In series of papers, the Boer-Mulders function for a given quark flavor has been extracted: (i) from data on semi-inclusive deep inelastic scattering, using the simplifying, but theoretically inconsistent, assumption that it is proportional to the Sivers function for each quark flavor and (ii) from data on Drell-Yan reactions. In earlier papers, using the semi-inclusive deep inelastic COMPASS deuteron data on the
⟨
cos
ϕ
h
⟩
and
⟨
cos
2
ϕ
h
⟩
asymmetries, we extracted the collinear
x
B
dependence of the Boer-Mulders function for the sum of the valence quarks
Q
V
=
u
V
+
d
V
using a small number of model dependent assumptions and found a significant disagreement with the analysis in (i). In the present paper, we provide a more complete analysis of the semi-inclusive deep inelastic scattering reaction, including a discussion of higher twist and interaction-dependent terms, and also a comparison with the Boer-Mulders function extracted from data on the Drell-Yan reaction. We confirm that the proportionality relation of the BM function to the Sivers function, for each quark flavor, fails badly, but find that it holds rather well if applied to the nonsinglet valence-quark combination,
Q
V
. We also find good agreement with the results of the Drell-Yan analysis. Furthermore, we obtain interesting information on the quark transverse momentum densities in the nucleon and on the hadron transverse momentum dependence in quark fragmentation.