Approximation of Distributions by Parametric Sets

Acta Applicandae Mathematicae

Volumn 78, Issue 1-3, 2003, Pages 175-183

  Kaarik M ^a   Parna K ^a  

^a UNIVERSITY OF TARTU   (Estonia)

Author keywords

Approximation of distributions; Discrepancy function; K centres; Loss function; M estimation

Indexed keywords

APPROXIMATION THEORY; ESTIMATION; SET THEORY; THEOREM PROVING;

DISCREPANCY FUNCTIONS;

PROBABILITY DISTRIBUTIONS;

EID: 0142157207     PISSN: 01678019     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1025773130947     Document Type: Conference Paper

References (13)

1. Averous, J. and Meste, M.: Median balls: an extension of the interquantile intervals to multivariate distributions, J. Multivariate Anal. 63 (1997), 222-241.
2. Billingsley, P.: Convergence of Probability Measures, Moscow, 1977 (in Russian).
3. Cuesta, J. A. and Matran, C: The strong law of large numbers for k-means and best possible nets of Danach valued random variables, Probah Theory Related Fields 78 (1988), 523-534.
4. Cuesta, J. A. and Matran, C.: Uniform consistency of r-means, Statist. Probab. Lett. 6 (1989), 65-71.
5. Graf, S. and Luschgy, H.: Foundations of Quantization for Probability Distributions, Springer-Verlag, New York, 2000.
6. Kääarik, M.: Approximation of distributions by sphere, In: Multivariate Statistics. New Trends in Probability and Statistics, VSP/TEV, Vilnius/Utrecht, 2000, pp. 61-66.
7. Lember, J.: Consistency of empirical k-centres, Dissertation, Tartu University Press, Tartu, 1999.
8. Pärna, K.: Strong consistency of k-means clustering criterion in separable metric spaces, Acta Comment. Univ. Tartuensis 733 (1986), pp. 86-96.
9. Pärna, K.: On the stability of k-means clustering criterion in separable metric spaces, Acta Comment. Univ. Tartuensis 798 (1988), 19-36.
10. Pärna, K.: On the existence and weak convergence of k-centres in Banach spaces, Acta Comment. Univ. Tartuensis 893 (1990), 17-28.
11. Pollard, D.: Strong consistency of k-means clustering, Ann. Statist. 9 (1981), 135-140.
12. Ranga Rao, R.: Relations between weak and uniform convergence of measures with applications, Ann. Math. Statist. 33 (1962), 659-680.
13. Varadarajan, V. S.: On the convergence of probability distributions, Sankhyā 19 (1958), 23-26.