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  • 1.
    Abramowicz, Konrad
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Seleznjev, Oleg
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Spline approximation of a random process with singularity2011In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 141, no 3, p. 1333-1342Article in journal (Refereed)
    Abstract [en]

    Let a continuous random process X defined on [0,1] be (m+β)-smooth, 0m, 0<β1, in quadratic mean for all t>0 and have an isolated singularity point at t=0. In addition, let X be locally like a m-fold integrated β-fractional Brownian motion for all nonsingular points. We consider approximation of X by piecewise Hermite interpolation splines with n free knots (i.e., a sampling design, a mesh). The approximation performance is measured by mean errors (e.g., integrated or maximal quadratic mean errors). We construct a sequence of sampling designs with asymptotic approximation rate n^(m+β) for the whole interval.

  • 2.
    Bondesson, Lennart
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    On univariate and bivariate generalized gamma convolutions2009In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 139, no 11, p. 3759-3765Article in journal (Refereed)
    Abstract [en]

    This paper has two parts. In the first part some results for generalized gamma convolutions (GGCs) are reviewed. A GGC is a limit distribution for sums of independent gamma variables. In the second part, bivariate gamma distributions and bivariate GGCs are considered. New bivariate gamma distributions are derived from shot-noise models. The remarkable property hyperbolic complete monotonicity (HCM) for a function is considered both in the univariate case and in the bivariate case.

  • 3.
    de Luna, Xavier
    et al.
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Johansson, Per
    Department of Economics, Uppsala University and Institute of Labour Market Policy Evaluation, Uppsala.
    Erratum to "Non-parametric inference for the effect of a treatment on survival times with application in the health and social sciences" [Journal of Statistical Planning and Inference 140 (7) (July) (2010) 2122–2137]2012In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 142, no 6, p. 1624-1625Article in journal (Refereed)
  • 4.
    de Luna, Xavier
    et al.
    Umeå University, Faculty of Social Sciences, Department of Statistics.
    Johansson, Per
    Uppsala University and IFAU, Uppsala.
    Non-parametric inference for the effect of a treatment on survival times with application in the health and social sciences2010In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 140, no 7, p. 2122-2137Article in journal (Refereed)
    Abstract [en]

    In this paper we perform inference on the effect of a treatment on survival times in studies where the treatment assignment is not randomized and the assignment time is not known in advance. Two such studies are discussed: a heart transplant program and a study of Swedish unemployed eligible for employment subsidy. We estimate survival functions on a treated and a control group which are made comparable through matching on observed covariates. The inference is performed by conditioning on waiting time to treatment, that is, time between the entrance in the study and treatment. This can be done only when sufficient data are available. In other cases, averaging over waiting times is a possibility, although the classical interpretation of the estimated survival functions is lost unless hazards are not functions of waiting time. To show unbiasedness and to obtain an estimator of the variance, we build on the potential outcome framework, which was introduced by J. Neyman in the context of randomized experiments, and adapted to observational studies by D.B. Rubin. Our approach does not make parametric or distributional assumptions. In particular, we do not assume proportionality of the hazards compared. Small sample performance of the estimator and a derived test of no treatment effect are studied in a Monte Carlo study.

  • 5.
    Ekström, Magnus
    Centre of Biostochastics, Swedish University of Agricultural Sciences, S-901 83 Umeå, Sweden.
    Alternatives to maximum likelihood estimation based on spacings and the Kullback-Leibler divergence2008In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 138, no 6, p. 1778-1791Article in journal (Refereed)
    Abstract [en]

    An alternative to the maximum likelihood (ML) method, the maximum spacing (MSP) method, is introduced in Cheng and Amin [1983. Estimating parameters in continuous univariate distributions with a shifted origin. J. Roy. Statist. Soc. Ser. B 45, 394–403], and independently in Ranneby [1984. The maximum spacing method. An estimation method related to the maximum likelihood method. Scand. J. Statist. 11, 93–112]. The method, as described by Ranneby [1984. The maximum spacing method. An estimation method related to the maximum likelihood method. Scand. J. Statist. 11, 93–112], is derived from an approximation of the Kullback–Leibler divergence. Since the introduction of the MSP method, several closely related methods have been suggested. This article is a survey of such methods based on spacings and the Kullback–Leibler divergence. These estimation methods possess good properties and they work in situations where the ML method does not. Important issues such as the handling of ties and incomplete data are discussed, and it is argued that by using Moran's [1951. The random division of an interval—Part II. J. Roy. Statist. Soc. Ser. B 13, 147–150] statistic, on which the MSP method is based, we can effectively combine: (a) a test on whether an assigned model of distribution functions is correct or not, (b) an asymptotically efficient estimation of an unknown parameter θ0θ0, and (c) a computation of a confidence region for θ0.

  • 6.
    Ekström, Magnus
    Umeå University, Faculty of Science and Technology, Mathematical statistics.
    On the consistency of the maximum spacing method1998In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 70, no 2, p. 209-224Article in journal (Refereed)
    Abstract [en]

    The main result of this paper is a consistency theorem for the maximum spacing method, a general method of estimating parameters in continuous univariate distributions, introduced by Cheng and Amin (J. Roy. Statist. Soc. Ser. A45 (1983) 394–403) and independently by Ranneby (Scand. J. Statist.11 (1984) 93–112). This main result generalizes a theorem of Ranneby (Scand. J. Statist.11 (1984) 93–112). Also, some examples are given, which shows that this estimation method works also in cases where the maximum likelihood method breaks down.

  • 7.
    Ekström, Magnus
    Centre of Biostochastics, Swedish University of Agricultural Sciences, Umeå.
    Sum-functions of spacings of increasing order2006In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 136, no 8, p. 2535-2546Article in journal (Refereed)
    Abstract [en]

    We discuss a class of statistics based on spacings of increasing order and show that these statistics are almost surely consistent. Special attention is devoted to estimation of φφ-divergences and to tests for uniformity on the unit interval. It is shown that tests for uniformity, based on sum-functions of spacings, are strongly consistent against all absolutely continuous alternatives having support [0,1].

  • 8.
    Ekström, Magnus
    et al.
    Centre of Biostochastics, Swedish University of Agricultural Sciences, Umeå.
    Jammalamadaka, S. R.
    UCSB, Santa Barbara, USA.
    Addendum to “An asymptotically distribution-free test of symmetry” [Journal of Statistical Planning and Inference 137 (2007) 799–810]2009In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 139, no 4, p. 1569-1571Article in journal (Refereed)
  • 9.
    Ekström, Magnus
    et al.
    Centre of Biostochastics, Swedish University of Agricultural Sciences, Umeå, Sweden.
    Jammalamadaka, S. Rao
    UCSB, USA.
    An asymptotically distribution-free test of symmetry2007In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 137, no 3, p. 799-810Article in journal (Refereed)
    Abstract [en]

    A procedure, based on sample spacings, is proposed for testing whether a univariate distribution is symmetric about some unknown value. The proposed test is a modification of a sign test suggested by Antille and Kersting [1977. Tests for symmetry. Z. Wahrscheinlichkeitstheorie verw. Gebiete 39, 235-255], but unlike Antille and Kersting's test, our modified test is asymptotically distribution-free and is usable in practice. A simulation study indicates that the proposed test maintains the nominal level of significance, alpha fairly accurately even for samples of size as small as 20, and a comparison with the classical test based on sample coefficient of skewness, shows that our test has good power for detecting different asymmetric distributions.

  • 10.
    Grafström, Anton
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Non-rejective implementations of the Sampford sampling design2009In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 139, p. 2111-2114Article in journal (Refereed)
    Abstract [en]

    Sampford sampling is a method for unequal probability sampling. There exist several implementations of the Sampford sampling design which all are rejective methods, i.e. the sample is not always accepted. Thus the existing methods can be time consuming or even infeasible in some situations. In this paper, a fast and non-rejective list-sequential method, which works in all situations, is presented. The method is a modification of a previously existing rejective list-sequential method. Another list-sequential implementation of Sampford sampling is also presented.

  • 11.
    Grafström, Anton
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    On a generalization of Poisson sampling2010In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 140, no 4, p. 982-991Article in journal (Other academic)
    Abstract [en]

    In real-time sampling, the units of a population pass a sampler one by one. Alternatively the sampler may successively visit the units of the population. Each unit passes only once and at that time it is decided whether or not it should be included in the sample. The goal is to take a sample and efficiently estimate a population parameter. The list sequential sampling method presented here is called correlated Poisson sampling. The method is an alternative to Poisson sampling, where the units are sampled independently with given inclusion probabilities. Correlated Poisson sampling uses weights to create correlations between the inclusion indicators. In that way it is possible to reduce the variation of the sample size and to make the samples more evenly spread over the population. Simulation shows that correlated Poisson sampling improves the efficiency in many cases.

  • 12.
    Svensson, Ingrid
    et al.
    Umeå University, Faculty of Social Sciences, Department of Statistics.
    Sjöstedt-de Luna, Sara
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Asymptotic properties of a stochastic EM algorithm for mixtures with censored data2010In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 140, no 1, p. 111-127Article in journal (Refereed)
    Abstract [en]

    Weak consistency and asymptotic normality is shown for a stochastic EM algorithm for censored data from a mixture of distributions under lognormal assumptions. The asymptotic properties hold for all parameters of the distributions, including the mixing parameter. In order to make parameter estimation meaningful it is necessary to know that the censored mixture distribution is identifiable. General conditions under which this is the case are given. The stochastic EM algorithm addressed in this paper is used for estimation of wood fibre length distributions based on optically measured data from cylindric wood samples (increment cores).

  • 13. Traat, Imbi
    et al.
    Bondesson, Lennart
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Meister, Kadri
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Sampling design and sample selection through distribution theory2004In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 123, no 2, p. 395-413Article in journal (Refereed)
    Abstract [en]

    This paper may be seen as in part a review covering basics of sampling theory in a different light. We use a multivariate approach with a unifying treatment of WOR and WR sampling designs. In this framework, we present probability functions of several important sampling designs, such as the hypergeometric, the conditional Poisson, the Sampford, and the general order sampling designs among others. Benefiting from the distributional feature of the sampling design, a list-sequential method for generating a sample from any given design is developed. The method is applied to hypergeometric, multinomial, conditional Poisson and Sampford designs. An order sampling procedure for a population with unknown size is described. Markov chain Monte Carlo methods are discussed.

  • 14.
    Waernbaum, Ingeborg
    Umeå University, Faculty of Social Sciences, Department of Statistics.
    Propensity score model specification for estimation of average treatment effects2010In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 140, no 7, p. 1948-1956Article in journal (Refereed)
    Abstract [en]

    Treatment effect estimators that utilize the propensity score as a balancing score, e.g., matching and blocking estimators are robust to misspecifications of the propensity score model when the misspecification is a balancing score. Such misspecifications arise from using the balancing property of the propensity score in the specification procedure. Here, we study misspecifications of a parametric propensity score model written as a linear predictor in a strictly monotonic function, e.g. a generalized linear model representation. Under mild assumptions we show that for misspecifications, such as not adding enough higher order terms or choosing the wrong link function, the true propensity score is a function of the misspecified model. Hence, the latter does not bring bias to the treatment effect estimator. It is also shown that a misspecification of the propensity score does not necessarily lead to less efficient estimation of the treatment effect. The results of the paper are highlighted in simulations where different misspecifications are studied.

  • 15.
    Zhou, Zhiyong
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Lin, Zhengyan
    School of Mathematical Sciences, Zhejiang University.
    Varying coefficient partially nonlinear models with nonstationary regressors2018In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 194, p. 47-64Article in journal (Refereed)
    Abstract [en]

    We study a varying coefficient partially nonlinear model in which the regressors are generated by the multivariate unit root processes. A profile nonlinear least squares estimation procedure is applied to estimate the parameter vector and the functional coefficients. Under some mild conditions, the asymptotic distribution theory for the resulting estimators is established. The rate of convergence for the parameter vector estimator depends on the properties of the nonlinear regression function. However, the rate of convergence for the functional coefficients estimator is the same and enjoys the super-consistency property. Furthermore, a simulation study is conducted to investigate the finite sample performance of the proposed estimating procedures.

1 - 15 of 15
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