Search

An asymptotic theory is developed for computing volumes of regions in the parameter space of a directed Gaussian graphical model that are obtained by bounding partial correlations. We study these volumes using the method of real log canonical thresholds from algebraic geometry. Our analysis involves the computation of the singular loci of correlation hypersurfaces. Statistical applications include the strong-faithfulness assumption for the PC algorithm and the quantification of confounder bias in causal inference. A detailed analysis is presented for trees, bow ties, tripartite graphs, and complete graphs. Keywords Causal inference * Real log canonical threshold * Resolution of singularities * Gaussian graphical model * Algebraic statistics * Singular learning theory Mathematics Subject Classification 62H05 * 62H20 * 14Q10, 1 Introduction Extensive theory has been established in recent years for causal inference based on directed acyclic graph (DAG) models. A popular method for estimating a DAG model from observational [...]

Incomplete longitudinal data often are analyzed with estimating equations for inference, on a parameter from a marginal mean regression model. Generalized estimating equations, although commonly used for incomplete longitudinal data, are invalid for data that are not missing completely at random. There exists a class of inverse probability weighted estimating equations that are valid under dropouts missing at random, including an easy-to-implement but inefficient member. A relatively computationally complex semiparametric efficient estimator in this class has been applied to continuous data. A specific form of this estimator is developed for binary data and used as a benchmark for assessing the efficiency of the simpler estimator in a simulation study. Both are applied in the estimation of 15-year cigarette smoking trends in the United States from a cohort of 5077 young adults. The results suggest that declines in smoking from previous reports have been exaggerated. KEY WORDS: Cohort; Correlated binary data; Dropout; Generalized estimating equation; Missing data.

Correlated data frequently arise in contexts such as, for example, repeated measures and meta-analysis. The amount of information in such data depends not only on the sample size, but also on the structure and strength of the correlations among observations from the same independent block. A general concept is discussed, the effective sample size, as a way of quantifying the amount of information in such data. It is defined as the sample size one would need in an independent sample to equal the amount of information in the actual correlated sample. This concept is widely applicable, for Gaussian data and beyond, and provides important insight. For example, it helps explain why fixed-effects and random-effects inferences of meta-analytic data can be so radically divergent. Further, we show that in some cases the amount of information is bounded, even when the number of measures per independent block approaches infinity. We use the method to devise a new denominator degrees-of-freedom method for fixed-effects testing. It is compared to the classical Satterthwaite and Kenward-Roger methods for performance and, more importantly, to enhance insight. A key feature of the proposed degrees-of-freedom method is that it, unlike the others, can be used for non-Gaussian data, too. This article has supplementary material online. KEY WORDS: Amount of information: Correlated data; Information limit: Mixed models: Small-sample inference.

Classical prediction methods, such as Fisher's linear discriminant function, were designed for small scale problems in which the number of predictors N is much smaller than the number of observations n. Modern scientific devices often reverse this situation. A microarray analysis, for example, might include n = 100 subjects measured on N = 10,000 genes, each of which is a potential predictor. This article proposes an empirical Bayes approach to large-scale prediction, where the optimum Bayes prediction rule is estimated employing the data from all of the predictors. Microarray examples are used to illustrate the method. The results demonstrate a close connection with the shrunken centroids algorithm of Tibshirani et al. (2002), a frequentist regularization approach to large-scale prediction, and also with false discovery rate theory. KEY WORDS: Correlated predictors; Effect size estimation; Empirical Bayes; Local false discovery rate; Microarray prediction; Shrunken centroid.

The assumption of approximate normality of a pivotal used for constructing confidence intervals or tests often is violated by a substantial correlation between the point estimator at hand and the estimator of its variance. This can be caused by underlying skewness of data, generating both bias and skewness of the pivotal and leading to, for example, confidence intervals with poorer coverage properties, especially for one-sided intervals. We present in a general setting a simple, yet effective procedure that takes into account this correlation and leads to alternative adjusted intervals with more appealing coverage properties. We provide examples, including a simulation study. KEY WORDS: Confidence interval; Correlation; Pivotal; Skewness.

It is well known that the magnitude of the cross correlation between any distinct constant multiple sequences of an M-ary power residue sequence of period p is upper bounded by [square root of p] + 2 and that of an M-ary Sidel'nikov sequence of period [p.sup.m] - 1 is upper bounded by [square root of [p.sup.m]] + 3, where p is a prime and m is a positive integer. In this paper, we first show that their cross-correlation functions are closely related to Jacobi sums and cyclotomic numbers. We then derive the cross-correlation distribution of constant multiple sequences of an M-ary power residue sequence. In the case of constant multiple sequences of an M-ary Sidel'nikov sequence, we get the possible cross-correlation values whose occurrence numbers are expressed in terms of the cyclotomic numbers of order M and are possibly zero. Index Terms--Cross correlation, cyclotomic numbers, Jacobi sum, multiplicative characters, power residue sequences, Sidel'nikov sequences.

Recently, graph-based semisupervised learning methods have been widely applied in multimedia research area. However, for the application of video semantic annotation in multilabel setting, these methods neglect an important characteristic of video data: The semantic concepts appear correlatively and interact naturally with each other rather than exist in isolation. In this paper, we adapt this semantic correlation into graph-based semisupervised learning and propose a novel method named correlative linear neighborhood propagation to improve annotation performance. Experiments conducted on the Text REtrieval Conference VIDeo retrieval evaluation data set have demonstrated its effectiveness and efficiency. Index Terms--Graph-based method, label propagation, semantic correlation, video annotation.

In this paper, we construct four M-ary sequence families from a power residue sequence of odd prime period p and its constant multiple sequences using the shift-and-add method, when M is a divisor of p - 1. We show that the maximum correlation values of the proposed sequence families are upper-bounded by 2 [square root of p + 5] or 3 [square root of p + 4]. In addition, we prove that the linear complexity of each sequence in the proposed families is either p - 1 or p - p-1/M - 1]. We also construct an M-ary sequence family from Sidel'nikov sequences of period [p.sup.m] - 1 by applying the same method, when M is a divisor of [p.sup.m] - 1. The proposed sequence family [[??].sub.s] has larger size than the known M-ary Sidel'nikov sequence families, whereas they all have the same upper bound on the maximum correlation. Index Terms--Linear complexity, low correlation, multiplicative character, polyphase sequences, power residue sequences, Sidel'nikov sequences, Weil's theorem.

The aim of this Letter is twofold: to propose a simulator for both the phase and the envelope of Nakagami fading channels with arbitrary parameters and to derive precise closed-form approximations to the correlation functions of the Nakagami envelope, phase, and quadrature components. Index Terms--Correlation, fading channels, Nakagami fading, rank statistics, simulation.

In this paper, we propose a high-resolution time--frequency-domain reflectometry technique as a methodology of detection and estimation of faults on a wire. This method adopts the time--frequency cross-correlation characteristics of the observed signal in both the time and frequency domains simultaneously. The accuracy of the proposed method is verified with experiments using a radio-guide-type coaxial cable and comparing it with traditional time-domain as well as frequency-domain reflectometry methods. It is clearly shown here that the proposed algorithm produces excellent results compared to the conventional methods for single as well as multiple fault cables. Index Terms--Chirp signal, fault detection, fault estimation, time--frequency cross-correlation function, time--frequency-domain reflectometry (TFDR), resolution.

Finding the cross correlation between two m-sequences {[s.sub.t]} and {[s.sub.dt]} of the same period [2.sup.m] - 1, that differ by a decimation d, has been a popular research problem since the 1960s. Many cases with three- and four-valued correlation have been determined. Several values of d are known to lead to five-valued cross correlation but their exact correlation distribution has been open. The correlation distribution is completely determined for one of these families with five-valued cross correlation by using evaluations of certain exponential sums including Kloosterman sums. The decimation considered is the special decimation d = [2.sup.2k] + 1/[2.sup.k] + 1 where m is odd and k = i, i.e., d = 5/3. The paper introduces some techniques that may be useful to obtain further results on related decimations. Index Terms--Cross-correlation function, exponential sums, Kloosterman sums, m-sequences.

In this paper, two new optimal families S and U of quadriphase sequences are presented. Compared to the family A constructed by Boztas et al. and the family D investigated by Tang et al. respectively, the proposed families have the same optimal correlation properties and family size, but larger linear spans. Index Terms--Correlation, finite field, Galois ring, linear span, quadriphase sequence.

We propose a new problem of correlation mining from graph databases, called Correlated Graph Search (CGS). CGS adopts Pearson's correlation coefficient as the correlation measure to take into account the occurrence distributions of graphs. However, the CGS problem poses significant challenges, since every subgraph of a graph in the database is a candidate, but the number of subgraphs is exponential. We derive two necessary conditions that set bounds on the occurrence probability of a candidate in the database. With this result, we devise an efficient algorithm that mines the candidate set from a much smaller projected database, and thus, we are able to obtain a significantly smaller set of candidates. Three heuristic rules are further developed to refine the candidate set. We also make use of the bounds to directly answer high-support queries without mining the candidates. Our experimental results demonstrate the efficiency of our algorithm. Finally, we show that our algorithm provides a general solution when most of the commonly used correlation measures are used to generalize the CGS problem. Index Terms--Correlation, graph databases, Pearson's correlation coefficient.

In the literature, many constructions of zero correlation zone (ZCZ) sequences have been reported. While most of them are suboptimal with respect to the known upper bound, some constructed by Matsufuji et al. and Torii et al. respectively, are almost optimal (or even optimal). In this paper, we propose a systematic construction of almost optimal ZCZ sequence sets which generalizes the aforementioned constructions so that more flexible relationships between the set size and the sequence length are allowed. In particular, the obtained almost optimal ZCZ sequence sets of size m and length mn are new for 1 < gcd(m, n) < min(m, n). In addition, their alphabets can be binary or nonbinary since our construction is only based on interleaving perfect sequences according to a certain orthogonal matrix. Index Terms--Orthogonal matrices, perfect autocorrelation, quasi-synchronous code-division multiple access (QS-CDMA), shift sequence, zero correlation zone (ZCZ) sequence.

Beyond conventional linear and kernel-based feature extraction, we present a more generalized formulation for feature extraction in this paper. Two representative algorithms using the correlation metric are proposed based on this formulation. Correlation Embedding Analysis (CEA), which incorporates both correlational mapping and discriminant analysis, boosts the discriminating power by mapping the data from a high-dimensional hypersphere onto another low-dimensional hypersphere and preserving the neighboring relations with local-sensitive graph modeling. Correlational Principal Component Analysis (CPCA) generalizes the Principal Component Analysis (PCA) algorithm to the case with data distributed on a high-dimensional hypersphere. Their advantages stem from two facts: 1) directly working on normalized data, which are often the outputs from data preprocessing, and 2) directly designed with the correlation metric, which is shown to be generally better than euclidean distance for classification purpose in many real-world applications. Extensive visual recognition experiments compared with existing feature extraction algorithms demonstrate the effectiveness of the proposed algorithms. Index Terms--Feature extraction, graph embedding, correlation embedding analysis, correlational principal component analysis, face recognition.

A single memoryless Gaussian source is observed by many terminals, subject to independent Gaussian observation noises. The terminals arc linked to a fusion center via a standard Gaussian multiple-access channel. The fusion center needs to recover the underlying Gaussian source with respect to mean-squared error. In this correspondence, a theorem of Witsenhauseu is shown to imply that an optimal communication strategy is uncoded transmission, i.e., each terminal's channel input is merely a scaled version of its noisy observation. Index Terms--Cut-set bound, joint source-channel coding, maximum correlation coefficient, source-channel separation theorem.

This paper introduces a methodology that permits presentation of the results of data envelopment analysis (DEA) graphically. A specialized form of multi-dimensional scaling, Co-Plot, enables presentation of the DEA results in a two-dimensional space, hence in a clear, understandable manner. When plotting ratios rather than original data, DEA efficient units can be visualized clearly, as well as their connections to specific variables and/or ratios. Furthermore, Co-Plot can be used in an exploratory data analysis to identity outliers, whose data require additional scrutiny, and potentially inconsequential variables that could be aggregated or removed from the analysis with little effect on the subsequent DEA results. The Co-Plot diagram of ratios presents super-efficient observations on an outer ring or sector of the plot and all reasonably efficient units on a slightly inner ring/sector, surrounding the remaining inefficient decision-making units. First, the well-known 35 Chinese Cities dataset is provided as an illustration. Second, a simulation study tests the applicability of Co-Plot to present the results of DEA. Keywords: Data envelopment analysis; Multi-dimensional scaling; Efficiency; Co-Plot, 1. Introduction The purpose of this paper is to suggest a methodology for presenting data envelopment analysis (DEA) graphically. The graphical display method, Co-Plot, is a variant of multi-dimensional scaling [...]

Correlated proportions arise in longitudinal (panel) studies. A typical example is the 'opinion swing' problem: 'Has the proportion of people favoring a politician changed after his recent speech to the nation on TV?' Because the same group of individuals is interviewed before and after the speech, the two proportions are correlated. A natural null hypothesis to be tested is whether the corresponding population proportions are equal. A standard Bayesian approach to this problem has already been considered in the literature, based on a Dirichlet prior for the cell probabilities of the underlying 2 x 2 table under the alternative hypothesis, together with an induced prior under the null. With a lack of specific prior information, a diffuse (e.g., uniform) distribution may be used. We claim that this approach is not satisfactory, because in a testing problem one should make sure that the prior under the alternative is adequately centered around the region specified by the null, in order to obtain a fairer comparison between the two hypotheses, especially when the data are in reasonable agreement with the null. Following an intrinsic prior methodology, we develop two strategies for the construction of a collection of objective priors increasingly peaked around the null. We provide a simple interpretation of their structure in terms of weighted imaginary sample scenarios. We illustrate our method by means of three examples, carrying out sensitivity analysis and providing comparison with existing results. KEY WORDS: Bayes factor: Bayesian robustness: Dirichlet prior; Marginal homogeneity: Matched pair: Objective Bayes.

By interleaving one length-N perfect sequence or ideal sequence according to elaborate phases, a new method of construction of zero correlation zone (ZCZ) and low correlation zone (LCZ) sequence sets is presented. The resultant sequence sets are optimal or almost optimal with respect to Tang, Fan, and Matsufuji bound. Furthermore, the new method provides flexible choice for the ZCZ and LCZ lengths. Index Terms--Low correlation zone (LCZ) sequence, quasi-synchronous code-division multiple access (QS-CDMA), shift sequence, zero correlation zone (ZCZ) sequence.

In 4 studies, the authors examined the hypothesis that the structure of the informational environment makes small samples more informative than large ones for drawing inferences about population correlations. The specific purpose of the studies was to test predictions arising from the signal detection simulations of R. B. Anderson, M. E. Doherty, N. D. Berg, and J. C. Friedrich (2005). The results of a simulation study in the present article confirmed and extended previous theoretical claims (R. B. Anderson et al., 2005) that in a yes/no correlation detection task, small-sample advantages should occur but should be restricted to particular decision conditions. In 3 behavioral studies, participants viewed larger or smaller samples of data pairs and judged whether each sample had been drawn from a population characterized by a zero correlation or from one characterized by a greater-than-zero correlation. Consistent with traditional statistical theory, accuracy tended to be greater for larger than for smaller samples, though there was a small-sample advantage in 1 experimental condition. The results are discussed in relation to alternative theoretical and behavioral paradigms such as those of Y. Kareev (e.g., 2005) and K. Fiedler and Y. Kareev (2006). Keywords: inference, judgment, correlation, signal detection

An algorithm for mixture of Dirichlet process (MDP) models is proposed with exponential family likelihoods and normal base measures. The proposal is accepted or rejected via a Metropolis-Hastings step. Where conclusion states that this method is remarkably effective in a large class of prolems and significantly reduces the autocorrelation times compared to existing simulation algorithms for nonconjugate MDP models.

The properties of the order statistics correlation coefficient are discussed. Findings reveal the usefulness of the order statistics correlation coefficient as an alternative to Pearson's coefficient in correlation analysis.

High dimensionality causes problems in various areas of statistics. A particular situation that rarely has been considered is the testing of hypotheses about multivariate regression models in which the dimension of the multivariate response is large. In this article a ridge regularization approach is proposed in which either the covariance or the correlation matrix is regularized to ensure nonsingularity irrespective of the dimensionality of the data. It is shown that the proposed approach can be derived through a penalized likelihood approach, which suggests cross-validation of the likelihood function as a natural approach for estimation of the ridge parameter. Useful properties of this likelihood estimator are derived, discussed, and demonstrated by simulation. For a class of test statistics commonly used in multivariate analysis, the proposed regularization approach is compared with some obvious alternative regularization approaches using generalized inverse and data reduction through principal components analysis. Essentially, the approaches considered differ in how they shrink eigenvalues of sample covariance and correlation matrices. This leads to predictable differences in power properties when comparing the use of different regularization approaches, as demonstrated by simulation. The proposed ridge approach has relatively good power compared with the alternatives considered. In particular, a generalized inverse is shown to perform poorly and cannot be recommended in practice. Finally, the proposed approach is used in analysis of data on macroinvertebrate biomasses that have been classified to species. KEY WORDS: Cross-validation; Generalized inverse; High-dimensional data; Multivariate analysis; Multivariate regression.

Correlation tensor analysis (CTA) is used for appearance-based discriminant subspace learning. Efficient dimensionality reduction, effective discriminative embedding and low computational cost are the main advantages of the CTA.

Theoretical and experimental analyses of phase-based ultrasonic deformation estimators with a new algorithm class are presented. The estimators offer greater accuracy for wide range of real-time application.

We consider the problem of efficiently allocating simulation replications in order to maximize the probability of selecting the best design under the scenario in which system performances are sampled in […]

We investigate the behavior of data-driven smoothing parameters for penalized spline regression in the presence of correlated data. It has been shown for other smoothing methods that mean squared error minimizers, such as (generalized) cross-validation or the Akaike information criterion, are extremely sensitive to misspecifications of the correlation structure resulting in over- or (under-)fitting the data. In contrast to this, we show that a maximum likelihood-based choice of the smoothing parameter is more robust and that for a moderately misspecified correlation structure over- or (under-) fitting does not occur. This is demonstrated in simulations and data examples and is supported by theoretical investigations. KEY WORDS: Correlation structure misspecification; Linear mixed model; Smoothing parameter selection.

In this paper we develop a simple test procedure for a linear trend which does not require knowledge of the form of serial correlation in the data, is robust to strong serial correlation, and has a standard normal limiting null distribution under either I(0) or I(1) shocks. In contrast to other available robust linear trend tests, our proposed test achieves the Gaussian asymptotic local power envelope in both the I(0) and I(1) cases. For near-I(1) errors our proposed procedure is conservative and a modification for this situation is suggested. An estimator of the trend parameter, together with an associated confidence interval, which is asymptotically efficient, again regardless of whether the shocks are I(0) or I(1), is also provided. JEL classification: C22 Keywords: Linear trend; Strong serial correlation: Asymptotic normality; Power envelope: Unit root tests; Stationarity tests

In this paper we consider semiparametric estimation of a generalized correlation coefficient in a generalized bivariate probit model. The generalized correlation coefficient provides a simple summary statistic measuring the relationship between the two binary decision processes in a general framework. Our semiparametric estimation procedure consists of two steps, combining semiparametric estimators for univariate binary choice models with the method of maximum likelihood for the bivariate probit model with nonparametrically generated regressors. The estimator is shown to be consistent and asymptotically normal. The estimator performs well in our simulation study. JEL classification: C31; C35 Keywords: Bivariate probit; Generalized correlation coefficient; Dependence measures

The forward-link capacity of a power-controlled code-division-multiple-access (CDMA) system was commonly obtained by assuming equal base-station (BS) power throughout the system and neglecting the correlation and interaction among BS powers, which is rarely true in real CDMA systems. We propose an iteratively analytical process to determine the dynamic capacity in CDMA systems with unequal BS power by considering the correlation and interaction among BS powers. Simulation results show that the Erlang capacity is significantly different by modeling the BS power as a random variate instead of a constant value. We also show that correlation among BS powers can be up to 0.13, and the reduction in Erlang capacity can be up to 30%. To efficiently evaluate the dynamic Erlang capacity and correlation among BS powers, a closed-form expression of the capacity in terms of certain outage and blocking probabilities is obtained by using the distribution of the BS power. Index Terms--Blocking, Erlang capacity, forward link, outage.

Two new models used to characterize polarization diversity at the mobile are presented and discussed. The first model is built upon existing theoretical models at a base station to demonstrate how those principles apply to the mobile fading environment. Due to limitations of antennas at the mobile, this extended model, although relevant, is not sufficient to characterize polarization diversity of the antennas; therefore, this paper moves on to show how a new approach to polarization diversity at the mobile exists as an inherent feature within an angular diversity system. Results show that, for two polarizations in a fading environment, the best overall output occurs with a [+ or -] 4-45[degree] element configuration, although the diversity combiner itself has optimum performance with a [+ or -] 67.5[degree] configuration due to lower correlation at the input. The second model is also used to demonstrate how differently polarized dipoles are using polarization diversity inherent within an angular diversity system. Index Terms--Antenna diversity, branch difference, correlation, cross-polar ratio, efficiency loss.

In this correspondence, we propose a wavelet-based hierarchical approach using mutual information (MI) to solve the correspondence problem in stereo vision. The correspondence problem involves identifying corresponding pixels between images of a given stereo pair. This results in a disparity map, which is required to extract depth information of the relevant scene. Until recently, mostly correlation-based methods have been used to solve the correspondence problem. However, the performance of correlation-based methods degrades significantly when there is a change in illumination between the two images of the stereo pair. Recent studies indicate MI to be a more robust stereo matching metric for images affected by such radiometric distortions. In this short correspondence paper, we compare the performances of MI and correlation-based metrics for different types of illumination changes between stereo images. MI, as a statistical metric, is computationally more expensive. We propose a wavelet-based hierarchical technique to counter the increase in computational cost and show its effectiveness in stereo matching. Index Terms--Correlation, mutual information (MI), stereo vision, wavelet decomposition.

A new deterministic technique is proposed for blind equalization of finite impulse response multiple-input multiple-output (FIR-MIMO) channels. The batch and adaptive algorithms are obtained by reformulating canonical correlation analysis (CCA) as a set of coupled least squares (LS) regression problems.

In this correspondence, we present a connection between designing low-correlation zone (LCZ) sequences and the results of correlation of sequences with subfield decompositions presented in a recent book by the first two authors. This results in LCZ signal sets with huge sizes over three different alphabetic sets: finite field of size q, integer residue ring modulo q, and the subset in the complex field which consists of powers of a primitive q th root of unity. We show a connection between these sequence designs and "completely noncyclic" Hadamard matrices and a construction for those sequences. We also provide some open problems along this direction. Index Terms--Hadamard matrices of completely noncyclic type, low-correlation zone (LCZ) sequences, subfield reducible sequences, two-tuple balance property.

We consider communication over binary-input memoryless symmetric channels with low-density parity-check (LDPC) codes. The relationship between maximum a posteriori and belief propagation decoding is investigated using a set of correlation inequalities that first appeared in statistical mechanics of Gaussian spin glasses. We prove bounds on generalized extrinsic information transfer (EXIT) functions, that are believed to be tight, and discuss their relationship with the ones obtained by the interpolation method. Index Terms--Low-density parity-check (LDPC) codes, belief propagation, correlation inequalities, density evolution, extrinsic information transfer (EXIT) curve, spin glasses.

Golay sequences and complementary sets of sequences for their application in multisensor and communication systems are analyzed.