Why do some stars have a negative parallax? I am constructing a Hertzsprung-Russell diagram for stars within some radius around Pleiades and have repeatedly come across stars that have negative parallaxes. For example, http://vizier.u-strasbg.fr/viz-bin/VizieR-5?-info=XML&-out.add=.&-source=I/239/tyc_main&recno=161838
I found three reasons listed in the following article for where these values come from, but I do not fully understand why the values are quoted as negative.

When a distant star, whether bright or faint, is observed through a scattered cluster, or perhaps rather a layer, of relatively near and faint stars, a negative parallax must be expected.

http://adsabs.harvard.edu/full/1943AnDea...4....1L
The article goes on to say that this parallax is the positive parallax of the comparison stars with respect to the distant star.
Is the magnitude of this parallax the distance between the distant star and the comparison stars, or between the Earth and the distant star?
 A: The parallaxes of very distant stars should be zero (or at least indistinguishable from zero). If the parallaxes have an observational uncertainty (which they do), then half of the parallaxes of very distant stars will be negative. I think this is all that you are finding in the case of absolute Hipparcos parallaxes (the catalogue your reference points to).
The quote you give from the 1943 paper is talking about relative parallaxes. When you determine relative parallax you find the apparent movement in the sky with respect to a bunch of comparision stars in the same region. You make the assumption that most of these stars are very far away and have zero parallax. In any random direction in the Galaxy this tends to be true. However, if a large fraction of the stars in fact have a positive and large parallax (because you are looking towards a nearby cluster), then the relative parallaxes of the genuinely distant stars in the cluster can end up negative on average.
I do not think that this should be the case for the Hipparcos/Tycho parallaxes because they use a different technique to get absolute parallax by looking simultaneously at patches of sky that are separated by an angle of 58 degrees - the so-called "basic angle" (see here for some follow-up on that.)
A: i think its the refraction effect. 
if parallax is given by (angle_final-angle_initial). and if this quantity is -ve, (due to refraction effect of stars lying in the foreground of the stars under observation), then parallax can be -ve.
