Problems of nonparametric ltering arises frequently in engineering and nancial economics. Nonparametric lters often involve some ltering parameters to choose. These parameters can be chosen to optimize the performance locally at each time point or globally over a time interval. In this article, the ltering parameters are chosen via minimizing the prediction error for a large class of lters. Under a general martingale setting, with mild conditions on the time series structure and virtually no assumption on lters, we show that the adaptive lter with ltering parameter chosen by historical data performs nearly as well as the one with the ideal lter in the class, in terms of ltering errors. The theoretical result is also veri ed via intensive simulations. Our approach is also useful for choosing the orders of parametric models such as AR or GARCH processes. It can also be applied to volatility estimation in nancial economics. We illustrate the proposed methods by estimating the volatility of the returns of the S&P500 index and the yields of the three-month Treasury bills.

Cryo-electron microscopy (cryo-EM) has recently emerged as a powerful tool for obtaining three-dimensional (3D) structures of biological macromolecules in native states. A minimum cryo-EM image data set for deriving a meaningful reconstruction is comprised of thousands of randomly orientated projections of identical particles photographed with a small number of electrons. The computation of 3D structure from 2D projections requires clustering, which aims to enhance the signal to noise ratio in each view by grouping similarly oriented images. Nevertheless, the prevailing clustering techniques are often compromised by three characteristics of cryo-EM data: high noise content, high dimensionality and large number of clusters. Moreover, since clustering requires registering images of similar orientation into the same pixel coordinates by 2D alignment, it is desired that the clustering algorithm can label misaligned images as outliers. Herein, we introduce a clustering algorithm γ-SUP to model the data with a q-Gaussian mixture and adopt the minimum γ-divergence for estimation, and then use a self-updating procedure to obtain the numerical solution. We apply γ-SUP to the cryo-EM images of two benchmark macromolecules, RNA polymerase II and ribosome. In the former case, simulated images were chosen to decouple clustering from alignment to demonstrate γ-SUP is more robust to misalignment outliers than the existing clustering methods used in the cryo-EM community. In the latter case, the clustering of real cryo-EM data by our γ-SUP method eliminates noise in many views to reveal true structure features of ribosome at the projection level.

No abstract uploaded!

The multiple testing procedure plays an important role in detecting the presence of spatial signals for large scale imaging data. Typically, the spatial signals are sparse but clustered. This paper provides empirical evidence that for a range of commonly used control levels, the conventional FDR procedure can lack the ability to detect statistical significance, even if the p-values under the true null hypotheses are independent and uniformly distributed; more generally, ignoring the neighboring information of spatially structured data will tend to diminish the detection effectiveness of the FDR procedure. This paper first introduces a scalar quantity to characterize the extent to which the lack of identification phenomenon(LIP) of the FDR procedure occurs. Second, we propose a new multiple comparison procedure, called FDR L, to accommodate the spatial information of neighboring p-values, via a local aggregation of p

When people in a society want to make inference about some parameter, each person would potentially want to use data collected by other people. Information (data) exchange in social contexts is usually costly, so to make sound statistical decisions, people need to compromise between benefits and costs of information acquisition. Conflicts of interests and coordination will arise. Classical statistics does not consider peoples interaction in the data collection process. To address this ignorance, this work explores multi-agent Bayesian inference problems with a game theoretic social network model. Bearing our interest in aggregate inference at the societal level, we propose a new concept finite population learning to address whether with high probability, a large fraction of people can make good inferences. Serving as a foundation, this concept enables us to study the long run trend of aggregate inference quality as population grows.