论文信息 - The strong law of large numbers for k-means and best possible nets of Banach valued random variables

The strong law of large numbers for k-means and best possible nets of Banach valued random variables

SummaryLet B be a uniformly convex Banach space, X a B-valued random variable and k a given positive integer number. A random sample of X is substituted by the set of k elements which minimizes a criterion. We found conditions to assure that this set converges a.s., as the sample size increases, to the set of k-elements which minimizes the same criterion for X.

J. A. Cuesta | C. Matrán

[1] A. Skorokhod. Limit Theorems for Stochastic Processes , 1956 .

[2] K. Parthasarathy,et al. Probability measures on metric spaces , 1967 .

[3] K. Parthasarathy. PROBABILITY MEASURES IN A METRIC SPACE , 1967 .

[4] I. Singer. Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces , 1970 .

[5] Richard B. Holmes,et al. A Course on Optimization and Best Approximation , 1972 .

[6] J. Retherford. Review: J. Diestel and J. J. Uhl, Jr., Vector measures , 1978 .

[7] Harald Sverdrup-Thygeson. Strong Law of Large Numbers for Measures of Central Tendency and Dispersion of Random Variables in Compact Metric Spaces , 1981 .

[8] D. Pollard. Strong Consistency of $K$-Means Clustering , 1981 .

[9] N. Herrndorf,et al. Approximation of vector-valued random variables by constants , 1983 .

[10] Juan Antonio Cuesta Albertos. Medidas de centralización multidimensionales (Ley fuerte de los grandes números) , 1984 .

[11] Carlos Matrán,et al. Uniform consistency of r-means , 1988 .