  The aim of this research is to make a step towards providing a tool for model
selection for log-density estimation. The author revisits the procedure for
local log-density estimation suggested by Clive Loader (1996) and extends the
theoretical results to finite-sample framework with the help of machinery of
Spokoiny (2012). The results include bias expression from "deterministic"
counterpart and Fisher and Wilks-type theorems from "stochastic". We elaborate
on bandwidth trade-off $ h(n) = \arg\min O(h^p) + O_p(1/\sqrt{nh^d}) $ with
explicit constants at big O notation.
  Explicit expressions involve (i) true density function and (ii) model that is
selected (dimension, bandwidth, kernel and basis, e.g. polynomial). Existing
asymptotic properties directly follow from our results. From the expressions
obtained it is possible to control "the curse of dimension" both from the side
of log-density smoothness and the inner space dimension.
