20,915 research outputs found

    A multivariate uniformity test for the case of unknown support

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    The final publication is available at http://dx.doi.org/10.1007/s11222-010-9222-

    Recent advances in directional statistics

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    Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page

    Testing multivariate uniformity based on random geometric graphs

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    We present new families of goodness-of-fit tests of uniformity on a full-dimensional set WāŠ‚RdW\subset\R^d based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the null hypothesis as well as under fixed alternatives. The derived tests are consistent and their behaviour for some contiguous alternatives can be controlled. A simulation study suggests that the procedures can compete with or are better than established goodness-of-fit tests. We show with a real data example that the new tests can detect non-uniformity of a small sample data set, where most of the competitors fail.Comment: 36 pages, 2 figure

    A common goodness-of-fit framework for neural population models using marked point process time-rescaling

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    A critical component of any statistical modeling procedure is the ability to assess the goodness-of-fit between a model and observed data. For spike train models of individual neurons, many goodness-of-fit measures rely on the time-rescaling theorem and assess model quality using rescaled spike times. Recently, there has been increasing interest in statistical models that describe the simultaneous spiking activity of neuron populations, either in a single brain region or across brain regions. Classically, such models have used spike sorted data to describe relationships between the identified neurons, but more recently clusterless modeling methods have been used to describe population activity using a single model. Here we develop a generalization of the time-rescaling theorem that enables comprehensive goodness-of-fit analysis for either of these classes of population models. We use the theory of marked point processes to model population spiking activity, and show that under the correct model, each spike can be rescaled individually to generate a uniformly distributed set of events in time and the space of spike marks. After rescaling, multiple well-established goodness-of-fit procedures and statistical tests are available. We demonstrate the application of these methods both to simulated data and real population spiking in rat hippocampus. We have made the MATLAB and Python code used for the analyses in this paper publicly available through our Github repository at https://github.com/Eden-Kramer-Lab/popTRT.This work was supported by grants from the NIH (MH105174, NS094288) and the Simons Foundation (542971). (MH105174 - NIH; NS094288 - NIH; 542971 - Simons Foundation)Published versio

    Should we be surprised by the unreliability of real-time output gap estimates? Density estimates for the Euro area

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    Recent work has found that, without the benefit of hindsight, it can prove difficult for policy-makers to pin down accurately the current position of the output gap; real-time estimates are unreliable. However, attention primarily has focused on output gap point estimates alone. But point forecasts are better seen as the central points of ranges of uncertainty; therefore some revision to real-time estimates may not be surprising. To capture uncertainty fully density forecasts should be used. This paper introduces, motivates and discusses the idea of evaluating the quality of real-time density estimates of the output gap. It also introduces density forecast combination as a practical means to overcome problems associated with uncertainty over the appropriate output gap estimator. An application to the Euro area illustrates the use of the techniques. Simulated out-of-sample experiments reveal that not only can real-time point estimates of the Euro area output gap be unreliable, but so can measures of uncertainty associated with them. The implications for policy-makers use of Taylor-type rules are discussed and illustrated. We find that Taylor-rules that exploit real-time output gap density estimates can provide reliable forecasts of the ECB's monetary policy stance only when alternative density forecasts are combinedOutput gap; Real-Time; Density Forecasts; Density Forecast Combination; Taylor Rules

    Measuring output gap uncertainty

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    We propose a methodology for producing density forecasts for the output gap in real time using a large number of vector autoregessions in inflation and output gap measures. Density combination utilizes a linear mixture of experts framework to produce potentially non-Gaussian ensemble densities for the unobserved output gap. In our application, we show that data revisions alter substantially our probabilistic assessments of the output gap using a variety of output gap measures derived from univariate detrending filters. The resulting ensemble produces well-calibrated forecast densities for US inflation in real time, in contrast to those from simple univariate autoregressions which ignore the contribution of the output gap. Combining evidence from both linear trends and more flexible univariate detrending filters induces strong multi-modality in the predictive densities for the unobserved output gap. The peaks associated with these two detrending methodologies indicate output gaps of opposite sign for some observations, reflecting the pervasive nature of model uncertainty in our US data

    Comparison of MSACD models

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    We propose a new framework for modelling time dependence in duration processes on financial markets. The well known autoregressive conditional duration (ACD) approach introduced by Engle and Russell (1998) will be extended in a way that allows the conditional expectation of the duration process to depend on an unobservable stochastic process which is modelled via a Markov chain. The Markov switching ACD model (MSACD) is a very flexible tool for description and forecasting of financial duration processes. In addition, the introduction of an unobservable, discrete valued regime variable can be justified in the light of recent market microstructure theories. In an empirical application we show that the MSACD approach is able to capture several specific characteristics of inter trade durations while alternative ACD models fail. JEL classification: C22, C25, C41, G1
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