sample covariance sentence in Hindi
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- Commonly used estimators include sample covariance.
- As far as sample covariance matrices are concerned, a theory was developed by Mar enko and Pastur.
- The product in the final line is therefore zero; there is no sample covariance between different principal components over the dataset.
- Similarly, the intrinsic inefficiency of the sample covariance matrix depends upon the Riemannian curvature of the space of positive-define matrices.
- Due to their ease of calculation and other desirable characteristics, the sample mean and sample covariance are widely used in statistics and applications to numerically represent the distribution.
- Simply by replacing the state covariance Q in Kalman gain matrix K by the sample covariance C computed from the ensemble members ( called the " ensemble covariance " ).
- The root mean square residual ( RMR ) and standardized root mean square residual ( SRMR ) are the square root of the discrepancy between the sample covariance matrix and the model covariance matrix.
- It can be seen in Eq . ( 4 ) that the penalty function of Eq . ( 9 ) is minimized by approximating the signal model to the sample covariance matrix as accurate as possible.
- Next, we apply a property of least square regression models, that the sample covariance between \ hat { Y } _ i and Y _ i-\ hat { Y } _ i is zero.
- Where " n " is the sample size, \ overline { \ mathbf x } is the vector of column means and { \ mathbf S } is a m \ times m sample covariance matrix.
- The use of the term " n " " 1 is called Bessel's correction, and it is also used in sample covariance and the sample standard deviation ( the square root of variance ).
- However, when \ alpha > 0, i . e ., when ridge regression is used, the addition of \ alpha I to the sample covariance matrix ensures that all of its eigenvalues will be strictly greater than 0.
- When \ alpha = 0, i . e ., in the case of ordinary least squares, the condition that d > n causes the sample covariance matrix X ^ T X to not have full rank and so it cannot be inverted to yield a unique solution.
- The reason the sample covariance matrix has \ textstyle N-1 in the denominator rather than \ textstyle N is essentially that the population mean \ operatorname { E } ( X ) is not known and is replaced by the sample mean \ mathbf { \ bar { X } }.
- Then " D " is the data transformed so every random variable has zero mean, and " T " is the data transformed so all variables have zero mean and zero correlation with all other variables the sample covariance matrix of " T " will be the identity matrix.
- If only one variable has had values observed, then the sample mean is a single number ( the arithmetic average of the observed values of that variable ) and the sample covariance matrix is also simply a single value ( a 1x1 matrix containing a single number, the sample variance of the observed values of that variable ).
- The sample mean is a matrix whose " i, j " element is the sample covariance ( an estimate of the population covariance ) between the sets of observed values of two of the variables and whose " i, i " element is the sample variance of the observed values of one of the variables.
- The sample mean and the sample covariance matrix are unbiased estimates of the mean and the covariance matrix of the random vector \ textstyle \ mathbf { X }, a row vector whose " j " th element ( " j " = 1, . . ., " K " ) is one of the random variables.
- Specifically, if \ mathbf { X } : = ( x _ { ij } ) \ in \ mathbb { R } ^ { n \ times m } is a prewhitened data matrix, that is, the sample mean of each column is zero and the sample covariance of the rows is the m \ times m dimensional identity matrix, Kernel ICA estimates a m \ times m dimensional orthogonal matrix \ mathbf { A } so as to minimize finite-sample \ mathcal { F }-correlations between the columns of \ mathbf { S } : = \ mathbf { X } \ mathbf { A } ^ { \ prime }.
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