Nonparametric estimation of distribution function

국문 초록 (Abstract)

數理統計學의 非母數(nonparametric)理論은, 資料의 分布法則은 未知인체로 展開되어있다. 그 未知의 分布函數가 推定가능하면 效率이 좋은 非母數 統計 量이 선택 가능하고, 결국 資料가 갖는 情報를 손실없이 이용할 수 있게 된다 일반적으로 分布函數의 표준적인 推定良으로서 經驗分布函數가 連續이라고 가 정하였을 때 離散形인 經驗分布函數는 連續性을 無視하는 것이다. 따라서 지 금까지 이용되었던 표준적인 方法을 대신하여,kernel函數와 smoothing para- meter을 이용한 방법이 脚光을 받고, 理論的으로도 그 좋은점이 證明되어져 있다. 本 論文에서는 kernel 函數에 의한 平滑化(smoothing)에 근거하여 推定量과 Smoothing Boostrap을 이용한 推定量에 관한 mean integrated squared error (MISE)와 intergrated squared error(ISE)를 중심으로 推定問題를 고찰하였다 첫째로,현재까지는 分布函數의 kernel형 推定量은 MISE를 最小로 하는 意味로 써 經驗分布函數를 이용한 推定方法보다 效率的이라는 것이 알려져 있다. 이 경우에는 平均하여 0이 되는 項은 無視되어버리지만 ISE의 경우에는 確率的으 로는 無視할 수 없다는 것을 本 論文의 結果에 의해 나타낼 수 있다. 둘째로, Boostrap Simulation에 있어서 經驗分布函數를 이용하는 方法을 대신하여 kernel형 推定量을 이용하는쪽이 效率的이라는 結果를 고려하여, 分布函數의 推定問題로써, MISE, ISE를 評價하는 方法論이 提示되었다.

다국어 초록 (Multilingual Abstract)

For an integrated understanding of developmental and cultural dimensiorls of pre-tend play, two issues \vere examined in the present researcll First, to examine how culture shapes children's play, the pretend play of I<orean- and Anglo-Americanpreschool children was compared Secondly, to understand hour individual diLferenccs lnfluence children's pretend play, the relatlonshlps between pretend play,social competence,and friendship wrere examined within and between the two cul-tures
Participants in the study were 46 Korean- and 46 Anglo-American preschoolchildren who were ol)served ln a free pla}' condltion and ln a toy play condition.Their parents completed play questlonnaires and preschool teachers completedteacher ratlngs of soclal competence Korean-American parents were asked tocomplete an acculturation scale
Results indicated that Korcan-American childrcn engaged less frequently in so-cial pretend play in the free play condltion. However, the dlfferences disappeared in the to}T condition Cultural differences were found ln parents' attitudes towardpla}T, play themes, and the way to comn-1unicate social pretend play between tlletwo cultures. Anglo-Amerjcan parents believed tllat chlldren's play is important for their children's development and joined their children's pretend play more oftenthan Korean-American parents. Korean-American children displayed more realisticthernes, whereas Anglo-American children enacted more fantastic themes. Therewere cultural differences in how children communicated play. Anglo-Atperican de-scribcd play in terms of their own activltles aDd rnade few attempt to influcne each
other In contrast, Korean-American children attempted to influence their peer'sbehavior using social bids. Moreover, the children who participated frequently insocial pretend play were rated as being sociable b}T their teachers regardless ofculture. However, these children were rated by teachers as ''difficult'' if they werefrom the Korean-American sample. In spite of cultural differences in number of mutual friends, the pattern of relations between social pretend play and mutualfriends was similar in the two samples.
These findings suggest that the capacity to engage in pretend play is universal.However, the expression of pretend play in terms of play themes and the way to communicate pretend play is influenced by culturc. Also, the relatlons between social pretend play, social competence, and friendship must be considered withinthe social-cultural context where children's play and their interaction take place