Sentence examples for in the finite sample from inspiring English sources

In the finite sample case, it has bounded conditional (and unconditional) bias and variance.

In the finite sample case, it always produces "smooth" regression function estimates, adapts "automatically and smoothly" to regions with sparse design, and has bounded conditional (and unconditional) bias and variance.

These systematic approaches aim at introducing MSE bounds that are lower than the unbiased Cramér Rao bound (CRB) for all values of the unknown parameters and at choosing biased estimators that beat the standard maximum-likelihood (ML) and/or least squares (LS) estimators in the finite sample case.

This result is used for obtaining modified versions of the AR order selection criteria FPE and AIC in the finite sample case.

The CMML presents a small bias on the estimation of the scatter matrix and then, ( {widehat{boldsymbol{Sigma}}}_{mathrm{CMML}} ) is not a MS-unbiased estimator [9] (at least in the finite sample regime).

The performance of these tests in the finite sample situation are evaluated through simulations.

The TSE uses global smoothing parameters and has advantages in both the finite sample and the asymptotic cases.

Our proposed estimator for the multivariate regression function has advantages in both the finite sample and the asymptotic cases.

The strength of the rejection of the null hypothesis of independence between errors is important in determining the finite sample properties of the IV estimator, particularly the bias.

Via intensive simulations, we show that our method consistently outperforms the existing frequentist approaches, e.g. the graphical LASSO, in the finite samples.

Moreover, due to the robustness of the check loss function to outliers in the finite samples, our proposed variable selection method is more robust than the ones based on the least squares criterion.