Some Methods for Estimation in a Negative-Binomial Model

To clarify the advantage of using the quasilikelihood method, lack of robustness of the maximum likelihood method was demonstrated for the negative-binomial model. Efficiency calculations of the method of moments and the pseudolikelihood method in the estimation of extra-Poisson parameters in a negative-binomial model were carried out. Especially when the overdispersion parameter is small, both methods are relatively highly efficient and the pseudolikelihood estimate is more efficient than the method of moments estimate. Two examples of the quasilikelihood analyses of count data with overdispersion are given. The bootstrap method also is applied to the data to illustrate the advantage of the method of moments or pseudolikelihood method in the estimation of the standard errors of the mean parameter estimates under the negative-binomial model.     

Quantitative assessment of the degree of hoarseness

By using a computer simulation, the author examined the theoretically expected discrepancy of the obtained H/N ratio from the real H/N value, the effects of perturbatios of pitch, and amplitude on the H/N ratio and others. Regarding the averaged wave as an estimate of the harmonic component, resulted in harmonic energy greater than its real value. The H/N ratio method detected perturbations of pitch and amplitude as a quantity of noise energy. The effect of pitch perturbation on the H/N ratio was much greater than that of amplitude perturbation. The error range of the measurement system did not contribute significantly to the calculated H/N ratios.     

Closed subsets of the domain whose image has the dimension of the range

It is shown that if dim Y < ∞ and if f(X) = Y is a mapping between compact metric spaces such that 1 ? m ? dim f^-1(y)?n for all y ? Y, then there exists a closed set K ? X such that dim K ? n ? m and dim f(K) = dim Y. This answers a question posed by J. Keesling and D. Wilson.     

Singular surfaces in a linear thermo-elastic dielectric material

Singular surfaces in a linear thermo-elastic dielectric material are considered, where the constitutive equations of the elastic dielectric proposed by Toupin and the heat equations with finite wave velocities are combined. There exist six types of singular surfaces including a stationary one. The velocities, the coupled fields and the variation of the amplitudes of the surfaces with respect to time are investigated. It is found that the amplitude of the mechanical transverse wave rotates during propagation and at the stationary surface the amplitude of the electric field periodically reverses in direction and the one of the polarization field rotates elliptically with the same period.     

Enantio- and diastereomerically pure threo-homoallylic alcohols via highly stereoselective reduction of α-methyl-β,γ-unsaturated ketones

Reduction of α-methyl-β,γ-unsaturated ketones with L-Selectride proceeded with high $\text{threo}$-selectivity to afford $\text{threo}$-β-methyl homoallylic alcohols of high enantio- and diastereomerical purities.