Malaysian Journal of Mathematical Sciences

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  • ISSN
    1823-8343

Publications in this journal

  • Malaysian Journal of Mathematical Sciences 01/2013;
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    ABSTRACT: Missing covariate data occur inevitably in various scientific researches. The response variable of interest in these studies may be continuous or categorical and the covariates may have a continuous or discrete nature. Multiple Imputation (MI) procedures may be used to properly or improperly impute the missing data several times and to find parameter estimates by combining the pseudo-complete-case analyses of the imputed data-sets. Although many efforts in the literature have been placed on analyzing continuous response data with missing covariates using MI, models for ordinal response data with missing covariates have received less attention. In this paper four different models for imputation of a missing continuous covariate, of which three are proper and one improper, are compared in models for ordinal responses. All models can be easily implemented in existing software. Data from a Steatosis study is used to illustrate the use of these models. The importance of using a fuller model for imputation compared to that of the analysis model is finally underlined.
    Malaysian Journal of Mathematical Sciences 01/2011; 5:27-44.
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    ABSTRACT: In [1], Alfsen and Shultz have proved that the state space () S A of a JB-algebra A has the Hilbert ball property: for each pair ρ, σ of extreme points of () S A , the face generated by ρ and σ is a norm-exposed face affinely isomorphic to the closed unit ball in some Hilbert space ([1], Corollary 3.12). Conversely, they have proved that the order unit space A being in spectral duality with its predual space is a JB − algebra if the state space of A has the Hilbert ball property ([1], Theorem 7.2). We define the Banach ball property for the state space of order unit spaces and study order unit spaces which have this property. Thus, we describe some class of order unit spaces, geometry of which is similar to geometry of JB-algebras. Due to this fact we can develop the theory of order unit spaces like the theory of Jordan Banach spaces and obtain new results.
    Malaysian Journal of Mathematical Sciences 01/2010; 4:77-83.
  • Malaysian Journal of Mathematical Sciences 01/2010; 4(2):241-254.
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    ABSTRACT: The paper intends to survey the subject of the title for an audience of mathematicians not necessarily expert in the areas of commutative algebra and algebraic geometry. It is devoted to the isomorphism invariants of low dimensional Complex filiform Leibniz Algebras under the action of the general linear group ("transport of structure"). The description of the field of invariant rational functions in low dimensional cases is presented.
    Malaysian Journal of Mathematical Sciences 01/2009; 3:147-159.
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    ABSTRACT: The mathematical modeling on the mapping function models should be revised and also simplified to improve the calculation of the GPS tropospheric delay. The zenith tropospheric delay can be amplified by a coefficient factor called mapping function to form total tropospheric delay. There are many mapping functions have been established to calculate the scale factor which can affect the total tropospheric delay. Most of the modern models have separated mapping functions for the hydrostatic and the wet part. Recently, the developed tropospheric delay models use mapping functions in the form of continued fractions which is quite tedious in calculation. There are 26 mathematical operations for Neill Mapping Function (NMF) to be done before getting the mapping function scale factor. There is a need to simplify the mapping function models to allow faster calculation and also better understanding of the models. The mapping functions for NMF models for hydrostatic and wet components are given in a form of continued fraction, whereby the elevation angle is the variable. These mapping function models have been selected to be simplified, because of their ability to achieve mapping function scale factor, down to 3 degree of elevation angle.
    Malaysian Journal of Mathematical Sciences 01/2009; 3(1):95–107.
  • Malaysian Journal of Mathematical Sciences 01/2009; 3(2):265- 277.
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    ABSTRACT: Statisticians face increasingly the task of analyzing large and high dimension multivariate data sets. This is due to the advances in computer technology which have facilitated greatly the collection of large data sets and, on the other hand, to the fact that most statistical experiments are multivariate in nature. One of the primary problems encountered in this task is robust estimation of location and scatter. In the literature the most popular and widely used robust parametric method for such parameter estimation is the so-called Fast MCD. However, although it is affine-equivariant and has high breakdown point, it is not apt when the data sets are of high dimension because its computational efficiency becomes lower. This is a direct consequence from the use of Mahalanobis distance or, equivalently, Mahalanobis depth in data ordering process which needs the inversion of covariance matrix and the use of MCD as the objective function. In this paper we propose a method which is as effective as Fast MCD but computationally more efficient. For this purpose, in multivariate ordering step, we use a new depth function which is equivalent to Mahalanobis depth and has lower computational complexity. Furthermore, in data concentration step, we use vector variance as the measure of multivariate scatter instead of covariance determinant and we replace the objective function MCD with minimum vector variance to reduce the complexity of this step. At the end of the paper we illustrate the effectiveness of this method using a simulation experiment.
    Malaysian Journal of Mathematical Sciences 01/2008; 2:1-24.

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