  We examine star formation activity in a distance- (z<0.1) and flux-limited
sample of quasars (QSOs). Mid-infrared (MIR) spectral diagnostics at high
spatial resolution (~0.4 arcsec) yield star formation rates (SFRs) in the inner
regions (~300 pc to 1 kpc) for 13 of 20 of the sample members. We group these
objects according to the size probed by the high angular resolution
spectroscopy, with characteristic scales of <0.7 and ~0.7-1 kpc. Using the
polycyclic aromatic hydrocarbon (PAH) feature at 11.3 um, we measure SFRs
around 0.2 and 1.6 M_{\odot}yr^{-1}. We also measure the larger aperture
PAH-derived SFRs in the individual IRS/Spitzer spectra of the sample and obtain
a clear detection in ~58 percent of them. We compare smaller and larger
aperture measurements and find that they are similar, suggesting that star
formation activity in these QSOs is more centrally concentrated, with the inner
region (>~1 kpc) accounting for the majority of star formation measured on
these scales, and that PAH molecules can be present in most local MIR-bright
QSOs within a few hundred pc from the central engine. By comparison with merger
simulations, we find that our estimation of the SFR and black hole (BH)
accretion rates are consistent with a scenario in which the star formation
activity is centrally peaked as predicted by simulations.
