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121.
Correspondence analysis was used to classify the pattern-like FT-IR spectra of intact bacteria. The analysis was performed on a data set of approximately 80 normalized spectral derivatives of a selection of pathogenic bacteria. The correspondence analysis proved that the various different bacterial species were clustering in distinct regions of the correspondence maps suggesting that there do exist correlations between spectral data and biochemical/microbiological classification. 相似文献
122.
Let X1, X2 ,…, Xp be p random variables with joint distribution function F(x1 ,…, xp). Let Z = min(X1, X2 ,…, Xp) and I = i if Z = Xi. In this paper the problem of identifying the distribution function F(x1 ,…, xp), given the distribution Z or that of the identified minimum (Z, I), has been considered when F is a multivariate normal distribution. For the case p = 2, the problem is completely solved. If p = 3 and the distribution of (Z, I) is given, we get a partial solution allowing us to identify the independent case. These results seem to be highly nontrivial and depend upon Liouville's result that the (univariate) normal distribution function is a nonelementary function. Some other examples are given including the bivariate exponential distribution of Marshall and Olkin, Gumbel, and the absolutely continuous bivariate exponential extension of Block and Basu. 相似文献
123.
Lajos Horváth 《Journal of multivariate analysis》1983,13(1):202-209
The general asymptotic order of magnitude is determined for the maximal deviation of the multivariate product-limit estimate from the estimated survival function on Rk. This order depends on the joint behavior of the censoring and censored distributions in a well-defined way. Corresponding to specific joint behaviors, several lim sup results are deduced generalizing everything that is known in the univariate case. The results are also extended for the variable censoring model. 相似文献
124.
Seiji Takano 《Journal of multivariate analysis》1973,3(1):93-101
The problem of multivariate information analysis is considered. First, the interaction information in each dimension is defined analogously according to McGill [4] and then applied to Markov chains. The property of interaction information zero deeply relates to a certain class of weakly dependent random variables. For homogeneous, recurrent Markov chains with m states, m ≥ n ≥3, the zero criterion of n-dimensional interaction information is achieved only by (n ? 2)-dependent Markov chains, which are generated by some nilpotent matrices. Further for Gaussian Markov chains, it gives the decomposition rule of the variables into mutually correlated subchains. 相似文献
125.
C.Radhakrishna Rao 《Journal of multivariate analysis》1979,9(3):362-377
Separation theorems for singular values of a matrix, similar to the Poincaré separation theorem for the eigenvalues of a Hermitian matrix, are proved. The results are applied to problems in approximating a given r.v. by an r.v. in a specified class. In particular, problems of canonical correlations, reduced rank regression, fitting an orthogonal random variable (r.v.) to a given r.v., and estimation of residuals in the Gauss-Markoff model are discussed. In each case, a solution is obtained by minimizing a suitable norm. In some cases a common solution is shown to minimize a wide class of norms known as unitarily invariant norms introduced by von Neumann. 相似文献
126.
Generalizing a classical idea of Biermann, we study a way of constructing a unisolvent array for Lagrange interpolation in Cn+m out of two suitably ordered unisolvent arrays respectively in Cn and Cm. For this new array, important objects of Lagrange interpolation theory (fundamental Lagrange polynomials, Newton polynomials, divided difference operator, vandermondian, etc.) are computed.
AMS subject classification 41A05, 41A63 相似文献
127.
Summary Let <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"7"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"8"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"9"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>{\cal
{X}}_{n} =(X_1,\ldots,X_n)$ be a random vector. Suppose that the random variables $(X_i)_{1\leq i\leq n}$ are stationary and
fulfill a suitable dependence criterion. Let $f$ be a real valued function defined on $\mathbbm{R}^n$ having some regular
properties. Let ${\cal {Y}}_{n}$ be a random vector, independent of ${\cal {X}}_{n}$, having independent and identically distributed
components. We control $\left|\mathbbm{E}(f({\cal {X}}_{n}))-\mathbbm{E} (f({\cal {Y}}_{n}))\right|$. Suitable choices of
the function $f$ yield, under minimal conditions, to rates of convergence in the central limit theorem, to some moment inequalities
or to bounds useful for Poisson approximation. The proofs are derived from multivariate extensions of Taylor's formula and
of the Lindeberg decomposition. In the univariate case and in the mixing setting the method is due to Rio (1995). 相似文献
128.
The Fréchet distance between two multivariate normal distributions having means μX, μY and covariance matrices ΣX, ΣY is shown to be given by . The quantity d0 given by is a natural metric on the space of real covariance matrices of given order. 相似文献
129.
In this paper a procedure of construction of β-expectation tolerance regions in the framework of the structural method of inference has been developed. The procedure has been applied to the generalized multivariate model and the β-expectation tolerance region for this case has been constructed assuming the normal distribution for the error variables of the model. 相似文献
130.