SMOOTHED VERSIONS OF STATISTICAL FUNCTIONALS FROM A FINITE POPULATION

スポンサーリンク

概要

• 論文の詳細を見る

• We will consider the central limit theorem for the smoothed version of statistical functionals in a finite population. For the infinite population, Reeds (1976) and Fernholz (1983) discuss the problem under the conditions of Hadamard differentiability of the statistical functionals and derive Taylor type expansions. Lindeberg-Feller's central limit theorem is applied to the leading term, and controlling the remainder terms, the central limit theorem for the statistical functionals are proved. We will modify Fernholz's method and apply it to the finite population with smoothed empirical distribution functions, and we will also obtain Taylor type expansions. We then apply the Erdos-Renyi central limit theorem to the leading linear term to obtain the central limit theorem. We will also obtain sufficient conditions for the central limit theorem, both for the smoothed influence function, and the original non-smoothed versions. Some Monte Carlo simulation results are also included.

• 一般社団法人日本統計学会の論文

著者

• Takahashi Hajime

  The Graduate School Of Economics Hitotsubashi University

• Motoyama Hitoshi

  The Graduate School of Economics, Hitotsubashi University

• Motoyama Hitoshi

  The Graduate School Of Economics Hitotsubashi University:statistical Information Institute For Consu

関連論文

• SMOOTHED VERSIONS OF STATISTICAL FUNCTIONALS FROM A FINITE POPULATION

スポンサーリンク