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1,947
Maximum likelihood from incomplete data via the EM algorithm
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY, SERIES B
, 1977
"... A broadly applicable algorithm for computing maximum likelihood estimates from incomplete data is presented at various levels of generality. Theory showing the monotone behaviour of the likelihood and convergence of the algorithm is derived. Many examples are sketched, including missing value situat ..."
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Cited by 11972 (17 self)
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situations, applications to grouped, censored or truncated data, finite mixture models, variance component estimation, hyperparameter estimation, iteratively reweighted least squares and factor analysis.
A subordinated stochastic process model with finite variance for speculative prices
 Econometrica
, 1973
"... Thanks are due to Hendrik Houthakker and Christopher Sims, for both encouragement and advice in developing this paper. As usual, all remaining errors are my own. This research was supported by a Harvard Dissertation Fellowship, NSF grant 33708, and the ..."
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Cited by 561 (1 self)
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Thanks are due to Hendrik Houthakker and Christopher Sims, for both encouragement and advice in developing this paper. As usual, all remaining errors are my own. This research was supported by a Harvard Dissertation Fellowship, NSF grant 33708, and the
Ballot theorems for random walks with finite variance
, 2008
"... We prove an analogue of the classical ballot theorem that holds for any mean zero random walk with positive but finite variance. Our result is best possible: we exhibit examples demonstrating that if any of our hypotheses are removed, our conclusions may no longer hold. ..."
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Cited by 7 (1 self)
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We prove an analogue of the classical ballot theorem that holds for any mean zero random walk with positive but finite variance. Our result is best possible: we exhibit examples demonstrating that if any of our hypotheses are removed, our conclusions may no longer hold.
Universality for the distance in finite variance random graphs
, 2008
"... We generalize the asymptotic behavior of the graph distance between two uniformly chosen nodes in the configuration model to a wide class of random graphs. Among others, this class contains the Poissonian random graph, the expected degree random graph and the generalized random graph (including the ..."
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Cited by 13 (7 self)
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are such that the degrees of a node has uniformly bounded moments of order strictly larger than two, so that, in particular, the degrees have finite variance. We prove that the graph distance grows like log ν N, where the ν depends on the capacities. In addition, the random fluctuations around this asymptotic mean log ν N
Distances in random graphs with finite variance degrees
, 2008
"... In this paper we study a random graph with N nodes, where node j has degree Dj and {Dj} N j=1 are i.i.d. with P(Dj ≤ x) = F(x). We assume that 1 − F(x) ≤ cx −τ+1 for some τ> 3 and some constant c> 0. This graph model is a variant of the socalled configuration model, and includes heavy tail ..."
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Cited by 29 (12 self)
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degrees with finite variance. The minimal number of edges between two arbitrary connected nodes, also known as the graph distance or the hopcount, is investigated when N → ∞. We prove that the graph distance grows like log ν N, when the base of the logarithm equals ν = E[Dj(Dj − 1)]/E[Dj]> 1
Do Stock Returns Follow a Finite Variance Distribution?
, 2000
"... In this paper we propose a test statistic to discriminate between models with finite variance and models with infinite variance. The test statistic is the ratio of the sample standard deviation and the sample interquartile range. Both asymptotic and finite sample properties of the test statistic are ..."
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In this paper we propose a test statistic to discriminate between models with finite variance and models with infinite variance. The test statistic is the ratio of the sample standard deviation and the sample interquartile range. Both asymptotic and finite sample properties of the test statistic
New results in linear filtering and prediction theory
 TRANS. ASME, SER. D, J. BASIC ENG
, 1961
"... A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary sta ..."
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Cited by 607 (0 self)
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A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary
BCCBJBATllON TIME FLUCTUATIONS OF POISSON AND EQUILIBRIUM FINITE VARIANCE BRANCHING SYSTEMS
"... Abstract. Functional limit theorems are presented for the rescaled occupation time fluctuation process of a critical finite variance branching particle system in Rd with symmetric astable motion starting off from either a standard Poisson random field or from the equilibrium distribution for int ..."
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Abstract. Functional limit theorems are presented for the rescaled occupation time fluctuation process of a critical finite variance branching particle system in Rd with symmetric astable motion starting off from either a standard Poisson random field or from the equilibrium distribution
PROBABILITY INEQUALITIES FOR SUMS OF BOUNDED RANDOM VARIABLES
, 1962
"... Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S is bounded or bounded above. The bounds for Pr(SES> nt) depend only on the endpoints of the ranges of the s ..."
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Cited by 2215 (2 self)
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of the smumands and the mean, or the mean and the variance of S. These results are then used to obtain analogous inequalities for certain sums of dependent random variables such as U statistics and the sum of a random sample without replacement from a finite population.
Universality for the distance in finite variance random graphs: Extended version
, 2008
"... The asymptotic behavior of the graph distance between two uniformly chosen nodes in the configuration model is generalized to a wide class of random graphs, where the degrees have finite variance. Among others, this class contains the Poissonian random graph and the generalized random graph (includi ..."
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The asymptotic behavior of the graph distance between two uniformly chosen nodes in the configuration model is generalized to a wide class of random graphs, where the degrees have finite variance. Among others, this class contains the Poissonian random graph and the generalized random graph
Results 1  10
of
1,947