共查询到20条相似文献,搜索用时 15 毫秒
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Warwick de Launey 《Journal of statistical planning and inference》1984,10(3):385-396
The determinant of a generalized Hadamard matrix over its group ring factored out by the relation ΣgεG G = 0 is shown to have certain number theoretic properties. These are exploited to prove the non-existence of many generalised Hadamard matrices for groups whose orders are divisible by 3, 5 or 7. For example the GH(15, C15), GH(15, C3) and GH(15, C5) do not exist. Also for certain n and G we find the set of determinants of the GH(n, G) matrices. 相似文献
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Pekka H.J. Lampio Patric R.J. Östergård 《Journal of statistical planning and inference》2011,141(3):1194-1207
The existence of difference matrices over small cyclic groups is investigated in this computer-aided work. The maximum values of the parameters for which difference matrices exist as well as the number of inequivalent difference matrices in each case is determined up to the computational limit. Several new difference matrices have been found in this manner. The maximum number of rows is 9 for an r ×15 difference matrix over Z3, 8 for an r ×15 difference matrix over Z5, and 6 for an r ×12 difference matrix over Z6; the number of inequivalent matrices with these parameters is 5, 2, and 7, respectively. 相似文献
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Identifying differentially expressed genes is a basic objective in microarray experiments. Many statistical methods for detecting differentially expressed genes in multiple-slide experiments have been proposed. However, sometimes with limited experimental resources, only a single cDNA array or two Oligonuleotide arrays could be made or only insufficient replicated arrays could be conducted. Many current statistical models cannot be used because of the non-availability of replicated data. Simply using fold changes is also unreliable and inefficient [Chen et al. 1997. Ratio-based decisions and the quantitative analysis of cDNA microarray images. J. Biomed. Optics 2, 364–374; Newton et al. 2001. On differential variability of expression ratios: improving statistical inference about gene expression changes from microarray data. J. Comput. Biol. 8, 37–52; Pan et al. 2002. How many replicates of arrays are required to detect gene expression changes in microarray experiments? a mixture model approach. Genome Biol. 3, research0022.1-0022.10]. We propose a new method. If the log-transformed ratios for the expressed genes as well as unexpressed genes have equal variance, we use a Hadamard matrix to construct a t-test from a single array data. Basically, we test whether each doubtful gene has significantly differential expression compared to the unexpressed genes. We form some new random variables corresponding to the rows of a Hadamard matrix using the algebraic sum of gene expressions. A one-sample t-test is constructed and the p-value is calculated for each doubtful gene based on these random variables. By using any method for multiple testing, adjusted p-values could be obtained from original p-values and significance of doubtful genes can be determined. When the variance of expressed genes differs from the variance of unexpressed genes, we construct a z-statistic based on the result from application of Hadamard matrix and find the confidence interval to retain the null hypothesis. Using the interval, we determine differentially expressed genes. This method is also useful for multiple microarrays, especially when sufficient replicated data are not available for a traditional t-test. We apply our methodology to ApoAI data. The results appear to be promising. They not only confirm the early known differentially expressed genes, but also indicate more genes to be differentially expressed. 相似文献
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A mixed-integer programing formulation for clustering is proposed, one that encompasses a wider range of objectives--and side conditions--than standard clustering approaches. The flexibility of the formulation is demonstrated in diagrams of sample problems and solutions. Preliminary computational tests in a practical setting confirm the usefulness of the formulation. 相似文献
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Christopher G. Small 《Revue canadienne de statistique》1992,20(4):463-468
We construct a counterexample to a conjecture in stereology. It is well known that two convex solid bodies which cast congruent orthographic shadows on any common plane must necessarily be congruent to each other. This characterization fails if the orientations of the shadows are allowed to differ. Such counterexamples as have been constructed for the latter case fail to have the same distribution of random shadows projected onto planes with random orientation. Therefore P. McCullagh has conjectured that two bodies whose random shadows have the same distribution are necessarily congruent. We construct a counterexample to this conjecture. Some implications are drawn for the development of a general theory of stereological reconstruction based upon random projected shadows or images. 相似文献
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The concept of d-resolvability of orthogonal arrays of strength (d+1) is introduced. This is used to construct orthogonal resolution-IV plans of the type . These plans are minimal and a large number of these plans are new. 相似文献
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James E. Stafford 《Statistics and Computing》2001,11(1):47-55
Intersection matrices help identify the common graphical structure of two or more objects. They arise naturally in a variety of settings. Several examples of their use in a computer algebra environment are given. These include: simplifying an expression involving array products, automating cumulant calculations, determining the behaviour of an expected value operator and identifying model hierarchy in a factorial experiment. The emphasis is placed on the graphical structure, and the symmetry of arrays help reduce the complexity of the graphical problem. 相似文献
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Jeffrey D. Hart 《统计学通讯:理论与方法》2013,42(12):2943-2945
P. Ghosh (1981) has claimed that the convolution of two symmetric multimodal distributions is symmetric and unimodal. A simple counterexample to this claim is constructed by considering the convolution f?f, where f is an appropriate mixture of two normal densities. 相似文献
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The pairwise comparison matrix is often used for the estimation of the priorities in the analytic hierarchy process. In this paper, we propose an estimation method based on the discrete probabilistic expression of each choice. Moreover, we show numerical examples to compare our method with commonly used ones. As a result, it is shown that, using a robust divergence measure for the estimation, the proposed method can extract the priorities more stably even if some outlying observations are included. 相似文献
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Studies on diffusion tensor imaging (DTI) quantify the diffusion of water molecules in a brain voxel using an estimated 3 × 3 symmetric positive definite (p.d.) diffusion tensor matrix. Due to the challenges associated with modelling matrix‐variate responses, the voxel‐level DTI data are usually summarized by univariate quantities, such as fractional anisotropy. This approach leads to evident loss of information. Furthermore, DTI analyses often ignore the spatial association among neighbouring voxels, leading to imprecise estimates. Although the spatial modelling literature is rich, modelling spatially dependent p.d. matrices is challenging. To mitigate these issues, we propose a matrix‐variate Bayesian semiparametric mixture model, where the p.d. matrices are distributed as a mixture of inverse Wishart distributions, with the spatial dependence captured by a Markov model for the mixture component labels. Related Bayesian computing is facilitated by conjugacy results and use of the double Metropolis–Hastings algorithm. Our simulation study shows that the proposed method is more powerful than competing non‐spatial methods. We also apply our method to investigate the effect of cocaine use on brain microstructure. By extending spatial statistics to matrix‐variate data, we contribute to providing a novel and computationally tractable inferential tool for DTI analysis. 相似文献
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This paper deals with the existence and nonexistence of BIB designs with repeated blocks. The approach is an algebraic one. The concept of a support matrix is introduced and some of its basic properties are noted. Some basic examples of support matrices are given when the block size is 3. The connection between full column rank proper support matrices and irreducible designs is explored and some examples of such matrices are given. 相似文献
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Walter Belluzzo 《Journal of the Royal Statistical Society. Series C, Applied statistics》2006,55(3):397-406
Summary. Contingent valuation researchers are often interested in a comparison of the underlying willingness-to-pay distributions in two independent studies. Since willingness to pay is not observable, traditional testing procedures for comparing distributions cannot be applied directly. The paper proposes a permutation test for this sort of comparison. The main distinguishing characteristic of the test proposed is that it does not rely on asymptotic approximations and facilitates the introduction of covariates. The permutation test is illustrated with the case of projects of investment for the improvement of two important Brazilian river basins. 相似文献
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《统计学通讯:理论与方法》2013,42(10):2099-2115
A simple method of setting linear hypotheses for a split mean vector testable by F-tests in a general linear model, when the covariance matrix has a general form and is completely unknown, is provided by extending the method discussed in Ukita et al. The critical functions in these F-tests are constructed as UMP invariants, when the covariance matrix has a known structure. Further critical functions in F-tests of linear hypotheses for the other split mean vector in the model are shown to be UMP invariant if the same known structure of the covariance matrix is assumed. 相似文献
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ABSTRACTMotivated by various applications in queueing theory, this article is devoted to the stochastic monotonicity and comparability of Markov chains with block-monotone transition matrices. First, we introduce the notion of block-increasing convex order for probability vectors, and characterize the block-monotone matrices in the sense of the block-increasing order and block-increasing convex order. Second, we characterize the Markov chain with general transition matrix by martingale and provide a stochastic comparison of two block-monotone Markov chains under the two block-monotone orders. Third, the stochastic comparison results for the Markov chains corresponding to the discrete-time GI/G/1 queue with different service distributions under the two block-monotone orders are given, and the lower bound and upper bound of the Markov chain corresponding to the discrete-time GI/G/1 queue in the sense of the block-increasing convex order are found. 相似文献
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The problem of optimum allocation in stratified sampling and its solution is well known in sampling literature for univariate populations (see Cochran, 1977; Sukhatme et al., 1984). In multivariate populations where more than one characteristics are to be studied on every selected unit of the population the problem of finding an optimum allocation becomes more complex due to conflicting behaviour of characteristics. Various authors such as Dalenius (1953, 1957), Ghosh (1958), Yates (1960), Aoyama (1963), Gren (1964, 1966), Folks and Antle (1965), Hartley (1965), Kokan and Khan (1967), Chatterjee (1972), Ahsan and Khan (1977, 1982), Chromy (1987), Wywial (1988), Bethel (1989), Kreienbrock (1993), Jahan et al. (1994), Khan et al. (1997), Khan et al. (2003), Ahsan et al. (2005), Díaz-García and Ulloa (2006, 2008), Ahsan et al. (2009) etc. used different compromise criteria to work out a compromise allocation that is optimum for all characteristics in some sense. Almost all the previous authors used some function of the sampling variances of the estimators of various characteristics to be measured as an objective that is to be minimized for a fixed cost given as a linear function of sample allocations. Because the variances are not unit free it is more logical to consider the minimization of some function of squared coefficient of variations as an objective. Previously this concept was used by Kozok (2006). Furthermore, investigators have to approach the sampled units in order to get the observations. This involves some travel cost. Usually this cost is neglected while constructing a cost function. This travel cost may be significant in some surveys. For example if the strata consist of some geographically difficult-to-approach areas. The authors problem of optimum allocation in multivariate stratified sampling is discussed with an objective to minimize simultaneously the coefficients of variation of the estimators of various characteristics under a cost constraint that includes the measurement as well as travel cost. The formulated problem of obtaining an optimum compromise allocation turns out to be a multiobjective all-integer nonlinear programming problem. Three different approaches are considered: the value function approach, ∈ –constraint method, and Distance–based method, to obtain compromise allocations. The cost function considered also includes the travel cost within stratum to reach the selected units. Additional restrictions are placed on the sample sizes to avoid oversampling and ensure the availability of the estimates of the strata variances. Numerical examples are also presented to illustrate the computational details of the proposed methods. 相似文献
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D.G. Kabe 《统计学通讯:理论与方法》2013,42(17):2053-2058
Richmond (1982) uses a linear programming approach to the construction of simultaneous confidence intervals for a set of linear estimable parametric functions of the normal mean vector. We present a quadratic programming approach which constructs narrower confidence intervals than the linear programming approach given by Richmond (1982). 相似文献
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Andrews and Phillips (1986) gave a simplified proof for the result that established the nonnegative definiteness of the difference of the Moore-Penrose inverses of two nonoegative definite matrices, a result originally due to Milliken and Akdeniz (1977), The purpose of this paper is to offer a simple proof for a generalization of this result, 相似文献
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针对长问卷存在无回答率和回答负担,从而导致统计调查精度降低的问题,采用问卷分割法解决该问题,并且通过小域估计的方法进行参数估计。模拟研究表明,利用小域估计方法对分割问卷进行参数估计显然优于用多重插补法进行参数估计。研究结果表明,运用小域估计方法对分割问卷进行参数估计,能显著提高统计调查的精度。 相似文献