A note on the satterthwaite confidence interval for a variance

When using a Satterthwaite chi-squared approximation, it is generally thought that the approximation is satisfactory when it is applied to a positive linear combination of mean squares. In this note, we describe how the Williams - Tukey idea for getting a confidence interval for the among groups variance in a random one-way model can be incorporated into Satterthwaite’s procedure for getting a confidence interval for a variance. This adjusted Satterthwaite procedure insures that his chi-squared approximation is always applied to positive linear combinations of mean squares. A small simulation is included which suggests that the adjustment to the Satterthwaite procedure is effective.     

Shortest prediction intervals for the birnbaum-saunders distribution

Shortest prediction intervals for a future observation from the Birnbaum-Saunders distribution are obtained from both frequentist and Bayesian perspectives. Comparisons are made with alternative intervals obtained via inversion. Monte Carlo simulations are performed to assess the approximate intervals.     

Best linear predictors for factor scores

From the literature three types of predictors for factor scores are available. These are characterized by the constraints: linear, linear conditionally unbiased, and linear correlation preserving. Each of these constraints generates a class of predictors. Best predictors are defined in terms of Lowner's partial matrix order applied to matrices of mean square error of prediction. It is shown that within the first two classes a best predictor exists and that it does not exist in the third.     

Discrimination of AR,MA and ARMA time series models

The problem of discrimination between two stationary ARMA time series models is considered, and in particular AR(p), MA(p), ARMA(1,1) models. The discriminant based on the likelihood ration leads to a quadratic form that is generally too complicated to evaluated explicitly. The discriminant can be expressed approximately as a linear combination of independent chi–squared random varianles each with one degree of freedom, the coefficients, of which are eigenvalues of cumbersome matrices. An analytical solution which gives the coefficients approximately is suggested.     

A note on information loss in analyzing a mixture model of count data

In this note we consider estimation of a mixture model of count data which is composed of two discrete random variables. Conditional and unconditional estimation procedures are given for estimating the unknown parameter(s) of interest using the likelihood function. Asymptotic relative efficiencies are given to examine the amount of information loss in using the two estimation procedures. Specifically, we study the change in asymptotic relative efficiency, if any, in different parameter settings.     

Maximum likelihood estimation of parameter structures for the Wishart distribution using constraints

Maximum likelihood estimation under constraints for estimation in the Wishart class of distributions, is considered. It provides a unified approach to estimation in a variety of problems concerning covariance matrices. Virtually all covariance structures can be translated to constraints on the covariances. This includes covariance matrices with given structure such as linearly patterned covariance matrices, covariance matrices with zeros, independent covariance matrices and structurally dependent covariance matrices. The methodology followed in this paper provides a useful and simple approach to directly obtain the exact maximum likelihood estimates. These maximum likelihood estimates are obtained via an estimation procedure for the exponential class using constraints.     

Semiparametric ARCH Models

This article introduces a semiparametric autoregressive conditional heteroscedasticity (ARCH) model that has conditional first and second moments given by autoregressive moving average and ARCH parametric formulations but a conditional density that is assumed only to be sufficiently smooth to be approximated by a nonparametric density estimator. For several particular conditional densities, the relative efficiency of the quasi-maximum likelihood estimator is compared with maximum likelihood under correct specification. These potential efficiency gains for a fully adaptive procedure are compared in a Monte Carlo experiment with the observed gains from using the proposed semiparametric procedure, and it is found that the estimator captures a substantial proportion of the potential. The estimator is applied to daily stock returns from small firms that are found to exhibit conditional skewness and kurtosis and to the British pound to dollar exchange rate.     

Relating Elasticities to Changes in Demand

This article specifies a class of equations relating the demand for a good to prices. It is shown that given this class of equations, one can relate the ratio of cross-elasticities to relative changes in demand, given arbitrary price changes.     

Sequential parameter learning and filtering in structured autoregressive state-space models

We present particle-based algorithms for sequential filtering and parameter learning in state-space autoregressive (AR) models with structured priors. Non-conjugate priors are specified on the AR coefficients at the system level by imposing uniform or truncated normal priors on the moduli and wavelengths of the reciprocal roots of the AR characteristic polynomial. Sequential Monte Carlo algorithms are considered and implemented for on-line filtering and parameter learning within this modeling framework. More specifically, three SMC approaches are considered and compared by applying them to data simulated from different state-space AR models. An analysis of a human electroencephalogram signal is also presented to illustrate the use of the structured state-space AR models in describing biomedical signals.