Order Statistics

David, H. A.; Nagaraja, Haikady N.

doi:10.1002/9781118445112.stat00830

Cited by 46 publications

(85 citation statements)

References 26 publications

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“…We also plot the 95% confidence interval for each ordered p -value, using the result that the k -th ordered uniform variate follows a Beta distribution ℬ( k, N sim − k + 1), where N sim is the number of independent simulations (David and Nagaraja, 1970). …”

Section: Methodsmentioning

confidence: 99%

Increasing power for voxel-wise genome-wide association studies: The random field theory, least square kernel machines and fast permutation procedures

et al. 2012

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Imaging traits are thought to have more direct links to genetic variation than diagnostic measures based on cognitive or clinical assessments and provide a powerful substrate to examine the influence of genetics on human brains. Although imaging genetics has attracted growing attention and interest, most brain-wide genome-wide association studies focus on voxel-wise single-locus approaches, without taking advantage of the spatial information in images or combining the effect of multiple genetic variants. In this paper we present a fast implementation of voxel- and cluster-wise inferences based on the random field theory to fully use the spatial information in images. The approach is combined with a multi-locus model based on least square kernel machines to associate the joint effect of several single nucleotide polymorphisms (SNP) with imaging traits. A fast permutation procedure is also proposed which significantly reduces the number of permutations needed relative to the standard empirical method and provides accurate small p-value estimates based on parametric tail approximation. We explored the relation between 448,294 single nucleotide polymorphisms and 18,043 genes in 31,662 voxels of the entire brain across 740 elderly subjects from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Structural MRI scans were analyzed using tensor-based morphometry (TBM) to compute 3D maps of regional brain volume differences compared to an average template image based on healthy elderly subjects. We find method to be more sensitive compared with voxel-wise single-locus approaches. A number of genes were identified as having significant associations with volumetric changes. The most associated gene was GRIN2B, which encodes the N-methyl-d-aspartate (NMDA) glutamate receptor NR2B subunit and affects both the parietal and temporal lobes in human brains. Its role in Alzheimer's disease has been widely acknowledged and studied, suggesting the validity of the approach. The various advantages over existing approaches indicate a great potential offered by this novel framework to detect genetic influences on human brains.

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Section: Methodsmentioning

confidence: 99%

Increasing power for voxel-wise genome-wide association studies: The random field theory, least square kernel machines and fast permutation procedures

et al. 2012

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“…. L, were independent, computing the ordered statistics is easy [11]. But the SINR's are not independent because of the common interferer locations Φ which introduces correlates across all the γ i .…”

Section: Order Statistics Of Sinrmentioning

confidence: 99%

“…From the theory of ordered random variables [11] and with basic algebra it follow that, where η z (x, a) = (1 + a�z� α �x� −α ) −1 . Using binomial expansion and averaging over the point process we obtain,…”

Section: B Comparison With Random Frequency Allocationmentioning

confidence: 99%

SINR order statistics in OFDMA systems

Ganti

Kuchi

2012

2012 IEEE Global Communications Conference (GLOBECOM)

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In orthogonal frequency division multiple access downlink, the signal-to-interference-noise ratio (SINR) of every subband at each user is estimated with the aid of pilots and the channel quality (some function of SINR's) is fed back to the base station (BS). This information is utilized by the BS for downlink scheduling. However, the SINR of the bands at each user are correlated due to the common interfering BSs. In this paper, we obtain the order statistics of band SINR's by considering the the co-channel interference and taking the correlations of interference across the bands into consideration. The order statistics are then used to analyse a best-m band feedback scheme, in which every users reports the index of their best-m bands to the BS. The BS utilizes this information and does greedy allocation of the bands to the users. We observe that utilizing the partial ordering of SINR's for channel allocation provides substantial gains over random allocation of bands to the users even in the presence of interference. I. INTRODUCTIONOrthogonal frequency division multiple access (OFDMA) is the ubiquitous downlink access technique in the next generation cellular standards. In OFDMA, the users utilize the pilots to estimate the channel quality of a physical resource block which we term as "band" for convenience. The users then report the channel quality (or some functions of them, for e.g., exponential effective SNR mapping (EESM)) of the best m-bands to the BS, which uses this information for scheduling the users. Hence the order statistics of the SINR's of different bands are important in the design and the analysis of the downlink scheduler.Interference from the other BSs critically influence the joint statistics of SINRs of the bands. At each user, while the small scale fading from the interfering BSs is independent across the bands, all the bands encounter the same path loss from the interfering BSs. Hence the interference is correlated across the bands.In the earlier works, only the signal-to-noise ratio is considered and the interference from other BSs is generally neglected in the analysis of order statistics. The main contribution of the paper is obtaining the order statistics of SINR's of the bands by explicitly taking into account the interference and its correlations across the bands. We use a spatial Poisson point process [1], [2] for the BS locations. This spatial model was introduced in [3] to model the interference in a cellular network. From the order statistics, we observe that in wideband systems with high frequency selectivity (and hence a large number of bands) there is a substantial gain using the best band scheduling even with interference. The obtained order statistics can potentially be used to analyse various schedulers. As an application, we

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“…Classical examples of these include non-parametric techniques that enable data-driven decision making, without making specific assumptions about the process distribution, and calculation or estimation of statistics as functions on a sample independent of parameter specifications [7, 8]. In these cases, scientific inference does not depend on fitting parametrized distributions but rather on ordering, comparing, ranking or stratifying statistics derived from the observed data [9]. Modern classification, prediction, and machine-learning inference approaches differ from model-based parametric methods by their underlying assumptions and the number of parameters that need to be estimated to generate the framework supporting the decision making process, data analytics, and inference.…”

Section: Big Data Analyticsmentioning

confidence: 99%

Volume and value of big healthcare data

Dinov¹

2016

J Med Stat Inform

102

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Modern scientific inquiries require significant data-driven evidence and trans-disciplinary expertise to extract valuable information and gain actionable knowledge about natural processes. Effective evidence-based decisions require collection, processing and interpretation of vast amounts of complex data. The Moore's and Kryder's laws of exponential increase of computational power and information storage, respectively, dictate the need rapid trans-disciplinary advances, technological innovation and effective mechanisms for managing and interrogating Big Healthcare Data. In this article, we review important aspects of Big Data analytics and discuss important questions like: What are the challenges and opportunities associated with this biomedical, social, and healthcare data avalanche? Are there innovative statistical computing strategies to represent, model, analyze and interpret Big heterogeneous data? We present the foundation of a new compressive big data analytics (CBDA) framework for representation, modeling and inference of large, complex and heterogeneous datasets. Finally, we consider specific directions likely to impact the process of extracting information from Big healthcare data, translating that information to knowledge, and deriving appropriate actions.

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Order Statistics

Cited by 46 publications

References 26 publications

Increasing power for voxel-wise genome-wide association studies: The random field theory, least square kernel machines and fast permutation procedures

Increasing power for voxel-wise genome-wide association studies: The random field theory, least square kernel machines and fast permutation procedures

SINR order statistics in OFDMA systems

Volume and value of big healthcare data

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