Maximum likelihood estimation using composite likelihoods for closed exponential families

Mardia, Kanti V.; Kent, John T.; Hughes, G.; Taylor, Charles

doi:10.1093/biomet/asp056

Cited by 42 publications

(34 citation statements)

References 16 publications

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“…We obtain the value of m through cross-validation but it is normally 5-15 for various large sets (images) we have experimented with. Indeed, the program takes a few minutes for n as large as 250 000, the total number of operations being proportional to n. The recent efficiency results given in Mardia et al (2010) on composite likelihood are also encouraging and relevant. I welcome a comprehensive comparison of the composite likelihood approach and the finite element method that is used in this paper.…”

Section: K V Mardia (University Of Leeds)mentioning

confidence: 86%

An Explicit Link between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach

Lindgren

Rue

Lindström

2011

Journal of the Royal Statistical Society Series B: Statistical Methodology

2,242

2,892

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Summary.Continuously indexed Gaussian fields (GFs) are the most important ingredient in spatial statistical modelling and geostatistics. The specification through the covariance function gives an intuitive interpretation of the field properties. On the computational side, GFs are hampered with the big n problem, since the cost of factorizing dense matrices is cubic in the dimension. Although computational power today is at an all time high, this fact seems still to be a computational bottleneck in many applications. Along with GFs, there is the class of Gaussian Markov random fields (GMRFs) which are discretely indexed. The Markov property makes the precision matrix involved sparse, which enables the use of numerical algorithms for sparse matrices, that for fields in R 2 only use the square root of the time required by general algorithms. The specification of a GMRF is through its full conditional distributions but its marginal properties are not transparent in such a parameterization. We show that, using an approximate stochastic weak solution to (linear) stochastic partial differential equations, we can, for some GFs in the Matérn class, provide an explicit link , for any triangulation of R d , between GFs and GMRFs, formulated as a basis function representation. The consequence is that we can take the best from the two worlds and do the modelling by using GFs but do the computations by using GMRFs. Perhaps more importantly, our approach generalizes to other covariance functions generated by SPDEs, including oscillating and non-stationary GFs, as well as GFs on manifolds. We illustrate our approach by analysing global temperature data with a non-stationary model defined on a sphere.

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Section: K V Mardia (University Of Leeds)mentioning

confidence: 86%

An Explicit Link between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach

Lindgren

Rue

Lindström

2011

Journal of the Royal Statistical Society Series B: Statistical Methodology

2,242

2,892

View full text Add to dashboard Cite

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“…, M, suppose that any element of t(x) is included in t A ,B (x) at least one . Then, the local Z-estimator using the composite likelihood ∑ M =1 log p θ (x A |x B ) is identical to the MLE [26]. Hence, the composite likelihood of the closed exponential family attains the efficiency bound of the MLE.…”

Section: Closed Exponential Familiesmentioning

confidence: 96%

“…The so-called closed exponential family has an interesting property from the viewpoint of localized estimators, as presented in [26]. Let p θ (x) = exp{θ T t(x) − c(θ)} be the exponential family defined for x = (x 1 , .…”

Section: Closed Exponential Familiesmentioning

confidence: 99%

Efficiency Bound of Local Z-Estimators on Discrete Sample Spaces

Kanamori

2016

Entropy

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Many statistical models over a discrete sample space often face the computational difficulty of the normalization constant. Because of that, the maximum likelihood estimator does not work. In order to circumvent the computation difficulty, alternative estimators such as pseudo-likelihood and composite likelihood that require only a local computation over the sample space have been proposed. In this paper, we present a theoretical analysis of such localized estimators. The asymptotic variance of localized estimators depends on the neighborhood system on the sample space. We investigate the relation between the neighborhood system and estimation accuracy of localized estimators. Moreover, we derive the efficiency bound. The theoretical results are applied to investigate the statistical properties of existing estimators and some extended ones.

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“…Note that bivariate Tikhonov distributions are not closed under the product operation [26], i.e., the product of two bivariate Tikhonov distributions is not another bivariate Tikhonov distribution. However in [26], it was conjectured that the product is approximately another bivariate Tikhonov pdf.…”

Section: A Forward Recursionmentioning

confidence: 99%

“…However in [26], it was conjectured that the product is approximately another bivariate Tikhonov pdf. The quality of this approximation cannot be assessed analytically.…”

Section: A Forward Recursionmentioning

confidence: 99%

Algorithms for Joint Phase Estimation and Decoding for MIMO Systems in the Presence of Phase Noise and Quasi-Static Fading Channels

Krishnan

Colavolpe

Amat

et al. 2015

IEEE Trans. Signal Process.

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In this work, we derive the maximum a posteriori (MAP) symbol detector for a multiple-input multiple-output system in the presence of Wiener phase noise due to noisy local oscillators. As in single-antenna systems, the computation of the optimum receiver is an analytically intractable problem and is unimplementable in practice. In this purview, we propose three suboptimal, low-complexity algorithms for approximately implementing the MAP symbol detector, which involve joint phase noise estimation and data detection. Our first algorithm is obtained by means of the sum-product algorithm, where we use the multivariate Tikhonov canonical distribution approach. In our next algorithm, we derive an approximate MAP symbol detector based on the smoother-detector framework, wherein the detector is properly designed by incorporating the phase noise statistics from the smoother. The third algorithm is derived based on the variational Bayesian framework. By simulations, we evaluate the performance of the proposed algorithms for both uncoded and coded data transmissions, and we observe that the proposed techniques significantly outperform the other important algorithms from prior works, which are considered in this work. Index Terms -Maximum a posteriori (MAP) detection, phase noise, sum-product algorithm (SPA), variational Bayesian (VB) framework, extended Kalman smoother (EKS), MIMO. , IEEE Transactions on Signal Processing 2 I. INTRODUCTIONEmploying multiple-input multiple-output (MIMO) systems has been shown to significantly enhance performance in terms of data rate and link reliability in wireless fading environments [1]. In general, the analysis and design of MIMO system is based on the assumption that the carrier phase is perfectly known at the receiver, and that there is no phase noise in the system. The phase noise manifests in a MIMO system as the random, time-varying phase differences between the oscillators connected to the antennas at the transmitter and the receiver. Practical designs of MIMO systems based on this assumption can result in significant performance losses and have to be addressed appropriately [2]. The detrimental effects of phase noise can be even more pronounced in scenarios where independent oscillators are connected to each transmit and receive antenna (or a subset of them). This scenario is particularly relevant for line-of-sight MIMO systems that operate at carrier frequencies of around 10 GHz or lesser. Here, separate oscillators are needed for each antenna [3], since the antennas are placed far from each other [4]. The scenario under consideration also corresponds to a massive MIMO system [5], [6], where a large number of antennas are placed at the base station and each user terminal is equipped with a single antenna.The problem of designing receiver algorithms in the presence of random, time-varying phase noise due to noisy local oscillators has been studied extensively for single-antenna systems. We refer the readers to [7]-[10] and the references therein. To address the problem of designin...

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Maximum likelihood estimation using composite likelihoods for closed exponential families

Cited by 42 publications

References 16 publications

An Explicit Link between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach

An Explicit Link between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach

Efficiency Bound of Local Z-Estimators on Discrete Sample Spaces

Algorithms for Joint Phase Estimation and Decoding for MIMO Systems in the Presence of Phase Noise and Quasi-Static Fading Channels

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