Author
Suman Majumdar
Other affiliations: New York University
Bio: Suman Majumdar is an academic researcher from University of Connecticut. The author has contributed to research in topics: Weak convergence & Multivariate normal distribution. The author has an hindex of 3, co-authored 16 publications receiving 78 citations. Previous affiliations of Suman Majumdar include New York University.
Papers
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TL;DR: In this article, a central limit theorem for a triangular array of row-wise independent Hilbert-valued random elements with finite second moment is proved under mild convergence requirements on the covariances of the row sums and the Lindeberg condition along the evaluations at an orthonormal basis.
58 citations
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TL;DR: In this article, the authors obtained uniform bounds on the regret of Bayes solutions in a family of probability models (compound with finite-mixture-state component) for MLEs and posterior means for quasi-uniform hyperpriors, both determined in the iid mixture sub-models.
7 citations
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TL;DR: It is shown that the orthogonal projection operator onto the range of the adjoint T⁎ of a linear operator T can be represented as UT, where U is an invertible linear operator, and it is proved that the conditional distribution of a Normal random vector Y given TY, where T is a linear transformation, is again a multivariate Normal distribution.
6 citations
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TL;DR: In this paper, the asymptotic solution to the problem of comparing the means of two heteroscedastic populations, based on two random samples from the populations, hinges on the pivot underpinning the construction.
Abstract: The asymptotic solution to the problem of comparing the means of two heteroscedastic populations, based on two random samples from the populations, hinges on the pivot underpinning the construction...
4 citations
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TL;DR: For a suitably chosen metric ρ for the topology of weak convergence in the space of prior distributions on the shift parameter of a compact Gaussian shift experiment, the posterior distribution (induced by a full support prior) of the shift parameters given independent and identically distributed observations from the experiment is uniformly (in the shift parameter) L 1 consistent in ρ.
3 citations
Cited by
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TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.
5,689 citations
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TL;DR: In this article, the convergence of Distri butions of Likelihood Ratio has been discussed, and the authors propose a method to construct a set of limit laws for Likelihood Ratios.
Abstract: 1 Introduction.- 2 Experiments, Deficiencies, Distances v.- 2.1 Comparing Risk Functions.- 2.2 Deficiency and Distance between Experiments.- 2.3 Likelihood Ratios and Blackwell's Representation.- 2.4 Further Remarks on the Convergence of Distri butions of Likelihood Ratios.- 2.5 Historical Remarks.- 3 Contiguity - Hellinger Transforms.- 3.1 Contiguity.- 3.2 Hellinger Distances, Hellinger Transforms.- 3.3 Historical Remarks.- 4 Gaussian Shift and Poisson Experiments.- 4.1 Introduction.- 4.2 Gaussian Experiments.- 4.3 Poisson Experiments.- 4.4 Historical Remarks.- 5 Limit Laws for Likelihood Ratios.- 5.1 Introduction.- 5.2 Auxiliary Results.- 5.2.1 Lindeberg's Procedure.- 5.2.2 Levy Splittings.- 5.2.3 Paul Levy's Symmetrization Inequalities.- 5.2.4 Conditions for Shift-Compactness.- 5.2.5 A Central Limit Theorem for Infinitesimal Arrays.- 5.2.6 The Special Case of Gaussian Limits.- 5.2.7 Peano Differentiable Functions.- 5.3 Limits for Binary Experiments.- 5.4 Gaussian Limits.- 5.5 Historical Remarks.- 6 Local Asymptotic Normality.- 6.1 Introduction.- 6.2 Locally Asymptotically Quadratic Families.- 6.3 A Method of Construction of Estimates.- 6.4 Some Local Bayes Properties.- 6.5 Invariance and Regularity.- 6.6 The LAMN and LAN Conditions.- 6.7 Additional Remarks on the LAN Conditions.- 6.8 Wald's Tests and Confidence Ellipsoids.- 6.9 Possible Extensions.- 6.10 Historical Remarks.- 7 Independent, Identically Distributed Observations.- 7.1 Introduction.- 7.2 The Standard i.i.d. Case: Differentiability in Quadratic Mean.- 7.3 Some Examples.- 7.4 Some Nonparametric Considerations.- 7.5 Bounds on the Risk of Estimates.- 7.6 Some Cases Where the Number of Observations Is Random.- 7.7 Historical Remarks.- 8 On Bayes Procedures.- 8.1 Introduction.- 8.2 Bayes Procedures Behave Nicely.- 8.3 The Bernstein-von Mises Phenomenon.- 8.4 A Bernstein-von Mises Result for the i.i.d. Case.- 8.5 Bayes Procedures Behave Miserably.- 8.6 Historical Remarks.- Author Index.
483 citations
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TL;DR: In this article, the authors admit that there are no definitive answers, considering, inter alia, the following questions: how convinced are we that the trends in climate change over the past thirty years are an indication of global warming rather than just random fluctuations? how much belief can there be in miracles? is the movement of share prices better explained by chaos theory than by statistics?
Abstract: distribution, queuing theory, random walks, and so on. On many topical issues he is prepared to admit that there are no definitive answers, considering, inter alia, the following questions: how convinced are we that the trends in climate change over the past thirty years are an indication of global warming rather than just random fluctuations? how much belief can there be in miracles? is the movement of share prices better explained by chaos theory than by statistics? He also emphasizes that issues such as psychology and economic efficiency sometimes have as much of a bearing on eventual decisions as purely statistical considerations.
219 citations
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TL;DR: The theoretical advances are completed by some simulation studies showing both the practical feasibility of the method and the good behavior for finite sample sizes of the kernel estimator and of the bootstrap procedures to build functional pseudo-confidence area.
106 citations
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TL;DR: In this paper, a flexible class of omnibus affine invariant tests for the hypothesis that a multivariate distribution is symmetric about an unspecified point is considered, and the test statistics are weighted integrals involving the imaginary part of the empirical characteristic function of suitably standardized given data, and they have an alternative representation in terms of an L2-distance of nonparametric kernel density estimators.
67 citations