Fitting probability distributions to economic growth: a maximum likelihood approach

The growth rate of the gross domestic product (GDP) usually carries heteroscedasticity, asymmetry and fat-tails. In this study three important and significantly heteroscedastic GDP series are examined. A Normal, normal-mixture, normal-asymmetric Laplace distribution and a Student's t-Asymmetric Laplace (TAL) distribution mixture are considered for distributional fit comparison of GDP growth series after removing heteroscedasticity. The parameters of the distributions have been estimated using maximum likelihood method. Based on the results of different accuracy measures, goodness-of-fit tests and plots, we find out that in the case of asymmetric, heteroscedastic and highly leptokurtic data the TAL-distribution fits better than the alternatives. In the case of asymmetric, heteroscedastic but less leptokurtic data the NM fit is superior. Furthermore, a simulation study has been carried out to obtain standard errors for the estimated parameters. The results of this study might be used in e.g. density forecasting of GDP growth series or to compare different economies.     

Multivariate Stochastic Volatility Models with Correlated Errors

We develop a Bayesian approach for parsimoniously estimating the correlation structure of the errors in a multivariate stochastic volatility model. Since the number of parameters in the joint correlation matrix of the return and volatility errors is potentially very large, we impose a prior that allows the off-diagonal elements of the inverse of the correlation matrix to be identically zero. The model is estimated using a Markov chain simulation method that samples from the posterior distribution of the volatilities and parameters. We illustrate the approach using both simulated and real examples. In the real examples, the method is applied to equities at three levels of aggregation: returns for firms within the same industry, returns for different industries, and returns aggregated at the index level. We find pronounced correlation effects only at the highest level of aggregation.     

Reduced-Form Versus Structural Models of Water Demand Under Nonlinear Prices

Increasing-block prices are common in markets for water, cellular phone service, and retail electricity. This study estimates demand models under block prices and conducts a Monte Carlo experiment to test the small-sample bias of structural and instrumental variables (IV) estimators. We estimate the price and income elasticity of water demand under increasing-block prices using a structural discrete/continuous choice (DCC) model, as well as random effects and IV. Elasticity estimates are sensitive to the modeling framework. The Monte Carlo experiment suggests that IV and DCC models estimate both price and income elasticity with bias, with no clear best choice among estimators.     

The gamma-Lomax distribution

For any continuous baseline G distribution, Zografos and Balakrishnan [On families of beta- and generalized gamma-generated distributions and associated inference. Statist Methodol. 2009;6:344–362] proposed a generalized gamma-generated distribution with an extra positive parameter. A new three-parameter continuous distribution called the gamma-Lomax distribution, which extends the Lomax distribution is proposed and studied. Various structural properties of the new distribution are derived including explicit expressions for the moments, generating and quantile functions, mean deviations and Rényi entropy. The estimation of the model parameters is performed by maximum likelihood. We also determine the observed information matrix. An application illustrates the usefulness of the proposed model.     

A note on the moments of stochastic shrinkage parameters in ridge regression

The purpose of this note is to gain insight on the performance of two well known operational Ridge Regression estimators by deriving the moments of their stochastic shrinkage parameters. We also show that, under certain conditions, one of them has bounded moments.     

A general class of capability indices in the case of asymmetric tolerances

Vannman has earlier studied a class of capability indices, containing the indices C _p , C _pk , C _pm and C _pmk , when the tolerances are symmetric. We study the properties of this class when the tolerances are asymmetric and suggest a new enlargened class of indices. Under the assumption of normality an explicit form of the distribution of the new class of the estimated indices is provided. Numerical investigations are made to explore the behavior of the estimators of the indices for different values of the parameters. Based on the estimator a decision rule that can be used to determine whether the process can be considered capable or not is provided and suitable criteria for choosing an index from the family are suggested.     

Oil the Equivalence of pavlov-ushakov and kaplan-meier estimators of survival probability in multiply censored sample

It is proved that the unbiased estimator of survival probability in a multiply censored sample suggested by Pavlov & Ushakov (1980, 1984) is equivalent to the Kaplan-Meier Product-Limit estimator.     

Alternative beta estimation for the market model using partially adaptive techniques

The leptokurtosls of many security market return distributions can contaminate ordinary least squares estimates of the β coefficient of the market model. Partially adaptive estimation techniques accommodate the possibility of fat tailed distributions. this methodology limits the influence of extremely large residuals and yields estimates which are both statistically and practically different from ordinary least squares.     

Estimation of probability of extinction of a multitype branchihg process

Maximoa likelihood estimation of the probability of ultimata extinction of a possibly age dependentaultitype branching process is studied when independent random samples from off spring distributions are available, In multitype daIton-fatson branching process