Library

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • Electronic Resource  (3)
  • 1980-1984  (3)
  • sample estimates  (2)
  • covariance matrices  (1)
Source
Material
  • Electronic Resource  (3)
Years
  • 1980-1984  (3)
Year
Keywords
  • 1
    Electronic Resource
    Electronic Resource
    Rank-reducibility of a symmetric matrix and sampling theory of minimum trace factor analysis (1982)
    Springer
    Psychometrika 47 (1982), S. 187-199 
    Details
    ISSN: 1860-0980
    Keywords: reduced rank ; reliability ; sample estimates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract One of the intriguing questions of factor analysis is the extent to which one can reduce the rank of a symmetric matrix by only changing its diagonal entries. We show in this paper that the set of matrices, which can be reduced to rankr, has positive (Lebesgue) measure if and only ifr is greater or equal to the Ledermann bound. In other words the Ledermann bound is shown to bealmost surely the greatest lower bound to a reduced rank of the sample covariance matrix. Afterwards an asymptotic sampling theory of so-called minimum trace factor analysis (MTFA) is proposed. The theory is based on continuous and differential properties of functions involved in the MTFA. Convex analysis techniques are utilized to obtain conditions for differentiability of these functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02296274
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Weighted minimum trace factor analysis (1982)
    Springer
    Psychometrika 47 (1982), S. 243-264 
    Details
    ISSN: 1860-0980
    Keywords: reliability ; reduced rank ; sample estimates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract In the last decade several authors discussed the so-called minimum trace factor analysis (MTFA), which provides the greatest lower bound (g.l.b.) to reliability. However, the MTFA fails to be scale free. In this paper we propose to solve the scale problem by maximization of the g.l.b. as the function of weights. Closely related to the primal problem of the g.l.b. maximization is the dual problem. We investigate the primal and dual problems utilizing convex analysis techniques. The asymptotic distribution of the maximal g.l.b. is obtained provided the population covariance matrix satisfies sone uniqueness and regularity assumptions. Finally we outline computational algorithms and consider numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02294158
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Minimum rank and minimum trace of covariance matrices (1982)
    Springer
    Psychometrika 47 (1982), S. 443-448 
    Details
    ISSN: 1860-0980
    Keywords: factor analysis ; covariance matrices ; minimum trace ; constrained minimum trace ; minimum rank
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract This paper considers some mathematical aspects of minimum trace factor analysis (MTFA). The uniqueness of an optimal point of MTFA is proved and necessary and sufficient conditions for a point x to be optimal are established. Finally, some results about the connection between MTFA and the classical minimum rank factor analysis will be presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02293708
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...