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By using the empirical likelihood method, Zhang et al. (see, e.g., [14, 15]) described how to build confidence regions for the unknown parameters.
The problem of interest here is to estimate the unknown parameter in model (1.1) by using the empirical likelihood method when auxiliary information is available.
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Similarly, we propose to use the empirical likelihood method to construct the confidence region for β.
Using the Empirical Maximum Likelihood Kriging (EMLK) method of Pardo-Igúzquiza and Dowd (2005a), prediction and prediction uncertainty surfaces (or maps) are found for each element, so that spatial distributions of elements in soil are determined.
Using the empirical amino acid substitution model of Whelan and Goldman [ 26] we maximized the likelihood under the three conflicting topologies shown in Figure 3a c.
Xue [5] used the validation data to explore the empirical likelihood inference of nonlinear semiparasitic error-in-variable models.
Finally, we use a data-driven approach to compare test statistics based on the empirical likelihood of observing between-group differences among replicates.
Modelling and inference use the empirical Bayesian approach via penalized likelihood technique.
Using the Markov regime-switching model, we describe the equilibrium correction via a non-linear algorithm that computes and maximizes the empirical likelihood in a two-regime model.
Based on the theoretical asymptotic behaviour of the empirical likelihood ratio statistic, we propose, for a fixed design, a simpler test statistic, easier to use in practice.
So we need to adjust the empirical likelihood function.
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