| 1. |
- Azmoodeh, Ehsan, et al.
(författare)
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Drift parameter estimation for fractional Ornstein-Uhlenbeck process of the second kind
- 2015
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Ingår i: Statistics (Berlin). - : Informa UK Limited. - 0233-1888 .- 1029-4910. ; 49:1, s. 1-18
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Tidskriftsartikel (refereegranskat)abstract
- The fractional Ornstein-Uhlenbeck process of the second kind (fOU(2)) is the solution of the Langevin equation with driving noise where B is a fractional Brownian motion with Hurst parameter H(0, 1). In this article, in the case H>1/2, we prove that the least-squares estimator introduced in [Hu Y, Nualart D. Parameter estimation for fractional Ornstein-Uhlenbeck processes. Stat. Probab. Lett. 2010;80(11-12):1030-1038], provides a consistent estimator. Moreover, using central limit theorem for multiple Wiener integrals, we prove asymptotic normality of the estimator valid for the whole range H(1/2, 1).
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| 2. |
- Belyaev, Yuri K
(författare)
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Asymptotical properties of nonparametric point estimators based on complexly structured reliability data with right-censoring
- 1991
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Ingår i: Statistics (Berlin). - : Taylor & Francis. - 0233-1888 .- 1029-4910. ; 22:4, s. 589-612
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a general approach to nonparametric estimation of unknown distribution functions and related characteristics such as cumulative hazard functions. It is based on the notion of portions of statistical data and on the property of discertely separated distributions of statistical data General assumptions are given under which the corresponding generalized maximum likelihood estimators are consistent and their deviations have asymptotically normal distributions, if the number of portions increases to indinity.
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| 3. |
- Bertin, Karine, et al.
(författare)
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Least-square estimators in linear regression models under negatively superadditive dependent random observations
- 2021
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Ingår i: Statistics (Berlin). - : Taylor & Francis. - 0233-1888 .- 1029-4910. ; 55:5, s. 1018-1034
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Tidskriftsartikel (refereegranskat)abstract
- In this article, we study the asymptotic behaviour of the least-square estimator in a linear regression model based on random observation instances. We provide mild assumptions on the moments and dependence structure on the randomly spaced observations and the residuals under which the estimator is strongly consistent. In particular, we consider observation instances that are negatively superadditive dependent within each other, while for the residuals we merely assume that they are generated by some continuous function. We complement our findings with a simulation study providing insights on finite sample properties.
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| 4. |
- Bodnar, Olha, senior lecturer, 1979-, et al.
(författare)
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CUSUM control schemes for monitoring the covariance matrix of multivariate time series
- 2016
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Ingår i: Statistics (Berlin). - : Taylor & Francis. - 0233-1888 .- 1029-4910. ; 51:4, s. 722-744
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Tidskriftsartikel (refereegranskat)abstract
- Modified cumulative sum (CUSUM) control charts and CUSUM schemes for residuals are suggested to detect changes in the covariance matrix of multivariate time series. Several properties of these schemes are derived when the in-control process is a stationary Gaussian process. A Monte Carlo study reveals that the proposed approaches show similar or even better performance than the schemes based on the multivariate exponentially weighted moving average (MEWMA) recursion. We illustrate how the control procedures can be applied to monitor the covariance structure of developed stock market indices.
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| 5. |
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| 6. |
- Ekström, Magnus, 1966-
(författare)
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Strong limit theorems for sums of logarithms of high order spacings
- 1999
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Ingår i: Statistics (Berlin). - : Gordon and Breach Publishers. - 0233-1888 .- 1029-4910. ; 33:2, s. 153-169
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Tidskriftsartikel (refereegranskat)abstract
- Several strong limit theorems are proved for sums of logarithms of mth order spacings from general distributions. In all given results, the order mof the spacings is allowed to increase to infinity with the sample size. These results provide a nonparametric strongly consistent estimator of entropy as well as a characterization of the uniform distribution on [0,1]. Furthermore, it is shown that Cressie's (1976) goodness of fit test is strongly consistent against all continuous alternatives.
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| 7. |
- Frisén, Marianne, 1943, et al.
(författare)
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Semiparametric estimation of outbreak regression
- 2010
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Ingår i: Statistics: A Journal of Theoretical and Applied Statistics. - : Informa UK Limited. - 0233-1888. ; 44:2, s. 107-117
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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.
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| 8. |
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| 9. |
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| 10. |
- Karlsson, Sune, Professor, 1960-, et al.
(författare)
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Statistical inference for the tangency portfolio in high dimension
- 2021
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Ingår i: Statistics. - : Taylor & Francis. - 0233-1888 .- 1029-4910. ; 55:3, s. 532-560
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we study the distributional properties of the tangency portfolio (TP) weights assuming a normal distribution of the logarithmic returns. We derive a stochastic representation of the TP weights that fully describes their distribution. Under a high-dimensional asymptotic regime, i.e., the dimension of the portfolio, k, and the sample size, n, approach infinity such that k/n -> c is an element of (0, 1), we deliver the asymptotic distribution of the TP weights. Moreover, weconsider tests about the elements of the TP and derive the asymptotic distribution of the test statistic under the null and alternative hypotheses. In a simulation study, we compare the asymptotic distribution of the TP weights with the exact finite sample density. Wealso compare the high-dimensional asymptotic test with an exact small sample test. We document a good performance of the asymptotic approximations except for small sample sizes combined with c close to one. In an empirical study, we analyse the TP weights in portfolios containing stocks from the S&P 500 index.
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