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  • 1
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Clinica Chimica Acta 6 (1961), S. 205-228 
    ISSN: 0009-8981
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Medicine
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Annals of the Institute of Statistical Mathematics 52 (2000), S. 630-645 
    ISSN: 1572-9052
    Keywords: Conditional density ; conditional mode ; smooth rank nearest neighbor estimators ; law of iterated logarithm ; uniform strong convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let (X i , Y i ) be a sequence of i.i.d. random vectors in R with an absolutely continuous distribution function H and let g x (y), y∈ R denote the conditional density of Y given X = x∈Λ(F), the support of F, assuming that it exists. Also let M(x) be the (unique) conditional mode of Y given X = x defined by M(x) = arg max y (y)). In this paper new classes of smoothed rank nearest neighbor (RNN) estimators of g x (y), its derivatives and M(x) are proposed and the laws of iterated logarithm (pointwise), uniform a.s. convergence over −∞ 〈 y 〈 ∞ and x∈ a compact C⫅Λ(F) and the asymptotic normality for the proposed estimators are established. Our results and proofs also cover the Nadayara-Watson (NW) case. It is shown using the concept of the relative efficiency that the proposed RNN estimator is superior (asymtpotically) to the corresponding NW type estimator of M(x), considered earlier in literature.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Annals of the Institute of Statistical Mathematics 43 (1991), S. 327-346 
    ISSN: 1572-9052
    Keywords: Kernel density estimation ; bias ; mean square error ; finite differences ; semi-groups ; linear operators
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let X 1, X 2, ..., X n be independent observations from an (unknown) absolutely continuous univariate distribution with density f and let % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GabmOzayaajaGaaiikaiaadIhacaGGPaGaeyypa0Jaaiikaiaad6ga% caWGObGaaiykamaaCaaaleqabaGaeyOeI0IaaGymaaaakmaaqadaba% Gaam4saiaacUfadaWcgaqaaiaacIcacaWG4bGaeyOeI0Iaamiwamaa% BaaaleaacaWGPbaabeaakiaacMcaaeaacaWGObGaaiyxaaaaaSqaai% aadMgacqGH9aqpcaaIXaaabaGaamOBaaqdcqGHris5aaaa!5356!\[\hat f(x) = (nh)^{ - 1} \sum\nolimits_{i = 1}^n {K[{{(x - X_i )} \mathord{\left/ {\vphantom {{(x - X_i )} {h]}}} \right. \kern-\nulldelimiterspace} {h]}}} \] be a kernel estimator of f(x) at the point x, \s-∞〈x〈∞, with h=h n (h n →O and nh n →∞, as n→∞) the bandwidth and K a kernel function of order r. “Optimal” rates of convergence to zero for the bias and mean square error of such estimators have been studied and established by several authors under varying conditions on K and f. These conditions, however, have invariably included the assumption of existence of the r-th order derivative for f at the point x. It is shown in this paper that these rates of convergence remain valid without any differentiability assumptions on f at x. Instead some simple regularity conditions are imposed on the density f at the point of interest. Our methods are based on certain results in the theory of semi-groups of linear operators and the notions and relations of calculus of “finite differences”.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Probability theory and related fields 12 (1969), S. 173-184 
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Let $$X_{vi} = (X_{vi1} ,X_{vi2} ,...,X_{viK_i } ) 1\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } i\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } n_v$$ be a sequence of independent random vectors following the regression model X vij = α + ΒC vij + σY vij, with −∞〈α, Β, C vij 〈∞, σ〈0, and where $$Y_{vi} = (Y_{vi1} ,...,Y_{viK_i } ), 1\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } i\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } n_v$$ , are independent random vectors with absolutely continuous distributions F (i) (x (i) ) and with densities $$f^{(i)} (x^{(i)} ) (x^{(i)} = (x_1 ,x_2 ,...x_{K_i } ))$$ . Define $$S_v = \sum\limits_i {\sum\limits_j {d_{vij} } \xi _{vR_{vij} } }$$ where $$\{ \xi _{vk} : 1\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } k\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } N_v \} (N_v = \sum\limits_{i = 1}^{n_v } {K_i } )$$ is a double sequence of real numbers, -∞〈d vij 〈∞ and R vij = rank of X vij in a combined ranking of N v components X vij , 1≦j≦K i, 1≦j≦K i, 1≦i≦K v. Under certain assumptions on the densities f (i) (x (i) ) and the sequences {ξ vij }, {d vij } and {C vij }, the asymptotic normality of the sequence S v , as n v → ∞, is proved. The results extend similar results of Hájek [3] and [4], from independently distributed components to the above pattern of dependence. An extension of the main theorem also covers the case when some of the distributions F (i) (x (i) ) are singular. The connection between the Hájek condition (1.8) of [4] and the present condition (6.1) on the multivariate densities f (i) (x (i) ) is also discussed.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical and applied genetics 41 (1971), S. 259-262 
    ISSN: 1432-2242
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary Many problems and difficulties are encountered in making genetic improvements in plants where both apomixis and polyploidy occur together. From biosystematic studies on an agamic species complex, Dichanthium annulatum, information is presented on: (A) Mechanisms which create variability in apomicts — (i) genome building and reduction, (ii) hybridization between ecotypes of facultative apomicts, (iii) fertilization of unreduced gametes, (iv) introgressive hybridization, (v) preferential pairing and genotypic control of bivalent formation and (vi) induced mutation; (B) Embryo-sac variations, vis-a-vis sexual/apomictic sacs — (i) production of sexual embryo-sac in apomicts, (ii) balance between apomixis and sexual process, (iii) effect of environment and experimental manipulation of the type of embryo-sac; and (C) Heterosis and fixation of apomixis. The utilization and exploitation of these mechanisms and phenomena for accelerating the genetic improvement of apomictic plants is discussed. Mating systems impose certain restrictions on the breeding methodology to be used in the genetic improvement of crop plants. Allogamous species have built-in mechanisms for self-improvement and, for them, the breeding techniques are well worked out. Little information is, however, available on the procedures to be followed for the genetic improvement of apomicts. Recently gathered information on the causal mechanisms of apomixis and its mode of inheritance, the genetic systems which regulate the balance between apomixis and sexuality, the physical and chemical agents for artificial induction of sexuality in apomicts, and the processes which promote variability and adaptive polymorphism in apomicts show a way for the creation, exploitation and fixation of superior genotypes. Such information, based on biosystematic studies on an agamic species complex, Dichanthium annulatum, at the Oklahoma State University, Stillwater, Oklahoma, U.S.A., is presented here. Breeding procedures commonly followed for the genetic improvement of apomicts are outlined below: 1. Collection of varieties, strains or ecotypes from diverse sources; 2. Evaluation of the germ plasm for the presence of desirable characters; 3. Building up of selection indices and estimation of genetic parameters; 4. Determination of mode of reproduction and isolation of sexual types or clones; 5. Hybridization using the sexual types; 6. Progeny testing, comparisons, multiplication and release of superior types. Thus, the success of the breeding programme would depend on the range of variability already present in the germ plasm collections, the relative proportion of sexual/apomictic seed produced and the exploitation of variability from the crossbred progenies. Since large collections of plants with different genotypes are not often available, one would like to look for the mechanisms which can create variability in the apomicts. Such mechanisms are as follows.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Potato research 15 (1972), S. 71-72 
    ISSN: 1871-4528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The leaf index was calculated using four different methods; namely, a. average index from 5 plants based only on 4th leaf from the top: b. average index of all the leaves of one plant; c. average index of 20 randomly selected leaves in a culture; d. average index of all the leaver of 5 plants of a culture. No significant differences between the four mthods were observed in the study. The method based only on 4th leaf from the top of the plant is recommended for calculating the leaf index in a potato crop. This method can be used very easily and conveniently in less time giving equivalent efficiency when compared with the other three methods.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Euphytica 20 (1971), S. 597-601 
    ISSN: 1573-5060
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The causative sources of common variation of seven components of fodder yield in oats were analysed, using the centroid method of factor analysis. Two factors together accounted for most of the inter-correlations of these characters. Factor 1 had different degrees of positive loading on all characters, the highest being on the fodder yield. Factor 2 affected negatively a few and positively the remaining characters. The plant height and fodder yield were affected positively by Factor 1 and negatively by Factor 2. Factor 1 and 2 were significantly negatively associated with each other. The fodder yield components in the material studied seem to be influenced by the two interacting hormonal systems. The implications of the findings, in selecting for high quality and high yielding varieties of fodder oats, are discussed.
    Type of Medium: Electronic Resource
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