Weighted Likelihood Equations with Bootstrap Root Search

Parabolic acceleration of the EM algorithm

“…See Markatou et al (1998), McLachlan and Peel (2000), Biernacki et al (2003), Biernacki (2004) about the choice of starting position and possible non optimality. Only the slow convergence is considered in the present paper.…”

Weighted model-based clustering for remote sensing image analysis

“…Weighted mixture models that downweight observations based on distance have previously been introduced [16]. However, our method is preferable for this particular task because it produces more accurate results for close and overlapping groups and because it uses fixed weights, creates more stable results, and converges in fewer iterations.…”

“…Using ideas similar to those of Markatou et al [16], we compare a clustering method that weights based on Mahalanobis distance (DW) to our previously described pixel-weighting technique (PW). In DW, we use Eq.…”

“…Alternatively, we could use a weighting scheme that explicitly downweights discrepant data values. A weighted-likelihood model that downweights observations inconsistent with the model was introduced by Markatou et al [16]. They introduce weights based on the Pearson residual, δ, where the weights are defined as…”

Notes on Pearson residuals and weighted likelihood estimating equations

“…In the discrete case we have f à ðx;F n Þ ¼ P n i¼1 1 x ðx i Þ=n and m à ðx; yÞ ¼ mðx; yÞ, where 1 x ðyÞ is 1 when x ¼ y and 0 otherwise. Lindsay (1994) uses the PR to define a class of minimum distance estimators and estimating equations in the discrete case, while Markatou et al (1998) define weighted likelihood estimating equations (WLEE) based on PR. Park et al (2002) have studied the properties of PR in relation to the residual adjustment function (Lindsay, 1994) and minimum disparity estimators.…”