THE LIMIT DISTRIBUTIONS OF EMPIRICAL DISTRIBUTIONS OF RANDOM PROJECTION PURSUIT OF CONTINUOUS FORM CmGm（||X||）2 multiply fromi=1 to m |xi|2ri-1

WANG Jingfang

WANG Jingfang. THE LIMIT DISTRIBUTIONS OF EMPIRICAL DISTRIBUTIONS OF RANDOM PROJECTION PURSUIT OF CONTINUOUS FORM CmGm（||X||）2 multiply fromi=1 to m |xi|2ri-1[J]. Chinese Journal of Applied Probability and Statistics, 1991, 7(3): 291-298.

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THE LIMIT DISTRIBUTIONS OF EMPIRICAL DISTRIBUTIONS OF RANDOM PROJECTION PURSUIT OF CONTINUOUS FORM C_mG_m（||X||）² multiply fromi=1 to m |x_i|^2ri-1

WANG Jingfang

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Let X= （x₁, x₂, …, x_m）, be a m-dimensional random vector, X₁, X₂, …, X_n subsamples from the population X, the m-dimensional random vector Z have the N_m（0, I_m） distribution and B_m＞0 be a sequence of real numbers. Let \hatF_n^Z / B m(x)=\frac1n \#\left\i: Z^\prime X_i / B_mr_i＞0 then \hatF_n^2 B m(x) \xrightarrowP N\left(0, \sigma^2\right) or \hatF_n^Z / B m(x) \xrightarrowP \mathscrL\left(T_k\right),as n→∞, m→∞, where ф（T_k） is the Student distrbution T_k with k degrees of freedom.

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THE LIMIT DISTRIBUTIONS OF EMPIRICAL DISTRIBUTIONS OF RANDOM PROJECTION PURSUIT OF CONTINUOUS FORM CmGm（||X||）2 multiply fromi=1 to m |xi|2ri-1

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THE LIMIT DISTRIBUTIONS OF EMPIRICAL DISTRIBUTIONS OF RANDOM PROJECTION PURSUIT OF CONTINUOUS FORM C_mG_m（||X||）² multiply fromi=1 to m |x_i|^2ri-1