62 research outputs found

    Linear Estimation of Location and Scale Parameters Using Partial Maxima

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    Consider an i.i.d. sample X^*_1,X^*_2,...,X^*_n from a location-scale family, and assume that the only available observations consist of the partial maxima (or minima)sequence, X^*_{1:1},X^*_{2:2},...,X^*_{n:n}, where X^*_{j:j}=max{X^*_1,...,X^*_j}. This kind of truncation appears in several circumstances, including best performances in athletics events. In the case of partial maxima, the form of the BLUEs (best linear unbiased estimators) is quite similar to the form of the well-known Lloyd's (1952, Least-squares estimation of location and scale parameters using order statistics, Biometrika, vol. 39, pp. 88-95) BLUEs, based on (the sufficient sample of) order statistics, but, in contrast to the classical case, their consistency is no longer obvious. The present paper is mainly concerned with the scale parameter, showing that the variance of the partial maxima BLUE is at most of order O(1/log n), for a wide class of distributions.Comment: This article is devoted to the memory of my six-years-old, little daughter, Dionyssia, who leaved us on August 25, 2010, at Cephalonia isl. (26 pages, to appear in Metrika

    Bid Increments in Second-Price Sealed Bid Auctions

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    This note concerns bidding in a hybrid first-price and second-price auction. The winning bidder sometimes pays his bid and sometimes pays an amount determined by the next highest bid. In internet auctions where bidders wait until the end of the auction to bid the auction reduces to a sealed-bid auction and the bid function we derive may be relevant in such cases.sniper bidding, bid increments

    Identification of Search Models with Initial Condition Problems

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    This paper extends previous work on the identification of search models in which observed worker productivity is imperfectly observed. In particular, it establishes that these models remain identified even when employment histories are left-censored (i.e. we do not get to follow workers from their initial job out of unemployment), as well as when workers set different reservation wages from one another. We further show that allowing for heterogeneity in reservation can affect the empirical estimates we obtain, specifically estimates of the rate at which workers receive job offers.

    Identification of search models with initial condition problems

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    This paper extends previous work on the identification of search models in which observed worker productivity is imperfectly observed. In particular, it establishes that these models remain identified even when employment histories are left-censored (i.e. we do not get to follow workers from their initial job out of unemployment), as well as when workers set different reservation wages from one another. We further show that allowing for heterogeneity in reservation can affect the empirical estimates we obtain, specifically estimates of the rate at which workers receive job offers.Labor mobility ; Wages

    Estimating Models of On-the-Job Search Using Record Statistics

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    This paper proposes a methodology for estimating job search models that does not require either functional form assumptions or ruling out the presence of unobserved variation in worker ability. In particular, building on existing results from record-value theory, a branch of statistics that deals with the timing and magnitude of extreme values in sequences of random variables, I show how we can use wage data to identify the distribution from which workers search. Applying this insight to wage data in the NLSY dataset, I show that the data supports the hypothesis that the wage offer distribution is Pareto, but not that it is lognormal.

    Exact and asymptotic solutions of the call auction problem

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    The call auction is a widely used trading mechanism, especially during the opening and closing periods of financial markets. In this paper, we study a standard call auction problem where orders are submitted according to Poisson processes, with random prices distributed according to a general distribution, and may be cancelled at any time. We compute the analytical expressions of the distributions of the traded volume, of the lower and upper bounds of the clearing prices, and of the price range of these possible clearing prices of the call auction. Using results from the theory of order statistics and a theorem on the limit of sequences of random variables with independent random indices, we derive the weak limits of all these distributions. In this setting, traded volume and bounds of the clearing prices are found to be asymptotically normal, while the clearing price range is asymptotically exponential. All the parameters of these distributions are explicitly derived as functions of the parameters of the incoming orders' flows.Comment: 24 pages, 7 figure

    A Probabilistic Upper Bound on Differential Entropy

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    A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the unknown distribution is required, nor is the distribution required to have a density. Previous distribution-free bounds on the cumulative distribution function of a random variable given a sample of that variable are used to construct the bound. A simple, fast, and intuitive algorithm for computing the entropy bound from a sample is provided

    Graphical Test for Discrete Uniformity and its Applications in Goodness of Fit Evaluation and Multiple Sample Comparison

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    Assessing goodness of fit to a given distribution plays an important role in computational statistics. The Probability integral transformation (PIT) can be used to convert the question of whether a given sample originates from a reference distribution into a problem of testing for uniformity. We present new simulation and optimization based methods to obtain simultaneous confidence bands for the whole empirical cumulative distribution function (ECDF) of the PIT values under the assumption of uniformity. Simultaneous confidence bands correspond to such confidence intervals at each point that jointly satisfy a desired coverage. These methods can also be applied in cases where the reference distribution is represented only by a finite sample. The confidence bands provide an intuitive ECDF-based graphical test for uniformity, which also provides useful information on the quality of the discrepancy. We further extend the simulation and optimization methods to determine simultaneous confidence bands for testing whether multiple samples come from the same underlying distribution. This multiple sample comparison test is especially useful in Markov chain Monte Carlo convergence diagnostics. We provide numerical experiments to assess the properties of the tests using both simulated and real world data and give recommendations on their practical application in computational statistics workflows
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