Asymptotic Distribution of the Mutual Variogram Estimate

• Autorzy: Troush N. , Tsekhovaya T.
• Konferencja: X Polish-Czech Mathematical School (10 ; 04-07.06.2003 ; Poraj near Częstochowa, Poland)
• Języki publikacji: EN

Abstrakty

EN

The article deals with the problem of a statistical analysis of time series connected with the estimation of mutual variogram, a measure of spatial correlation. G. Matheron [1] has coined the term variogram, although earlier appearances of this function can be found in the scientific literature [2, 3]. The problem of estimating the mutual variogram and examination the statistical properties of this statistics has been considered in [1, 4, 5]. We present the limiting expressions of the first two moments and the higher order cumulants of the mutual variogram estimate of the second-order-stationary stochastic process with discrete time. These expressions are then used to prove the theorem concerning the asymptotic distribution of the mutual variogram estimate. The approach is similar to the approach taken in the time series literature, and the reader is referred to D. Brillinger [6] for theorems regarding the asymptotic distribution of the spectral density estimate of a time series.

Słowa kluczowe

EN

statistical analysis of time series; variogram; asymptotic distribution; estimation process

PL

statystyczna analiza szeregów czasowych; wariogram; rozkład asymptotyczny; proces szacowania

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2003
• Tom: Vol. 9
• Strony: 109--114
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Troush N.

• Academia Podlaska, Siedlce, Poland

autor

Tsekhovaya T.

• Belarus State University, Minsk, Belarus

Bibliografia

• [1] G. Matheron, Principles of geostatistics, Econ. Geol, 58, 1246-1266,1963.
• [2] A. N. Kolmogorov, The local structure of turbulence in an incompressible, fluid at very large Reynolds numbers. Doklady Akademii Nauk SSSR, 30, 301-305, 1941.
• [3] A. M. Yaglom, Some classes of random fields in n - dimensional space, related to stationary random processes, Theory of Probability and Its Applications, 2, 273-320, 1957.
• [4] A. G. Journel, C. J. Huijbregts, Mining Geostatistics. Academic Press, London, 1978.
• [5] N. Cressie, Statistics for Spatial Data. John Wiley and Sons, New York, 1991.
• [6] D. R. Brillinger, Time Series, Data Analysis and Theory. Holt, New York. 1975.