vector

(noun)

in statistics, a set of real-valued random variables that may be correlated

Related Terms

Examples of vector in the following topics:

  • Multivariate Testing

    • For a one-sample multivariate test, the hypothesis is that the mean vector ($\mu$) is equal to a given vector (${ \mu }_{ 0 }$).
    • where $n$ is the sample size, $\bar { x }$ is the vector of column means and $S$ is a $m \times m$ sample covariance matrix.
    • For a two-sample multivariate test, the hypothesis is that the mean vectors (${ \mu }_{ 1 },{ \mu }_{ 2 }$) of two samples are equal.

  • Degrees of Freedom

    • The degrees of freedom are also commonly associated with the squared lengths (or "sum of squares" of the coordinates) of random vectors and the parameters of chi-squared and other distributions that arise in associated statistical testing problems.
    • In fitting statistical models to data, the random vectors of residuals are constrained to lie in a space of smaller dimension than the number of components in the vector.
    • In statistical terms, a random vector is a list of mathematical variables each of whose value is unknown, either because the value has not yet occurred or because there is imperfect knowledge of its value.
    • The individual variables in a random vector are grouped together because there may be correlations among them.

  • Which Average: Mean, Mode, or Median?

    • Unlike median, the concept of mean makes sense for any random variable assuming values from a vector space.
    • Vector addition and scalar multiplication: a vector $v$ (blue) is added to another vector $w$ (red, upper illustration).

  • Computing R.M.S. Error

    • If Y^\hat { Y } is a vector of $n$ predictions, and YY is the vector of the true values, then the (estimated) MSE of the predictor is as given as the formula:

  • Categorical Data and the Multinomial Experiment

    • Then if the random variables Xi indicate the number of times outcome number $i$ is observed over the $n$ trials, the vector $X = (X_1, \cdots , X_k)$ follows a multinomial distribution with parameters $n$ and $p$, where $p = (p_1, \cdots , p_k)$.

  • Alternatives to the t-Test

    • Let $\{X_n\}$, $\{Y_n\}$ be sequences of scalar/vector/matrix random elements.

  • Summation Notation

    • Besides numbers, other types of values can be added as well: vectors, matrices, polynomials and, in general, elements of any additive group.

  • Experimental Design

    • Contrasts can be represented by vectors and sets of orthogonal contrasts are uncorrelated and independently distributed if the data are normal.