Nonparametric Curve Estimation in the Presence of Nuisance Functions

该提案的重点是发展统计方法，理论和方法的自适应非参数曲线估计在滋扰功能的存在。它的动机是生物和医学应用。研究者主要研究四类被考虑的问题。每一个分类的估计如何可以匹配的Oracle知道潜在的滋扰功能的性能。它们是：（a）Estimate可以匹配Oracle。一个例子是一个回归问题，光滑的设计密度是滋扰函数。(b)如果有补充观测，则估计值可以匹配oracle。例子是去卷积和回归与测量误差的预测，其中需要补充的意见，以估计测量误差的分布。(c)估计值无法与Oracle匹配。一个例子是当滋扰回归函数不够平滑时回归误差密度的估计。(d)上述配方设置的混合物。建议为上述类别的统计问题开发一个自适应估计的一般理论，特别适用于：缺失，分层和删失数据，隐藏组件，涉及连续和名义或有序分类变量的混合多变量模型，以及时间序列。理论结果进行了测试，并应用于ChIP芯片微阵列和超快fMRI的分析。研究的主要重点是创建自适应的统计程序，可以在滋扰功能的存在下工作。这项研究的动机是在统计分析中充分理解的应用程序进行测试：（i）ChIP芯片微阵列用于在细菌基因组中找到调节蛋白结合位点。蛋白质和DNA之间的相互作用是生命的基础。它们促进和介导基因表达、DNA复制和修复。所提出的ChIP芯片微阵列的统计分析指出了蛋白质-DNA结合位点的确切位置。由于统计分析不需要测量讨厌的功能，它使微阵列实验更便宜，更快，更准确。(ii)超快速功能磁共振图像，有助于了解衰老和大脑疾病，如阿尔茨海默氏症和帕金森氏症。超快速功能磁共振成像是一种令人兴奋的研究大脑功能的新技术，其时间分辨率为50毫秒。这种分辨率揭示了大脑中的神经元和生理活动。建议的统计分析，这是强大的滋扰功能，可以去噪情绪动力学反应，研究认知功能，如记忆，语音和情感，并创建一个地图的生理活动的人脑。

The proposal focuses on developing statistical methodology, theory and methods of adaptive nonparametric curve estimation in the presence of nuisance functions. It is motivated by biological and medical applications. The investigator studies four main classes of considered problems. Each is classified by how an estimator can match the performance of an oracle knowing underlying nuisance functions. They are: (a) Estimator can match oracle. An example is a regression problem with a smooth design density being nuisance function. (b) Estimator can match oracle if complementary observations are available. Examples are deconvolution and regression with measurement errors in predictors where complementary observations are needed to estimate distribution of measurement error. (c) Estimator cannot match oracle. An example is estimation of the density of regression error when a nuisance regression function is not sufficiently smooth. (d) A mixture of the above-formulated settings. It is proposed to develop a general theory of adaptive estimation for the aforementioned classes of statistical problems with particular applications to: missing, stratified and censored data, hidden components, mixed multivariate models involving continuous and nominal or ordinal categorical variables, and time series. Theoretical results are tested and applied to the analysis of ChIP-on-chip microarrays and ultra-fast fMRI.The primary focus of the research is to create adaptive statistical procedures which can work in the presence of nuisance functions. This research is motivated by and tested on well-understood applications in the statistical analysis of: (i) ChIP-on-chip microarrays used to find regulatory protein binding sites in a bacterial genome. Interactions between protein and DNA are fundamental to life. They facilitate and mediate gene expression, DNA replication and repair. The proposed statistical analysis of ChIP-on-chip microarrays points on exact location of protein-DNA binding sites. Because the statistical analysis does not require measuring of nuisance functions, it makes microarray experiments cheaper, faster and more accurate. (ii) Ultra-fast functional magnet resonance images, which help in understanding aging and brain diseases such as Alzheimer's and Parkinson's Diseases. Ultra-fast fMRI is an exciting new technology for studying brain functions with the temporal resolution of 50 milliseconds. This resolution sheds light on both neurons and physiological activities in the brain. Proposed statistical analysis, which is robust to nuisance functions, can denoise emodynamic responses, study cognitive functions like memory, speech and emotion, and create a map of physiological activities of the human brain.