主題：An Integrated GMM Shrinkage Approach with Consistent Moment Selection from Multiple External Sources 基于多源外部信息一致矩選擇的集成廣義矩估計(jì)壓縮方法
主講人：美國(guó)威斯康星大學(xué)麥迪遜分校統(tǒng)計(jì)系 邵軍教授
主持人：統(tǒng)計(jì)學(xué)院副院長(zhǎng) 蘭偉教授
時(shí)間：12月26日15:00-16:00
地點(diǎn)：柳林校區(qū)誠(chéng)正樓1320
主辦單位：統(tǒng)計(jì)學(xué)院 科研處
主講人簡(jiǎn)介：
邵軍，美國(guó)威斯康星大學(xué)麥迪遜分校統(tǒng)計(jì)系、華東師范大學(xué)統(tǒng)計(jì)學(xué)院教授，入選國(guó)家海外高層次人才計(jì)劃，國(guó)際數(shù)理統(tǒng)計(jì)學(xué)會(huì)（IMS）和美國(guó)統(tǒng)計(jì)學(xué)會(huì)（ASA）會(huì)士。他是Statistical Theory and Related Fields的創(chuàng)始主編，曾擔(dān)任JASA及Statistica Sinica等眾多權(quán)威統(tǒng)計(jì)學(xué)期刊的主編、聯(lián)合主編及副主編；曾任美國(guó)威斯康星大學(xué)麥迪遜分校統(tǒng)計(jì)系主任（2005-2009）、國(guó)際泛華統(tǒng)計(jì)學(xué)會(huì)會(huì)長(zhǎng)（2007）。自1987年以來(lái)，在統(tǒng)計(jì)學(xué)領(lǐng)域的國(guó)際頂尖期刊上發(fā)表論文40余篇，在重抽樣技術(shù)、變量選擇、生物統(tǒng)計(jì)和缺失數(shù)據(jù)的統(tǒng)計(jì)處理等方面做了大量開(kāi)創(chuàng)性工作。
內(nèi)容提要：
Interest has grown in analyzing primary internal data by utilizing some independent external aggregated statistics for efficiency gain. However, when population heterogeneity exists, inappropriate incorporation may lead to a biased estimator. With multiple external sources under generalized estimation equations and possibly heterogeneous populations, we propose an integrated generalized moment method that can perform a data-driven selection of valid moment equations from external sources and make efficient parameter estimation simultaneously. Moment equation selection consistency and asymptotic normality are established for the proposed estimator. Further, when the sample sizes of all external sources are large compared to the internal sample size, asymptotically the proposed estimator is more efficient than the estimator based on the internal data only and is oracle-efficient in the sense that it is as efficient as the oracle estimator based on all valid moment equations. Simulation studies confirm the theoretical results and the efficiency of the proposed method empirically. An example is also included for illustration.
在分析內(nèi)部數(shù)據(jù)時(shí)，研究者越來(lái)越傾向于利用一些獨(dú)立的外部匯總信息來(lái)提高估計(jì)效率。然而，當(dāng)存在數(shù)據(jù)異質(zhì)性時(shí)，不恰當(dāng)?shù)恼峡赡軙?huì)導(dǎo)致估計(jì)量產(chǎn)生偏差。針對(duì)存在多個(gè)外部數(shù)據(jù)源且數(shù)據(jù)源總體可能存在異質(zhì)性的廣義估計(jì)方程，我們提出了一種集成廣義矩估計(jì)方法，該方法可以從外部數(shù)據(jù)源中進(jìn)行數(shù)據(jù)驅(qū)動(dòng)的有效矩方程選擇，并同時(shí)進(jìn)行高效的參數(shù)估計(jì)。我們?yōu)樗岢龅墓烙?jì)量建立了矩方程選擇的一致性和漸近正態(tài)性。并且當(dāng)所有外部數(shù)據(jù)源的樣本量遠(yuǎn)大于內(nèi)部數(shù)據(jù)樣本量時(shí)，本文所提出估計(jì)量的漸近效率高于僅基于內(nèi)部數(shù)據(jù)的估計(jì)量，且具有Oracle效率，即其效率與基于所有有效矩方程的Oracle估計(jì)量相當(dāng)。模擬結(jié)果驗(yàn)證了該方法的理論結(jié)果和有效性。此外，我們還通過(guò)一個(gè)實(shí)際例子進(jìn)行了說(shuō)明。
