Empirical Process Theory for Dual Norms

2016 ◽  
pp. 121-131
Author(s):  
Sara van de Geer
Keyword(s):  
Empirical Process ◽  
Process Theory ◽  
Empirical Process Theory

scholarly journals General Bootstrap for Dual ϕ-Divergence Estimates

2012 ◽  
Vol 2012 ◽  
pp. 1-33 ◽  
Author(s):  
Salim Bouzebda ◽  
Mohamed Cherfi
Keyword(s):  
Coverage Probability ◽  
Empirical Process ◽  
Asymptotic Properties ◽  
Process Theory ◽  
General Notion ◽  
Finite Sample ◽  
Confidence Set ◽  
Empirical Process Theory ◽  
Divergence Estimates ◽  
Simulation Results

A general notion of bootstrappedϕ-divergence estimates constructed by exchangeably weighting sample is introduced. Asymptotic properties of these generalized bootstrappedϕ-divergence estimates are obtained, by means of the empirical process theory, which are applied to construct the bootstrap confidence set with asymptotically correct coverage probability. Some of practical problems are discussed, including, in particular, the choice of escort parameter, and several examples of divergences are investigated. Simulation results are provided to illustrate the finite sample performance of the proposed estimators.

Outlier Detection

2018 ◽  
Author(s):  
Bent Nielsen
Keyword(s):  
Asymptotic Theory ◽  
Empirical Process ◽  
Robust Statistics ◽  
Formal Theory ◽  
Simulation Studies ◽  
Asymptotic Results ◽  
Forthcoming Article ◽  
Empirical Process Theory ◽  
Impulse Indicator Saturation ◽  
Detection Of Outliers

This is an advance summary of a forthcoming article in the Oxford Research Encyclopedia of Economics and Finance. Please check back later for the full article. Detection of outliers is an important explorative step in empirical analysis. Once detected, the investigator will have to decide how to model the outliers depending on the context. Indeed, the outliers may represent noisy observations that are best left out of the analysis or they may be very informative observations that would have a particularly important role in the analysis. For regression analysis in time series a number of outlier algorithms are available, including impulse indicator saturation and methods from robust statistics. The algorithms are complex and their statistical properties are not fully understood. Extensive simulation studies have been made, but the formal theory is lacking. Some progress has been made toward an asymptotic theory of the algorithms. A number of asymptotic results are already available building on empirical process theory.

scholarly journals Complexity of possibly gapped histogram and analysis of histogram

2018 ◽  
Vol 5 (2) ◽  
pp. 171026 ◽  
Author(s):  
Hsieh Fushing ◽  
Tania Roy
Keyword(s):  
Clustering Algorithm ◽  
Empirical Process ◽  
Minimum Energy ◽  
Complex Problem ◽  
Second Phase ◽  
Empirical Process Theory ◽  
Technical Developments ◽  
Macroscopic States ◽  
Hierarchical Clustering Algorithm ◽  
Multiple Treatments

We demonstrate that gaps and distributional patterns embedded within real-valued measurements are inseparable biological and mechanistic information contents of the system. Such patterns are discovered through data-driven possibly gapped histogram, which further leads to the geometry-based analysis of histogram (ANOHT). Constructing a possibly gapped histogram is a complex problem of statistical mechanics due to the ensemble of candidate histograms being captured by a two-layer Ising model. This construction is also a distinctive problem of Information Theory from the perspective of data compression via uniformity. By defining a Hamiltonian (or energy) as a sum of total coding lengths of boundaries and total decoding errors within bins, this issue of computing the minimum energy macroscopic states is surprisingly resolved by applying the hierarchical clustering algorithm. Thus, a possibly gapped histogram corresponds to a macro-state. And then the first phase of ANOHT is developed for simultaneous comparison of multiple treatments, while the second phase of ANOHT is developed based on classical empirical process theory for a tree-geometry that can check the authenticity of branches of the treatment tree. The well-known Iris data are used to illustrate our technical developments. Also, a large baseball pitching dataset and a heavily right-censored divorce data are analysed to showcase the existential gaps and utilities of ANOHT.

scholarly journals Stochastic Equicontinuity for Unbounded Dependent Heterogeneous Arrays

1996 ◽  
Vol 12 (2) ◽  
pp. 347-359 ◽  
Author(s):  
Bruce E. Hansen
Keyword(s):  
Empirical Process ◽  
Dependent Data ◽  
Strong Mixing ◽  
Martingale Difference ◽  
Lipschitz Continuous ◽  
Empirical Process Theory ◽  
Dependence Conditions ◽  
Bounded Functions ◽  
Parametric Functions ◽  
Stochastic Equicontinuity

This paper establishes stochastic equicontinuity for classes of mixingales. Attention is restricted to Lipschitz-continuous parametric functions. Unlike some other empirical process theory for dependent data, our results do not require bounded functions, stationary processes, or restrictive dependence conditions. Applications are given to martingale difference arrays, strong mixing arrays, and near-epoch dependent arrays.

A challenge for predictive coding: Representational or experiential diversity?

2020 ◽  
Vol 43 ◽  
Author(s):  
Martina G. Vilas ◽  
Lucia Melloni
Keyword(s):  
Brain Function ◽  
Predictive Coding ◽  
Predictive Processing ◽  
Process Theory

Abstract To become a unifying theory of brain function, predictive processing (PP) must accommodate its rich representational diversity. Gilead et al. claim such diversity requires a multi-process theory, and thus is out of reach for PP, which postulates a universal canonical computation. We contend this argument and instead propose that PP fails to account for the experiential level of representations.

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