  The Compact Symmetric Objects (CSOs) are small (<1 kiloparsec) and powerful
extragalactic radio sources showing emission on both sides of an active
galactic nucleus and no signs of strong relativistic beaming. They may be young
radio sources, progenitors of large FRII radio galaxies. We aim to study the
statistical properties of CSOs by constructing and investigating a new large
sample of CSO candidates on the basis of dual-frequency, parsec-scale
morphology. For the candidate selection we utilized VLBI data for 4170
extragalactic objects obtained simultaneously at 2.3 and 8.6 GHz (S and X band)
within the VLBA Calibrator Survey 1-6 and the Research and Development - VLBA
projects. Properties of their broad-band radio spectra were characterized by
using RATAN-600 observations. Numerical modeling was applied in an attempt to
explain the observed effects. A sample of 64 candidate CSOs is identified. The
median two-point S-X band spectral index of parsec-scale hotspots is found to
be -0.52; with the median brightness temperature ~10^9 K at X band. Statistical
analysis reveals a systematic difference between positions of brightest CSO
components (associated with hotspots) measured in the S and X bands. The
distance between these components is found to be on average 0.32+/-0.06 mas
greater at 8.6 GHz than at 2.3 GHz. This difference in distances cannot be
explained by different resolutions at the S and X bands. It is a manifestation
of spectral index gradients across CSO components, which may potentially
provide important physical information about them. Despite our detailed
numerical modeling of a CSO hotspot, the model was not able to reproduce the
magnitude of the observed positional difference. A more detailed modeling may
shed light on the origin of the effect.
