| 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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| 11. |
- Kuljus, Kristi, et al.
(författare)
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Asymptotic linearity of a linear rank statistic in the case of symmetric nonidentically distributed variables
- 2013
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Ingår i: Statistics (Berlin). - : Informa UK Limited. - 0233-1888 .- 1029-4910. ; 47:1, s. 156-171
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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.
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| 12. |
- Kuljus, Kristi, et al.
(författare)
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Asymptotic properties of a rank estimate in linear regression with symmetric non-identically distributed errors
- 2013
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Ingår i: Statistics (Berlin). - : Informa UK Limited. - 0233-1888 .- 1029-4910. ; 47:6, s. 1160-1183
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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.
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| 13. |
- Larsson, Rolf, 1962-, et al.
(författare)
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Likelihood Ratio Tests for a Unit Root in Panels with Random Effects
- 2017
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Ingår i: Statistics (Berlin). - : Informa UK Limited. - 0233-1888 .- 1029-4910. ; 51:3, s. 627-654
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Tidskriftsartikel (refereegranskat)abstract
- Because of the fixed heterogeneity of their models, most panel unit root tests impose restrictions on the rate at which the number of time periods, T, and the number of rosssection units, N, go to infinity. A common example of such a restriction is N/T → 0, which in practice means that T >> N, a condition that is not always met. In the current paper the heterogeneity is given a parsimonious random effects specification, which is used as a basis for developing a new likelihood ratio test for a unit root. The asymptotic analysis shows that the new test is valid for all (N, T) expansion paths satisfying N/T5 → 0, which represents a substantial improvement when compared to the existing fixed effects literature.
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| 14. |
- Pavlenko, Tatjana, et al.
(författare)
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Effect of dimensionality on discrimination
- 2001
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Ingår i: Statistics. - : Informa UK Limited. - 0233-1888 .- 1029-4910. ; 35:3, s. 191-213
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Tidskriftsartikel (refereegranskat)abstract
- Discrimination problems in a high-dimensional setting are considered. New results are concerned with the role of dimensionality in the performance of the discrimination procedure. Assuming that data consist of a block structurc two different asymptotic approaches are presented. These approaches are characterized by different types of relations between the dimensionality and the size of the training samples.par Asymptotic expressions for the error probabilities are obtained and a consistent approximation of the discriminant function is proposed. Throughout the paper the importance of the dimensionality in the asymptotic analysis is stressed.
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| 15. |
- Pingel, Ronnie, et al.
(författare)
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Effects of correlated covariates on the asymptotic efficiency of matching and inverse probability weighting estimators for causal inference
- 2015
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Ingår i: Statistics (Berlin). - : Informa UK Limited. - 0233-1888 .- 1029-4910. ; 49:4, s. 795-814
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Tidskriftsartikel (refereegranskat)abstract
- In observational studies, the overall aim when fitting a model for the propensity score is to reduce bias for an estimator of the causal effect. To make the assumption of an unconfounded treatment plausible researchers might include many, possibly correlated, covariates in the propensity score model. In this paper, we study how the asymptotic efficiency of matching and inverse probability weighting estimators for average causal effects change when the covariates are correlated. We investigate the case with multivariate normal covariates, a logistic model for the propensity score and linear models for the potential outcomes and show results under different model assumptions. We show that the correlation can both increase and decrease the large sample variances of the estimators, and that the correlation affects the asymptotic efficiency of the estimators differently, both with regard to direction and magnitude. Moreover, the strength of the confounding towards the outcome and the treatment plays an important role.
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| 16. |
- Velilla, Santiago, et al.
(författare)
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A new diagnostic tool for VARMA(p,q) models
- 2019
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Ingår i: Statistics (Berlin). - : Informa UK Limited. - 0233-1888 .- 1029-4910. ; 53:4, s. 866-884
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Tidskriftsartikel (refereegranskat)abstract
- A new diagnostic method for VARMA(p,q) time series models is introduced. The procedure is based on a statistic that generalizes to a multivariate setting the properties of the usual univariate ARMA(p,q) residual correlations. A multiple version of the cumulative periodogram statistic is also suggested. Simulation studies and one real data application are presented.
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| 17. |
- Von Rosen, Dietrich
(författare)
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Non-negative estimation of variance components in heteroscedastic one-way random-effects ANOVA models
- 2010
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Ingår i: Statistics. - : Informa UK Limited. - 0233-1888 .- 1029-4910. ; 44, s. 557-569
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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.
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| 18. |
- Vännman, Kerstin
(författare)
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Families of capability indices for one-sided specification limits
- 1998
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Ingår i: Statistics (Berlin). - : Informa UK Limited. - 0233-1888 .- 1029-4910. ; 31:1, s. 43-66
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Tidskriftsartikel (refereegranskat)abstract
- We study, when the specification interval is one-sided, two new classes of indices, which are based on the classes of indices for asymmetric tolerances earlier defined by us in Commun. Stat., Theory Methods 26, 2049-2072 (1997). These classes generalize indices for one-sided specification limits earlier suggested in the literature. By varying the parameters of the classes various indices with suitable properties can be obtained. Under the assumption of normality, explicit forms of the distributions of the two new classes of the estimated indices are provided. Numerical investigations are made to explore the behavior of the estimators of the indices for different values of the parameters. Based on the estimators a decision rule that can be used to determine whether the process can be considered capable or not is provided and suitable criteria for choosing an index from the families are suggested.
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| 19. |
- Xie, Yingfu
(författare)
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Consistency of maximum likelihood estimators for the regime-switching GARCH model
- 2009
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Ingår i: Statistics. - : Informa UK Limited. - 0233-1888 .- 1029-4910. ; 43, s. 153-165
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Tidskriftsartikel (refereegranskat)abstract
- The regime-switching GARCH (generalized autoregressive conditionally heteroscedastic) model incorporates the idea of Markov switching into the more restrictive GARCH model, which significantly extends the GARCH model. However, the statistical inference for such an extended model is rather difficult because observations at any time point then depend on the whole regime path and the likelihood becomes intractable quickly as the length of observations increases. In this paper, by transforming it into an infinite order ARCH model, we obtain the possibility of writing a likelihood which can be handled directly and the consistency of the maximum likelihood estimators is proved. Simulation studies to illustrate the consistency and asymptotic normality of the estimators (for both Gaussian and non-Gaussian innovations) and a model specification problem are presented.
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