| 1. |
- Frisén, Marianne, 1943, et al.
(författare)
-
Semiparametric estimation of outbreak regression
- 2010
-
Ingår i: Statistics: A Journal of Theoretical and Applied Statistics. - : Informa UK Limited. - 0233-1888. ; 44:2, s. 107-117
-
Tidskriftsartikel (refereegranskat)abstract
- A regression may be constant for small values of the independent variable (for example time), but then a monotonic increase starts. Such an ‘outbreak’ regression is of interest for example in the study of the outbreak of an epidemic disease. We give the least square estimators for this outbreak regression without assumption of a parametric regression function. It is shown that the least squares estimators are also the maximum likelihood estimators for distributions in the regular exponential family such as the Gaussian or Poisson distribution. The approach is thus semiparametric. The method is applied to Swedish data on influenza, and the properties are demonstrated by a simulation study. The consistency of the estimator is proved.
|
|
| 2. |
- Kuljus, Kristi, et al.
(författare)
-
Asymptotic linearity of a linear rank statistic in the case of symmetric nonidentically distributed variables
- 2013
-
Ingår i: Statistics (Berlin). - : Informa UK Limited. - 0233-1888 .- 1029-4910. ; 47:1, s. 156-171
-
Tidskriftsartikel (refereegranskat)abstract
- Let Y 1, ...., Y n be independent but not identically distributed random variables with densities f 1, ...., f n symmetric around zero. Suppose c 1, n , ...., c n, n are given constants such that ? i c i, n =0 and . Denote the rank of Y i -? c i, n for any ??R by R(Y i -? c i, n ) and let a n (i) be a score defined via a score function ?. We study the linear rank statistic and prove that S n (?) is asymptotically uniformly linear in the parameter ? in any interval [-C, C], C>0.
|
|
| 3. |
- Kuljus, Kristi, et al.
(författare)
-
Asymptotic properties of a rank estimate in linear regression with symmetric non-identically distributed errors
- 2013
-
Ingår i: Statistics (Berlin). - : Informa UK Limited. - 0233-1888 .- 1029-4910. ; 47:6, s. 1160-1183
-
Tidskriftsartikel (refereegranskat)abstract
- In this article, a simple linear regression model with independent and symmetric but non-identically distributed errors is considered. Asymptotic properties of the rank regression estimate defined in Jaeckel [Estimating regression coefficients by minimizing the dispersion of the residuals, Ann. Math. Statist. 43 (1972), pp. 1449-1458] are studied. We show that the studied estimator is consistent and asymptotically normally distributed. The cases of bounded and unbounded score functions are examined separately. The regularity conditions of the article are exemplified for finite mixture distributions.
|
|
| 4. |
- Von Rosen, Dietrich
(författare)
-
Non-negative estimation of variance components in heteroscedastic one-way random-effects ANOVA models
- 2010
-
Ingår i: Statistics. - : Informa UK Limited. - 0233-1888 .- 1029-4910. ; 44, s. 557-569
-
Tidskriftsartikel (refereegranskat)abstract
- There is a considerable amount of literature dealing with inference about the parameters in a heteroscedastic one-way random-effects ANOVA model. In this paper, we primarily address the problem of improved quadratic estimation of the random-effect variance component. It turns out that such estimators with a smaller mean squared error compared with some standard unbiased quadratic estimators exist under quite general conditions. Improved estimators of the error variance components are also established.
|
|
