The Hough transform-based method provides a bad performance in the fourth row due to invalid scale estimation.
In the case that there are no invalid elements, estimation of α can be accomplished by solving a MMV problem based on l 1-norm minimization: begin{array}rcl@ minlimits_{boldsymbol{tilde{X}}} {left| {{{boldsymbol{tilde{x}}}^{{l_{2}}}}} right|_{1}},s.t.left| {boldsymbol{Y} - {{boldsymbol{tilde{A}}}^{L}}boldsymbol{tilde{X}}} right|_{F}^{2}< {sigma_{1}^{2}}, end{array} (16).
Bowden, J., Davey Smith, G. & Burgess, S. Mendelian randomization with invalid instruments: effect estimation and bias detection through Egger regression.
A Backtracking PF recalculates the previous state estimation without invalid trajectories to improve performance.
In [5], the transmission of Gaussian symbols through a flat-fading channel was considered and it was demonstrated that when the Gaussianity assumption on the additive noise is rendered invalid due to channel estimation errors, scaled nearest neighbor detection is suboptimal.
Given significant heterogeneity among these components, a composite outcome may be judged as being invalid or un-interpretable for estimation of the treatment effect.
It is preferable to set the pixels with a large distance as invalid and filter them out after the estimation process enters the steady state.
Bowden, J., Davey Smith, G., Haycock, P. C. & Burgess, S. Consistent estimation in Mendelian randomization with some invalid instruments using a weighted median estimator.
Our key finding is that researchers fail to address at least 66% and up to 90% of design and estimation conditions that make causal claims invalid.
Notice the difference for the invalid regions with our models and the Kernel Density Estimation model.
With a variance of, we see in Figure 1 d) that the Kernel Density Estimation predicts that events may occur in our invalid region.
