Frederic Udina

Universal smoothing factor selection in density estimation: theory and practice

AbstractIn earlier work with Gabor Lugosi, we introduced a method to select a smoothing factor for kernel density estimation such that, forall densities in all dimensions, theL1 error of the corresponding kernel estimate is not larger than 3+∈ times the error of the estimate with the optimal smoothing factor plus a constant times

Measuring the stability of histogram appearance when the anchor position is changed

\sqrt {\log n/n}

Interactive local bandwidth choice

, wheren is the sample size, and the constant only depends on the complexity of the kernel used in the estimate. The result is nonasymptotic, that is, the bound is valid for eachn. The estimate uses ideas from the minimum distance estimation work of Yatracos. We present a practical implementation of this estimate, report on some comparative results, and highlight some key properties of the new method.

Visualizing Categorical Data

The purpose of this paper is to introduce sequential investment strategies that guarantee an optimal rate of growth of the capital, under minimal assumptions on the behavior of the market. The new strategies are analyzed both theoretically and empirically. The theoretical results show that the asymptotic rate of growth matches the optimal one that one could achieve with a full knowledge of the statistical properties of the underlying process generating the market, under the only assumption that the market is stationary and ergodic. The empirical results show that the performance of the proposed investment strategies measured on past nyse and currency exchange data is solid, and sometimes even spectacular.

Environmental versus Human-Induced Scarcity in the Commons: Do They Trigger the Same Response?

Although the histogram is the most widely used density estimator, it is well--known that the appearance of a constructed histogram for a given bin width can change markedly for different choices of anchor position. In this paper we construct a stability index

High-dimensional random geometric graphs and their clique number

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Interactive Biplot Construction

that assesses the potential changes in the appearance of histograms for a given data set and bin width as the anchor position changes. If a particular bin width choice leads to an unstable appearance, the arbitrary choice of any one anchor position is dangerous, and a different bin width should be considered. The index is based on the statistical roughness of the histogram estimate. We show via Monte Carlo simulation that densities with more structure are more likely to lead to histograms with unstable appearance. In addition, ignoring the precision to which the data values are provided when choosing the bin width leads to instability. We provide several real data examples to illustrate the properties of

The Health of Lisp-Stat

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