zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Local mixtures of the exponential distribution. (English) Zbl 1108.62018
Summary: A new class of local mixture models called local scale mixture models is introduced. This class is particularly suitable for the analysis of mixtures of the exponential distribution. The affine structure revealed by specific asymptotic expansions is the motivation for the construction of these models. They are shown to have very nice statistical properties which are exploited to make inferences in a straightforward way. The effect on inference of a new type of boundaries, called soft boundaries, is analyzed. A simple simulation study shows the applicability of this type of models.

62F10Point estimation
62F99Parametric inference
62E20Asymptotic distribution theory in statistics
62A01Foundations and philosophical topics in statistics
Full Text: DOI
[1] Amari, S., Nagaoka, H. (2000). Methods of information geometry. American Mathematical Society · Zbl 0960.62005
[2] Anaya-Izquierdo, K.A. (2006). Statistical and geometrical analysis of local mxiture models and a proposal of some new tests of fit for censored data. PhD Thesis. Universidad Nacional Autónoma de México.
[3] Anaya-Izquierdo, K.A., Marriott, P.K. (2006). Local mixture models of exponential families (Submitted). · Zbl 1129.62005
[4] Chang H.-Y., Suchindran C.M. (1997). Testing overdispersion in data with censoring using the mixture of exponential families. Communications in Statistics: Theory and Methods 26, 2945--2966 · Zbl 0955.62544
[5] Critchley F., Marriott P. (2004). Data-informed influence analysis. Biometrika 91, 125--140 · Zbl 1132.62309 · doi:10.1093/biomet/91.1.125
[6] Darling D.A. (1953). On a class of problems related to the random division of an interval. Annals of Mathematical Statistics 24, 239--253 · Zbl 0053.09902 · doi:10.1214/aoms/1177729030
[7] Embrechts P., Kluppelberg C., Mikosch T. (1997). Modelling extremal events: For insurance and finance. Berlin Heidelberg New York, Springer. · Zbl 0873.62116
[8] Feller W. (1970). An Introduction to Probability Theory and it Applications. London, Wiley.
[9] Heckman J.J., Robb R., Walker J.R. (1990). Testing the mixture of exponentials hypothesis and estimating the mixing distribution by the method of moments. Journal of the American Statistical Association 85, 582--589 · Zbl 0702.62040 · doi:10.2307/2289802
[10] Jaggia S. (1997). Alternative forms of the score test for heterogeneity in a censored exponential model. The Review of Economics and Statistics 79(2): 340--343 · doi:10.1162/003465397556728
[11] Janson S. (1988). Normal convergence by higher order semiinvariants with applications to sums of dependent random variables and random graphs. Annals of Applied Probability 16(1): 305--312 · Zbl 0639.60029
[12] Jewell N.P. (1982). Mixtures of exponential distributions. The Annals of Statistics 10, 479--484 · Zbl 0495.62042 · doi:10.1214/aos/1176345789
[13] Johnson N.L., Rogers C.A. (1951). The moment problem for unimodal distributions. Annals of Mathematical Statistics 22: 432--439 · Zbl 0044.32303
[14] Jorgensen B. (1997). The theory of dispersion models. London, Chapman & Hall.
[15] Keilson J., Steutel F.W. (1974). Mixtures of distributions, moment inequalities and measures of exponentiality and normality. The Annals of Probability 2, 112--130 · Zbl 0325.60019 · doi:10.1214/aop/1176996756
[16] Kiefer N.M. (1984). A simple test for heterogeneity in exponential models of duration. Journal of Labor Economics, 3--4, 539--549
[17] Klaassen C.A.J., Mokveld P.J., van Es B. (2000). Squared skewness minus kurtosis bounded by 186/125 for unimodal distributions. Statistics & Probability Letters 50, 131--135 · Zbl 0966.60006 · doi:10.1016/S0167-7152(00)00090-0
[18] Lindsay, Bruce G. (1989). Moment matrices: applications in mixtures. The Annals of Statistics 17(2): 722--740 · Zbl 0672.62063 · doi:10.1214/aos/1176347138
[19] Lindsay, B.G. (1995). Mixture models: theory, geometry, and applications. Institute of Mathematical Statistics. · Zbl 1163.62326
[20] Marriott P. (2002). On the local geometry of mixture models. Biometrika 89(1): 77--93 · Zbl 0998.62002 · doi:10.1093/biomet/89.1.77
[21] Marriott P. (2003). On the geometry of measurement error models. Biometrika 90(3): 567--576 · doi:10.1093/biomet/90.3.567
[22] McLachlan G.J., Peel D. (2001). Finite mixture models. London, Wiley. · Zbl 0963.62061
[23] Mosler K., Seidel W. (2001). Testing for Homogeneity in an Exponential Mixture Model. Australian & New Zealand Journal of Statistics 43(2): 231--247 · Zbl 0992.62095 · doi:10.1111/1467-842X.00168
[24] O’Reilly F., Stephens M.A. (1982). Characterizations and goodness-of-fit tests. Journal of the Royal Statistical Society, Series B 44, 353--360 · Zbl 0541.62011
[25] Shaked M. (2003). On mixtures from exponential families. Journal of the Royal Statistical Society, Series B 42: 192--198 · Zbl 0443.62009
[26] Ulrich G., Watson L.T. (1994). Positivity conditions for quartic polynomials. SIAM Journal on Scientific Computing 15(3): 528--544 · Zbl 0805.65012 · doi:10.1137/0915035
[27] Wong R. (2001). Asymptotic approximations of integrals (Classics in applied mathematics). Philadelphia, SIAM.