In the presence of heteroskedasticity, the instrumental variables estimator yields consistent, but inefficient, estimates of the coefficients and an inconsistent estimate of the covariance matrix [ 19].
Most methods proposed so far for nonparametric hemodynamic response function (HRF) estimation in fMRI data do not account for these confounding effects, and thus produce biased and inefficient estimates.
Removing those observations can lead to biased or inefficient estimates.
This assumption, as noted by Chaudhuri [14] leads to inefficient estimates not only in the main parameters of interest but also in the vulnerability estimates.
In a linear regression framework, measurement error in the right-hand side results in both biased (attenuation bias, with estimates biased towards zero) and inefficient estimates, while the presence of this problem in the left-hand side variable implies less efficient estimates.
If cross-sectional methods are used to estimate models whose parameters do in fact vary over time, the resulting estimation may fail to yield statistically valid results, fail to identify the true model parameters, and produce inefficient estimates (Bowen and Wiersema 1999).
Although expression (6) is an incorrect specification of the likelihood function of the model we are using, since the assumption v ~ N 0, I) ignores the existence of intra-individual correlation induced by u i, its maximisation yields consistent but inefficient estimates of the parameters of interest.
When the variance exceeds the mean, this overdispersion feature leads to inconsistent and inefficient estimates.
Additionally, because reduced sample size may result in inefficient estimates and inflated standard error, we used multiple imputation, which was proposed by Rubin in 1987 [ 31], to impute the missing data.
