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searching for Quadratic form (statistics) 47 found (60 total)

alternate case: quadratic form (statistics)

Generalized chi-squared distribution (2,076 words) [view diff] no match in snippet view article find links to article

parameters of the second expression (quadratic form of a normal vector). The parameters of the second expression (quadratic form of a normal vector) can also

Degenerate bilinear form (850 words) [view diff] no match in snippet view article find links to article

chosen basis. If for a quadratic form Q there is a non-zero vector v ∈ V such that Q(v) = 0, then Q is an isotropic quadratic form. If Q has the same sign

Clifford algebra (9,191 words) [view diff] no match in snippet view article find links to article

a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure of

Null (mathematics) (361 words) [view diff] no match in snippet view article

vector mapped to some null by a function under consideration (such as a quadratic form coming with the vector space, see null vector, a linear mapping given

Thomas Lumley (statistician) (465 words) [view diff] no match in snippet view article

methods approximating the distribution of a large quadratic form in normal variables". Computational Statistics & Data Analysis. 139: 75–81. doi:10.1016/j.csda

Principal axis theorem (1,495 words) [view diff] no match in snippet view article find links to article

technique of diagonalization can be applied. The trick is to write the quadratic form as 5 x 2 + 8 x y + 5 y 2 = [ x y ] [ 5 4 4 5 ] [ x y ] = x T A x {\displaystyle

Loss function (2,800 words) [view diff] no match in snippet view article find links to article

desired values of all target variables. Often loss is expressed as a quadratic form in the deviations of the variables of interest from their desired values;

Symmetrization (768 words) [view diff] no match in snippet view article find links to article

skew-symmetric form, and there is no difference between a symmetric form and a quadratic form. At 2, not every form can be decomposed into a symmetric form and a

V-statistic (1,401 words) [view diff] no match in snippet view article find links to article

functional T. In this case the asymptotic distribution is called a quadratic form of centered Gaussian random variables. The statistic V2,n is called

Energy distance (2,370 words) [view diff] no match in snippet view article find links to article

{\displaystyle T={\frac {nm}{n+m}}E_{n,m}(X,Y)} converges in distribution to a quadratic form of independent standard normal random variables. Under the alternative

Square (algebra) (1,990 words) [view diff] no match in snippet view article

the inner product. The inertia tensor in mechanics is an example of a quadratic form. It demonstrates a quadratic relation of the moment of inertia to the

Wald test (2,232 words) [view diff] no match in snippet view article find links to article

}}_{n}-r)\,\xrightarrow {\mathcal {D}} \,N(0,RVR')} Recalling that a quadratic form of normal distribution has a Chi-squared distribution: n ( R θ ^ n −

Divergence (statistics) (2,629 words) [view diff] no match in snippet view article

positive-definite quadratic form for infinitesimal displacements d p {\displaystyle dp} from p {\displaystyle p} . In applications to statistics, the manifold

Chi-squared distribution (6,817 words) [view diff] no match in snippet view article find links to article

symmetric, idempotent matrix with rank k − n {\displaystyle k-n} , then the quadratic form Y T A Y {\displaystyle Y^{T}AY} is chi-square distributed with k − n

Carus Mathematical Monographs (734 words) [view diff] no match in snippet view article find links to article

Sherman K. Stein and Sándor Szabó - ISBN 9780883850282 The Sensual (Quadratic) Form, by John H. Conway assisted by Francis Y. C. Fung, 1997, ISBN 978-0-88385-030-5

Norm (mathematics) (5,937 words) [view diff] no match in snippet view article

those cases the norm is a definite quadratic form. In the split algebras the norm is an isotropic quadratic form. For any norm p : X → R {\displaystyle

Null distribution (836 words) [view diff] no match in snippet view article find links to article

use t statistics which have Gaussian null distribution, while F statistics, testing k groups of population means, which have Gaussian quadratic form the

Ellipsoid (5,912 words) [view diff] no match in snippet view article find links to article

that has a homogeneous part of degree two which is a positive definite quadratic form. One can also define a hyperellipsoid as the image of a sphere under

Definite matrix (8,687 words) [view diff] no match in snippet view article find links to article

positive-definite if and only if it is the matrix of a positive-definite quadratic form or Hermitian form. In other words, a matrix is positive-definite if

Matrix (mathematics) (13,737 words) [view diff] no match in snippet view article

symmetric real matrix A is called positive-definite if the associated quadratic form f ( x ) = x T A x {\displaystyle f({\mathbf {x}})={\mathbf {x}}^{\rm

Multivariate normal distribution (9,594 words) [view diff] no match in snippet view article find links to article

that σ i i = σ i 2 {\displaystyle \sigma _{ii}=\sigma _{i}^{2}} . A quadratic form of a normal vector x {\displaystyle {\boldsymbol {x}}} , q ( x ) = x

MINQUE (2,981 words) [view diff] no match in snippet view article find links to article

{\displaystyle \theta =\sum _{i=1}^{k}p_{i}\sigma _{i}^{2}} using a quadratic form θ ^ = Y ⊤ A Y {\displaystyle {\hat {\theta }}=\mathbf {Y} ^{\top }\mathbf

Degrees of freedom (statistics) (4,530 words) [view diff] no match in snippet view article

definitions can include the trace of the hat matrix, tr(H), the trace of the quadratic form of the hat matrix, tr(H'H), the form tr(2H – H H'), or the Satterthwaite

Diehard tests (2,923 words) [view diff] no match in snippet view article find links to article

counts are made of the number of occurrences of each state. Then the quadratic form in the weak inverse of the 120×120 covariance matrix yields a test equivalent

Block design (5,604 words) [view diff] no match in snippet view article find links to article

elliptic quadric, the set of zeros of the quadratic form x1x2 + f(x3, x4), where f is an irreducible quadratic form in two variables over GF(q). [f(x,y) =

Normal distribution (22,625 words) [view diff] no match in snippet view article find links to article

ft(Y_{1}^{2}+Y_{2}^{2}+\cdots +Y_{m}^{2}\right)/m}}\sim F_{n,m}.} A quadratic form of a normal vector, i.e. a quadratic function q = ∑ x i 2 + ∑ x j +

Geodesic (4,256 words) [view diff] no match in snippet view article find links to article

metric – Concept in geometry/topology Isotropic line – Line along which a quadratic form applied to any two points' displacement is zero Jacobi field Morse theory –

Gaussian function (5,023 words) [view diff] no match in snippet view article find links to article

which e is raised in the Gaussian function is any negative-definite quadratic form. Consequently, the level sets of the Gaussian will always be ellipses

Vector generalized linear model (4,746 words) [view diff] no match in snippet view article find links to article

these is taken as the latent variable) and the quadratic is for the quadratic form in the latent variables ν {\displaystyle {\boldsymbol {\nu }}} on the

Sum-of-squares optimization (2,695 words) [view diff] no match in snippet view article find links to article

added to make X {\displaystyle X} respect the symmetries present in the quadratic form x ≤ d ( x ≤ d ) ⊤ {\displaystyle x^{\leq d}(x^{\leq d})^{\top }} . One

Kullback–Leibler divergence (13,054 words) [view diff] no match in snippet view article find links to article

Hellinger distance, histogram intersection, Chi-squared statistic, quadratic form distance, match distance, Kolmogorov–Smirnov distance, and earth mover's

Bures metric (2,475 words) [view diff] no match in snippet view article find links to article

developed for that purpose. For 2x2 and 3x3 systems, respectively, the quadratic form of the Bures metric is calculated as [ D B ( ρ , ρ + d ρ ) ] 2 = 1 4

Feynman diagram (15,967 words) [view diff] no match in snippet view article find links to article

motion are linear, the propagator will always be the reciprocal of the quadratic-form matrix that defines the free Lagrangian, since this gives the equations

Expected utility hypothesis (5,562 words) [view diff] no match in snippet view article find links to article

distributed, or in the unlikely case in which the utility function has a quadratic form—however, David E. Bell proposed a measure of risk that follows naturally

Bregman divergence (4,475 words) [view diff] no match in snippet view article find links to article

D_{F}(x,y)={\tfrac {1}{2}}(x-y)^{T}Q(x-y)} is generated by the convex quadratic form F ( x ) = 1 2 x T Q x {\displaystyle F(x)={\tfrac {1}{2}}x^{T}Qx} .

Batch normalization (5,891 words) [view diff] no match in snippet view article find links to article

also significant, since the variance is often large. Secondly, the quadratic form of the loss Hessian with respect to activation in the gradient direction

Inner product space (7,357 words) [view diff] no match in snippet view article find links to article

correctly called a scalar product in this context, as the nondegenerate quadratic form in question need not be positive definite (need not be an inner product)

Real coordinate space (4,248 words) [view diff] no match in snippet view article find links to article

but it is not the only possible one. Actually, any positive-definite quadratic form q defines its own "distance" √q(x − y), but it is not very different

Algebra (14,097 words) [view diff] no match in snippet view article find links to article

vector space Clifford algebra – Algebra based on a vector space with a quadratic form Commutative algebra – Branch of algebra that studies commutative rings

Srinivasa Ramanujan (11,700 words) [view diff] no match in snippet view article find links to article

graph Ramanujan summation Ramanujan's constant Ramanujan's ternary quadratic form Rank of a partition /ˈsriːnɪvɑːsə rɑːˈmɑːnʊdʒən/ SREE-nih-vah-sə rah-MAH-nuuj-ən;

Ising model (20,177 words) [view diff] no match in snippet view article find links to article

{\displaystyle Z_{ij}\,\partial _{i}H\,\partial _{j}H} is a positive definite quadratic form, and can be used to define the metric for space. So any translationally

Eigenvalues and eigenvectors (13,619 words) [view diff] no match in snippet view article find links to article

largest eigenvalue of H {\displaystyle H} is the maximum value of the quadratic form x T H x / x T x {\displaystyle \mathbf {x} ^{\textsf {T}}H\mathbf {x}

Sub-Gaussian distribution (7,008 words) [view diff] no match in snippet view article find links to article

vector X {\displaystyle X} is subgaussian in a certain sense, then any quadratic form A {\displaystyle A} of this vector, X T A X {\displaystyle X^{T}AX}

Exterior algebra (12,116 words) [view diff] no match in snippet view article find links to article

Clifford algebra, a generalization of exterior algebra to a nonzero quadratic form Geometric algebra Koszul complex Multilinear algebra Symmetric algebra

Christiaan Huygens (14,153 words) [view diff] no match in snippet view article find links to article

stated what is now known as the second of Newton's laws of motion in quadratic form. He derived geometrically the now standard formula for the centrifugal

Symmetry of second derivatives (5,372 words) [view diff] no match in snippet view article find links to article

the local behavior of the function at (0, 0) cannot be described as a quadratic form, and the Hessian matrix thus fails to be symmetric. In general, the

Experimental uncertainty analysis (15,097 words) [view diff] no match in snippet view article find links to article

propagation of error approximation then can be written concisely as the quadratic form σ z 2 ≈ γ T C γ E q ( 15 ) {\displaystyle \sigma _{z}^{2}\,\,\approx