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39
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 ..."
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Cited by 22 (3 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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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
Modeling Losses with the Mixed Exponential Distribution
 PCAS, LXXXVI, 1999 {3] Annual Stat/stical Bullet~n, 1998 Edition, National Council on Compensation Insurance, Inc
"... Finding a parametric model that fits loss data well is often difficult. This paper offers an alternative—the semiparametric mixed exponential distribution. The paper gives the reason why this is a good model and explains maximum likelihood estimation for the mixed exponential distribution. The pa ..."
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Cited by 7 (0 self)
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Finding a parametric model that fits loss data well is often difficult. This paper offers an alternative—the semiparametric mixed exponential distribution. The paper gives the reason why this is a good model and explains maximum likelihood estimation for the mixed exponential distribution. The paper also presents an algorithm to find parameter estimates and gives an illustrative example. The paper compares variances of estimates obtained with the mixed exponential distribution with variances obtained with a traditional parametric distribution. Finally, the paper discusses adjustments to the model and other uses of the model. 1.
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 3 (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.
Corrected phasetype approximations of heavytailed risk models using perturbation analysis
 Insur Math Econ
, 2013
"... Numerical evaluation of ruin probabilities in the classical risk model is an important problem. If claim sizes are heavytailed, then such evaluations are challenging. To overcome this, an attractive way is to approximate the claim sizes with a phasetype distribution. What is not clear though is ho ..."
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Numerical evaluation of ruin probabilities in the classical risk model is an important problem. If claim sizes are heavytailed, then such evaluations are challenging. To overcome this, an attractive way is to approximate the claim sizes with a phasetype distribution. What is not clear though is how many phases are enough in order to achieve a specific accuracy in the approximation of the ruin probability. The goals of this paper are to investigate the number of phases required so that we can achieve a prespecified accuracy for the ruin probability and to provide error bounds. Also, in the special case of a completely monotone claim size distribution we develop an algorithm to estimate the ruin probability by approximating the excess claim size distribution with a hyperexponential one. Finally, we compare our approximation with the heavy traffic and heavy tail approximations. 1.
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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Cited by 3 (2 self)
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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.
Nonparametric Estimation for Inverse Problems  Algorithms . . .
 SPECIAL TOPICS COURSE 593C
, 1998
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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 3 (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).
Mixtures and Monotonicity: a Review of Estimation under Monotonicity Constraints
 IMS LECTURE NOTES–MONOGRAPH SERIES
, 2005
"... Monotone and multiply monotone densities have wellknown 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 d ..."
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Cited by 2 (0 self)
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Monotone and multiply monotone densities have wellknown 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.