アブストラクト
	セッション２：ノンパラメトリック法の最近の展開 Exploiting the moment-preserving density function and its applications 寒河江雅彦（金沢大学）、小暮厚之（慶応大学） 局所モーメント情報を満たすノンパラメトリック密度推定量の性質を簡単にレビューし、与えられたモーメント情報をもつ密度関数を作るためのカーネル関数による構成法を示す。また、カーネル関数とモーメントの関係についても述べる。 Estimation of Stochastic Volatility Models by Nonparametric Filtering 金谷 信 (Cambridge Univ.) and Dennis Kristensen (Columbia Univ.) A new estimation method of stochastic volatility models is proposed based on the nonparametric filter of the instantaneous volatility process of Kristensen (2008). We propose to use standard estimation methods for fully observed diffusion processes but with the filtered volatility process replacing the latent process. The proposed estimators will carry biases due to the use of the filtered volatility instead of the actual volatility, but under regularity conditions this vanishes asymptotically and our estimators inherit the asymptotic properties of the infeasible estimators based on observations of the volatility process. Our estimation strategy is applicable to both parametric and nonparametric stochastic volatility models, and we give theoretical results for both. A simulation study examines the finite-sample properties of the proposed estimators. Difference-based Estimation for Semiparametric Varying-Coefficient Partially Linear Models Qingfeng Liu (京都大学)*, Yichao Wu (North Carolina State Univ.), Jianqing Fan (Princeton Univ.) The varying-coefficient partially linear model (VCPLM) is a mixture of the varying-coefficient model (VCM) and partially linear model (PLM). It improves over both of them in terms of flexibility. It allows the coefficient of the nonlinear component to vary according to some additional variables so that the model is flexible enough to express complicated real-world phenomena. In addition VCPLM can alleviate the so-called "curse of dimensionality" of VCM. This paper targets at the asymptotic properties of the differenced based estimator (DBE) for the linear components of VCPLM. Regularity conditions for asymptotic normality of DBE are derived. We further show that when the difference order q grows to infinity with the sample size n, the efficiency of the estimator can be improved by choosing appropriate weights. We propose a type of optimal weight matrix, spike and compund spike weights. We call such spike and compund spike weights optimal weights because the efficiency of the DBE cannot be improved anymore by using other weight matrix. A plug-in method is provided for estimating the non-parametric component and its convergence rate is provided. The compund spike weight is applied to some simulation experiments and real data to demonstrate its finite-sample performance. A Nonparametric Test for the Existence of Moments 人見光太郎（京都工芸繊維大学），西山慶彦 (京都大学) ，永井 圭二 (横浜国立大学) In many statistical procedures, the existence of moments of certain order is required. For example, laws of large numbers require the existence of mean, and central limit theorems entail the existence of variance. They play essential roles in proving the consistency of estimators and hypothesis testing respectively. In the case of fully parametric approach, specified models determine if moments of some order exist or not, possibly depending on the parameter values. If the existence depends on the parameter values, as in, say, Pareto distribution, t distribution and many more, we will be able to test for the existence of moments using the parameter estimates. Obviously, the correct specification is essential there. To the best of our knowledge, however, there is no test for the existence of moments proposed before in nonparametric framework. The present paper proposes a nonparametric test for the existence of moments. We consider a class of distributions in which the characteristic function is differentiable as many times as one wishes except the origin. It is, we believe, a sufficiently broad class in empirical applications, which is characterized using the theory of hyperfunctions. We use the estimates of left (and right) limit(s) of the first two derivatives of the characteristic function to construct the test statistics. We examine the property by some Monte Carlo simulation.