Hi, If I have n samples of d-dimensional vectors, in order for the covariance to do not be rank defficient I would need n>d (assuming the samples are independent). However for high d if I want a good estimation of the covariance matrix (not just full rank) usually I would need much more than d, i.e. n>>d. Does anybody any theoretical study of how many samples would I need to have a good estimation of the covatriance? Since the covariance would have d(d+1)/2 do I need at least this samples?
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