Energy Substitution,Separability, and Technical Progress in the Australian Iron and Steel Industry

The effects of the “energy crisis” on the Australian iron and Steel industry are analyzed by using a flexible functional form, the transcendental logarithmic (translog) function, which represents a second-order approximation of any twice differentiable function. The robustness of the translog is analyzed with special attention paid to factor aggregation and separability conditions as they relate to the specification of the functions. The estimation results suggest that capital and energy are substitutes, that aggregation of administrative workers and production labor is inappropriate, and that materials are weakly separable, thereby allowing the estimation of a capital, labor, and energy model. The data set developed covers the financial years from 1946–47 to 1978–79. This 33-year time series allows the use of different temporal subsets. Technical progress is shown to be capital and energy using and labor and material saving. An energy submodel is specified using solid fuels, oil, electricity, and gas; and the interfuel substitutions are estimated.     

Bayesian multivariate normal analysis with a wishart prior

This paper considers the Bayesian analysis of the multivariate normal distribution when its covariance matrix has a Wishart prior density under the assumption of a multivariate quadratic loss function. New flexible marginal posterior distributions of the mean μ and of the covariance matrix Σ are developed and univariate cases with graphical representations are given.     

Some applications,properties and conjectures for higher order cumulants of a markovian stepping-stone model

This paper investigates certain tridiagonal coefficient matrices from linear differential equations for the joint cumulants of a Markovian stepping-stone model. The model is used to describe the dynamics of insect population growth, and is illustrated with an application to the spread of Africanized honey bees. The coefficient matrices are shown to have certain structure. A conjecture concerning their eigenvalues is proven for a special case of interest, and is also investigated numerically and by symbolic mathematical analysis.     

On two asymptotic normal distributions for the generalized wilks lambda statistic

In this paper we.present a Normal asymptotic distribution for the logarithm of the generalized Wilks Lambda statistic based on an asymptotic distribution for the determinant of a Wishart matrix. This distribution is obtained through the combined use of Taylor expansions of random variables whose exponentials have chi-square distributions and the Lindeberg-Feller version of the Central Limit Theorem, Another asymptotic Normal distribution for the logarithm of the generalized Wilks Lambda statistic for the case when at most one of the sets has an odd number of variables is derived directly from the exact distribution. Both distributions are non-degenerate and non-singular. The first Normal distribution compares favorably with other known approximations and asymptotic distributions namely for large numbers of variables and small sample sizes, while the second Normal distribution, which has a more restricted application, compares in most cases highly favorably with other known asymptotic distributions and approximations. Finally, a method to compute approximate quantiles which lay very close and converge steadily to the exact ones is presented.     

Nonnull distribution of Wilks' statistic for Manova in the complex case

In this paper, the exact distribution of Wilks' likelihood ratio criterion, A, for MANOVA, in the complex case when the alternate hypothesis is of unit rank (i.e. the linear case) has been derived and the explicit expressions for the same for p = 2 and 3 (where p is the number of variates) and general f₁ (the error degrees of freedom) and f₂ (the hypothesis degrees of freedom), are given. For an unrestricted number of variables, a general form of the density and the distribution of A in this case, is also given. It has been shown that the total integral of the series obtained by taking a few terms only, rapidly approaches the theoretical value one as more terms are taken into account, and some percentage points have also been computed.     

The effect of parameter estimation on phase II monitoring of poisson regression profiles

ABSTRACT

The effect of parameters estimation on profile monitoring methods has only been studied by a few researchers and only the assumption of a normal response variable has been tackled. However, in some practical situation, the normality assumption is violated and the response variable follows a discrete distribution such as Poisson. In this paper, we evaluate the effect of parameters estimation on the Phase II monitoring of Poisson regression profiles by considering two control charts, namely the Hotelling’s T² and the multivariate exponentially weighted moving average (MEWMA) charts. Simulation studies in terms of the average run length (ARL) and the standard deviation of the run length (SDRL) are carried out to assess the effect of estimated parameters on the performance of Phase II monitoring approaches. The results reveal that both in-control and out-of-control performances of these charts are adversely affected when the regression parameters are estimated.     

Proof of phenomenon B

In their paper “Some application, properties and conjectures for higher order cumulants of a Markovian stepping-stone model”, Zheng and Matis make use of a conjecture known as “Phenomenon B” regarding the eigenvalues of a tridiagonal matrix having a certain form. While the conjecture was shown to hold for particular cases, it was not proven in general. To supplement the Zheng and Matis paper, a formal proof of Phenomenon B is given here.     

Convergence of a Discrete-Time Age-Structured Population Toward a Given Steady State Through Controlled Immigration

To explore the concept of stability in an age-structured population with migration, a Markov transition matrix model is built, where age classes can be of different length, and the time step is not necessarily equal to the length of the age class. The conditions under which a vector of the model has a steady population structure are identified, as well as those under which the age structure converges to a given steady state, through a series of decisions or controls of letting immigrants in or forbidding them entry into the country. The decisions are expressed as vectors of proportions of immigrants. In the steady state, when the increment of population is proportional to its size, the age- or stage-structure remains unchanged between transitions.     

Covariance Matrix Formula for Generalized Linear Models with Unknown Dispersion

In this paper, the existence of the Uniformly Minimum Risk Equivariant (UMRE) estimator of parameters in SURE model under some quadratic losses and matrix losses is studied. The necessary and sufficient conditions for existence of the UMRE estimator of linearly estimable function vectors of regression coefficients under an affine group of transformations are obtained. It is proved that no UMRE estimator of the covariance matrix under any one of two affine groups of transformations exists.     

Small sample behavior of a robust heteroskedasticity consistent covariance matrix estimator

In heteroskedastic regression models, the least squares (OLS) covariance matrix estimator is inconsistent and inference is not reliable. To deal with inconsistency one can estimate the regression coefficients by OLS, and then implement a heteroskedasticity consistent covariance matrix (HCCM) estimator. Unfortunately the HCCM estimator is biased. The bias is reduced by implementing a robust regression, and by using the robust residuals to compute the HCCM estimator (RHCCM). A Monte-Carlo study analyzes the behavior of RHCCM and of other HCCM estimators, in the presence of systematic and random heteroskedasticity, and of outliers in the explanatory variables.