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Bayesian Model Selection in Finite Mixtures by Marginal Density Decompositions
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 2001
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Estimation of a kmonotone density: Limit distribution theory and the spline connection, with complete proofs
, 2006
"... We study the asymptotic behavior of the Maximum Likelihood and Least Squares Estimators of a kmonotone density g0 at a fixed point x0 when k> 2. We find that the jth derivative of the estimators at x0 converges at the rate n −(k−j)/(2k+1) for j = 0,...,k − 1. The limiting distribution depends on an ..."
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Cited by 9 (1 self)
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We study the asymptotic behavior of the Maximum Likelihood and Least Squares Estimators of a kmonotone density g0 at a fixed point x0 when k> 2. We find that the jth derivative of the estimators at x0 converges at the rate n −(k−j)/(2k+1) for j = 0,...,k − 1. The limiting distribution depends on an almost surely uniquely defined stochastic process Hk that stays above (below) the kfold integral of Brownian motion plus a deterministic drift when k is even (odd). Both the MLE and LSE are known to be splines of degree k −1 with simple knots. Establishing the order of the random gap τ + n − τ − n, where τ ± n denote two successive knots, is a key ingredient of the proof of the main results. We show that this “gap problem ” can be solved if a conjecture about the upper bound on the error in a particular Hermite interpolation via odddegree splines holds. 1. Introduction. 1.1. The estimation problem and motivation. A density function g on
Modeling User Activities in a Large IPTV System ∗
"... Internet Protocol Television (IPTV) has emerged as a new delivery method for TV. In contrast with native broadcast in traditional cable and satellite TV system, video streams in IPTV are encoded in IP packets and distributed using IP unicast and multicast. This new architecture has been strategicall ..."
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Cited by 7 (0 self)
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Internet Protocol Television (IPTV) has emerged as a new delivery method for TV. In contrast with native broadcast in traditional cable and satellite TV system, video streams in IPTV are encoded in IP packets and distributed using IP unicast and multicast. This new architecture has been strategically embraced by ISPs across the globe, recognizing the opportunity for new services and its potential toward a more interactive style of TV watching experience in the future. Since user activities such as channel switches in IPTV impose workload beyond local TV or settop box (different from broadcast TV systems), it becomes essential to characterize and model the aggregate user activities in an IPTV network to support various system design and performance evaluation functions such as network capacity planning. In this work, we perform an indepth study on several intrinsic characteristics of IPTV user activities by
Efficient estimation using both direct and indirect observations
, 1992
"... The Ibragimov Hasminskii model postulates observing X1,..., Xm independent, identically distributed according to an unknown distribution G and Y1,..., Yn independent and identically distributed according to ∫ k(·, y)dG(y) where k is known, for example, Y is obtained from X by convolution with a Gaus ..."
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Cited by 2 (0 self)
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The Ibragimov Hasminskii model postulates observing X1,..., Xm independent, identically distributed according to an unknown distribution G and Y1,..., Yn independent and identically distributed according to ∫ k(·, y)dG(y) where k is known, for example, Y is obtained from X by convolution with a Gaussian density. We exhibit sieve type estimates of G which are efficient under minimal conditions which include those of Vardi and Zhang (1992) for the special case, G on [0, ∞], k(x, y) = 11(x ≤ y).
The singularity of the information matrix of the mixed proportional hazard model
 Econometrica
, 2003
"... This paper presents new identification conditions for the mixed proportional hazard model. In particular, the baseline hazard is assumed to be bounded away from 0 and ∞ near t = 0. These conditions ensure that the information matrix is nonsingular. The paper also presents an estimator for the mixed ..."
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Cited by 2 (1 self)
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This paper presents new identification conditions for the mixed proportional hazard model. In particular, the baseline hazard is assumed to be bounded away from 0 and ∞ near t = 0. These conditions ensure that the information matrix is nonsingular. The paper also presents an estimator for the mixed proportional hazard model that converges at rate N −1/2.
Estimating a parameter in incidental and structural models by approximate maximum likelihood
, 1988
"... Estimating a parameter in incidental and structural models by approximate maximum likelihood Aad van der Vaart 1 Free University Amsterdam ..."
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Estimating a parameter in incidental and structural models by approximate maximum likelihood Aad van der Vaart 1 Free University Amsterdam
INFORMATION IN SEMIPARAMETRIC MIXTURES OF EXPONENTIAL FAMILIES 1
"... In a class of semiparametric mixture models, the score function Žand consequently the effective information. for a finitedimensional parameter can be made arbitrarily small depending upon the direction taken in the parameter space. This result holds for a broad range of semiparametric mixtures over ..."
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In a class of semiparametric mixture models, the score function Žand consequently the effective information. for a finitedimensional parameter can be made arbitrarily small depending upon the direction taken in the parameter space. This result holds for a broad range of semiparametric mixtures over exponential families and includes examples such as the gamma semiparametric mixture, the normal mean mixture, the Weibull semiparametric mixture and the negative binomial mixture. The nearzero information rules out the usual parametric 'n rate for the finitedimensional parameter, but even more surprising is that the rate continues to be unattainable even when the mixing distribution is constrained to be countably discrete. Two key conditions which lead to a loss of information are the smoothness of the underlying density and whether a sufficient statistic is invertible.
HOW MANY LAPLACE TRANSFORMS OF PROBABILITY MEASURES ARE THERE?
, 2010
"... A bracketing metric entropy bound for the class of Laplace transforms of probability measures on [0, ∞) is obtained through its connection with the small deviation probability of a smooth Gaussian process. Our results for the particular smooth Gaussian process seem to be of independent interest. ..."
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A bracketing metric entropy bound for the class of Laplace transforms of probability measures on [0, ∞) is obtained through its connection with the small deviation probability of a smooth Gaussian process. Our results for the particular smooth Gaussian process seem to be of independent interest.
Some reflections on and experiences with SPLIFs
"... Starting from the uniqueness question for mixtures of distributions this review centers around the question under which formally weaker assumptions one can prove the existence of SPLIFs, in other words perfect statistics and tests. We mention a couple of positive and negative results which complemen ..."
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Starting from the uniqueness question for mixtures of distributions this review centers around the question under which formally weaker assumptions one can prove the existence of SPLIFs, in other words perfect statistics and tests. We mention a couple of positive and negative results which complement the basic contribution of David Blackwell in 1980. Typically the answers depend on the choice of the set theoretic axioms and on the particular concepts of measurability. The following pages describe some of my personal experiences and motivations connected to the subject of David Blackwell's 1980 note 'There are no Borel SPLIFs' [2]. I hope to show how this two page paper with a mysterious title (SPLIF stands for 'strong probability limit identification function') leads us directly to the foundations of the probabilistic formalism. The measure theoretic language of probability provided by S. Ulam and N. Kolmogorov is used by many without much attention. We all use English without being e...
Standard Errors for EM Estimates in Generalized Linear Models with Random Effects
, 2000
"... A procedure is derived for computing standard errors of EM estimates in generalized linear models with random effects. Quadrature formulae are used to approximate the integrals in the EM algorithm, where two different approaches are pursued: GauHermite quadrature, in case of Gaussian random effects ..."
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A procedure is derived for computing standard errors of EM estimates in generalized linear models with random effects. Quadrature formulae are used to approximate the integrals in the EM algorithm, where two different approaches are pursued: GauHermite quadrature, in case of Gaussian random effects, and nonparametric maximum likelihood estimation for an unspecified random effect distribution. An approximation of the expected Fisher information matrix is derived from an expansion of the EM estimating equations. This allows for inferential arguments based on EM estimates, as demonstrated by an example and simulations. Keywords: EM algorithm, Estimating equations, GauHermite quadrature, Mixture model, Nonparametric maximum likelihood estimation, Random effect model. Institute of Statistics