL DISTRIBUTION

ABSTRACT

In the empirical Bayes (EB) decision problem consisting of squared error estimation of the failure rate in exponential distribution, a prior Λ is placed on the gamma family of prior distributions to produce Bayes EB estimators which are admissible. A subclass of such estimators is shown to be asymptotically optimal (a.o.). The results of a Monte Carlo study are presented to demonstrate the a.o. property of the Bayes EB estimators.     

PERFORMANCE OF THE LOCATION LINEAR DISCRIMINANT FUNCTION UNDER ACROSS-LOCATION HETEROSCEDASTICITY

ABSTRACT

Classification of data consisting of both categorical and continuous variables between two groups is often handled by the sample location linear discriminant function confined to each of the locations specified by the observed values of the categorical variables. Homoscedasticity of across-location conditional dispersion matrices of the continuous variables is often assumed. Quite often, interactions between continuous and categorical variables cause across-location heteroscedasticity. In this article, we examine the effect of heterogeneous across-location conditional dispersion matrices on the overall expected and actual error rates associated with the sample location linear discriminant function. Performance of the sample location linear discriminant function is evaluated against the results for the restrictive classifier adjusted for across-location heteroscedasticity. Conclusions based on a Monte Carlo study are reported.     

A test for gamma DFR alternative

In this article, a test for exponentiality against gamma DFR alternative based on a quadratic form of the logarithmic observations is proposed. The percentage points and the power of the test are computed through Monte-Carlo simulation. The test is seen to perform well as compared to a chi-square test proposed by Bain and Engelhardt(1975).     

Sampling hyperparameters in hierarchical models: Improving on Gibbs for high-dimensional latent fields and large datasets

ABSTRACT

A common Bayesian hierarchical model is where high-dimensional observed data depend on high-dimensional latent variables that, in turn, depend on relatively few hyperparameters. When the full conditional distribution over latent variables has a known form, general MCMC sampling need only be performed on the low-dimensional marginal posterior distribution over hyperparameters. This improves on popular Gibbs sampling that computes over the full space. Sampling the marginal posterior over hyperparameters exhibits good scaling of compute cost with data size, particularly when that distribution depends on a low-dimensional sufficient statistic.     

A comparison of three methods of estimating the logistic regression coefficients

A Sampling experiment performed using data collected for a large clinical trial shows that the discriminant function estimates of the logistic regression coefficients for discrete variables may be severely biased. The simulations show that the mixed variable location model coefficient estimates have bias which is of the same magnitude as the bias in the coefficient estimates obtained using conditional maximum likelihood estimates but require about one-tenth of the computer time.     

A Metropolis algorithm to obtain co-sufficient samples with applications in conditional tests

ABSTRACT

Conditional tests are constructed by conditioning a fit measure to a minimal sufficient statistic. To calculate the p-value of these tests, Monte Carlo methods with co-sufficient samples can be used. In this paper we show how to simulate co-sufficient samples when the data distribution belongs to the exponential family with doubly transitive sufficient statistics. The proposed method is illustrated using the beta distribution.     

A multiparameter extension of two stage modified shrinkage estimator

A multiparameter extension is made to modified two stage shrinkage estimator proposed by Handa andKambo (1990), For aparticular class of shrinkage estimator, the local optimality of the extended modified estimator is shown over the two stage shrinkage estimator defined by Bhattacharya and Prakasa Rao(1990) in terms of quadratic loss.     

A consistent method of estimation for the parameters of the three-parameter inverse Gaussian distribution

In this paper, we propose a consistent method of estimation for the parameters of the three-parameter inverse Gaussian distribution. We then discuss some properties of these estimators and show by means of a Monte Carlo simulation study that the proposed estimators perform better than some other prominent estimators in terms of bias and root mean squared error. Finally, we present two real-life examples to illustrate the method of inference developed here.     

Non-ergodic martingale estimating functions and related asymptotics

Well-known estimation methods such as conditional least squares, quasilikelihood and maximum likelihood (ML) can be unified via a single framework of martingale estimating functions (MEFs). Asymptotic distributions of estimates for ergodic processes use constant norm (e.g. square root of the sample size) for asymptotic normality. For certain non-ergodic-type applications, however, such as explosive autoregression and super-critical branching processes, one needs a random norm in order to get normal limit distributions. In this paper, we are concerned with non-ergodic processes and investigate limit distributions for a broad class of MEFs. Asymptotic optimality (within a certain class of non-ergodic MEFs) of the ML estimate is deduced via establishing a convolution theorem using a random norm. Applications to non-ergodic autoregressive processes, generalized autoregressive conditional heteroscedastic-type processes, and super-critical branching processes are discussed. Asymptotic optimality in terms of the maximum random limiting power regarding large sample tests is briefly discussed.