1,720,977 research outputs found
Background
No full textIt is proved that for any given integer k> 2 and a k-monotone function g, there exists a k-monotone function ˜g ≤ g of the form c(a − x) k−1 + and passing through a fixed point in the support of g. The result is motivated by the problem of the existence of the LSE of a k-monotone density
Revisiting the Hodges-Lehmann estimator in a location mixture model: Is asymptotic normality good enough?
No full textThe distribution of the maximal difference between a Brownian bridge and its concave majorant
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Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
A Kiefer- Wolfowitz Theorem for Convex Densities
No full textAbstract: Kiefer and Wolfowitz [14] showed that if F is a strictly curved concave distribution function (corresponding to a strictly monotone density f), then the Maximum Likelihood Estimator �Fn, which is, in fact, the least concave majorant of the empirical distribution function Fn, differsfromthe empirical distribution function in the uniform norm by no more than a constant times (n −1 log n) 2/3 almost surely. We review their result and give an updated version of their proof. We prove a comparable theorem for the class of distribution functions F with convex decreasing densities f, but with the maximum likelihood estimator �Fn of F replaced by the least squares estimator �Fn: if X1,...,Xn are sampled from a distribution function F with strictly convex density f, then the least squares estimator �Fn of F and the empirical distribution function Fn differ in the uniform norm by no more than a constant times (n −1 log n) 3/5 almost surely. The proofs rely on bounds on the interpolation error for complete spline interpolation due to Hall [12], Hall and Meyer [13], building on earlier work by Birkhoff and de Boor [4]. These results, which are crucial for the developments here, are all nicely summarized and exposited in de Boor [5]
Mixtures and Monotonicity: a Review of Estimation under Monotonicity Constraints
No full textMonotone and multiply monotone densities have well-known mixture representations. The underlying mixture representations give rise to a wide variety of fascinating inverse problems. We review the forward problems (estimation of the mixed density) and the inverse problems (estimation of the mixing distribution in two different guises), including Hampel’s bird resting time problem and generalizations thereof. Section 5 gives a brief review of the current status of estimation theory in a subset of these problems
Estimation of a k-monotone density, part 2: algorithms for computation and numerical results
No full textThe iterative (2k − 1)−spline algorithm is an extension of the iterative cubic spline algorithm developed and used by Groeneboom, Jongbloed, and Wellner (2001b) to compute the Least Squares Estimator (LSE) of a nonincreasing and convex density on (0, ∞), and to find an approximation of the “invelope ” of the integrated two-sided Brownian motion+t 4 that is involved in the limiting distribution of both the Maximum Likelihood Estimator (MLE) and the LSE (Groeneboom, Jongbloed, and Wellner (2001a)). The iterative (2k − 1) − spline algorithm was developed to compute the LSE of a k-monotone density on (0, ∞) for any integer k>2, and also to calculate an approximation of the envelopes ( “ invelopes”) of the (k − 1)-fold integral of two-sided Brownian motion + (k!/(2k)!) t 2k when k is odd (even) on a finite interval [−c, c] for some fixed c>0. Existence and uniqueness of the latter processes are the subject of Balabdaoui and Wellner (2004c). To compute the MLE of a k-monotone density, another variation of the algorithm involving quadratic approximation is described. This algorithm involves the computation of a spline of degree k − 1 instead of a spline of degree 2k − 1. The principles of both algorithms are explained in detail. We also give several applications to real and artificial data
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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