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We use the maximum quasi-likelihood3 method to estimate the regression model with fractional dependent variable.
The problem in using OLS on fractional dependent variable is that it is not asymptotically efficient estimator.
McDonald (2008) shows that the use of OLS, Tobit, and transformed logistic-normal model for fractional dependent variable data would yield inefficient results because the distribution of error terms is likely to be heteroskedastic.4 This is because, as the conditional variance of the error term approach zero, the conditional mean approaches either of the boundary points of the fractional data.
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Afterwards, the predictor corrector method is used to solve the nonlinear fractional time-dependent equation.
Sequence alignments are then examined; sequences having >=25% pairwise identity to the seed and passing minimum fractional (length-dependent) bi-directional overlap between the database hit and the seed (termed the "coverage") are accepted.
The rate of reaction was found to be proportional to a temperature dependent fractional power of the hydrochloric acid concentration.
The increase of the biosorption with raising the MB concentration is attributed to the fact that at higher concentrations, the ratio of the initial number of MB molecules to the available surface area is large; consequently, the fractional biosorption becomes dependent on the initial concentration.
Indeed, fractional shortening is dependent on both SR Ca2+ release and myofilaments Ca2+ sensitivity, where the latter may explain the dissociation between fractional shortening and the intracellular Ca2+ transient amplitude in the present study, as shown directly by others after exercise training (de Waard et al. 2007; Diffee et al. 2001).
A new method for evaluating penetrant-dependent fractional free volume proved to be a valuable tool in determining the effects of structural changes on gas transport behavior.
This work is concerned with the parareal algorithm for system of ODEs u′(t)+Au(t)="f that arising from semi-discretizations of time-dependent fractional diffusion equations with nonsymmetric Riemann Liouville fractional derivatives.
Zhang and Han [10] developed a quasi-wavelet-based numerical method for time-dependent fractional partial differential equation.
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