Sains Malaysiana 34(1): 119-123 (2005)

A Multivariate Measure of Dispersion and its Limiting Distribution

(Ukuran Multivariat bagi Dispersi dan Hal Taburannya)

Suwanda bin Idris

Department of Mathematics

Institut Teknologi Bandung JI. Ganesha 10

Bandung 40132, Indonesia

ABSTRAK

Jumlah Varians dan Varians Teritlak kebiasaannya digunakan sebagai ukuran dispersi multivariate. Namun begitu, kedua-dua statistik ini mempunyai beberapa kelemahan. Dalam tulisan ini akan dicadankgan satu ukuran dispersi multivariate yang baru, dikenali sebagai varians bervektor (VV) yang merupakan suatu hasil darab terkedalam bagi set pengoperasi yang tertakrif ke atas suatu ruang Hilbert-Smith. Oleh kerana taburan pensampilan tepat dari statistik vv tersebut sangat sukar untuk ditentukan, maka taburan pensampilan asimtot telah diperolehi.

ABSTRACT

Total Variance (TV) and Generalized Variance (GV) are commonly used as a measure multivariate dispersion.  However, these two statistics has some drawbacks. This paper proposes a new measure of multivariate dispersion, named Vectorial Variance (VV) an inner product for set of operators defined on a Hilbert-Smith space. Since, the exact sampling distribution of VV is difficult to find, therefore the asymptotic sampling distribution is obtained.

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