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  • State Occupation Probabilities in Non-Markov Models
    Math. Meth. Stat. Pub Date : 2020-01-24
    M. Overgaard

    The consistency of the Aalen—Johansen-derived estimator of state occupation probabilities in non-Markov multi-state settings is studied and established via a new route. This new route is based on interval functions and relies on a close connection between additive and multiplicative transforms of interval functions, which is established. Under certain assumptions, the consistency follows from explicit

    更新日期:2020-01-24
  • Admissibility of Invariant Tests for Means with Covariates
    Math. Meth. Stat. Pub Date : 2020-01-24
    Ming-Tien Tsai

    For a multinormal distribution with a p-dimensional mean vector θ and an arbitrary unknown dispersion matrix Σ, Rao ([8], [9]) proposed two tests for the problem of testing H0: θ1 = 0, θ2 = 0, Σ unspecified, versus H1: θ1 ≠ 0, θ2 = 0, Σ unspecified. These tests are known as Rao’s W-test and Rao’s U-test, respectively. In this paper, it is shown that Rao’s U-test is admissible while Hotelling’s T2-test

    更新日期:2020-01-24
  • Relative Error Prediction for Twice Censored Data
    Math. Meth. Stat. Pub Date : 2020-01-24
    S. Khardani

    In this paper we consider the problem of non-parametric relative regression for twice censored data. We introduce and study a new estimate of the regression function when it is appropriate to assess performance in terms of mean squared relative error of prediction. We establish the uniform consistency with rate over a compact set and asymptotic normality of the estimator suitably normalized. The asymptotic

    更新日期:2020-01-24
  • An Asymptotically Optimal Transform of Pearson’s Correlation Statistic
    Math. Meth. Stat. Pub Date : 2020-01-24
    I. Pinelis

    It is shown that for any correlation-parametrized model of dependence and any given significance level α ∈ (0, 1), there is an asymptotically optimal transform of Pearson’s correlation statistic R, for which the generally leading error term for the normal approximation vanishes for all values ρ ∈ (−1, 1) of the correlation coefficient. This general result is then applied to the bivariate normal (BVN)

    更新日期:2020-01-24
  • On the Skewness Order of van Zwet and Oja
    Math. Meth. Stat. Pub Date : 2020-01-24
    A. Eberl, B. Klar

    Van Zwet (1964) [16] introduced the convex transformation order between two distribution functions F and G, defined by F ≤cG if G−1 ∘ F is convex. A distribution which precedes G in this order should be seen as less right-skewed than G. Consequently, if F ≤cG, any reasonable measure of skewness should be smaller for F than for G. This property is the key property when defining any skewness measure

    更新日期:2020-01-24
  • Maxiset Point of View for Signal Detection in Inverse Problems
    Math. Meth. Stat. Pub Date : 2019-09-27
    F. Autin, M. Clausel, J.-M. Freyermuth, C. Marteau

    This paper extends the successful maxiset paradigm from function estimation to signal detection in inverse problems. In this context, the maxisets do not have the same shape compared to the classical estimation framework. Nevertheless, we introduce a robust version of these maxisets allowing to exhibit tail conditions on the signals of interest. Under this novel paradigm we are able to compare direct

    更新日期:2019-09-27
  • Central Limit Theorems for Conditional Empirical and Conditional U -Processes of Stationary Mixing Sequences
    Math. Meth. Stat. Pub Date : 2019-09-27
    S. Bouzebda, B. Nemouchi

    In this paper we are concerned with the weak convergence to Gaussian processes of conditional empirical processes and conditional U-processes from stationary β-mixing sequences indexed by classes of functions satisfying some entropy conditions. We obtain uniform central limit theorems for conditional empirical processes and conditional U-processes when the classes of functions are uniformly bounded

    更新日期:2019-09-27
  • Density Deconvolution with Small Berkson Errors
    Math. Meth. Stat. Pub Date : 2019-09-27
    R. Rimal, M. Pensky

    The present paper studies density deconvolution in the presence of small Berkson errors, in particular, when the variances of the errors tend to zero as the sample size grows. It is known that when the Berkson errors are present, in some cases, the unknown density estimator can be obtained by simple averaging without using kernels. However, this may not be the case when Berkson errors are asymptotically

    更新日期:2019-09-27
  • The Empirical Process of Residuals from an Inverse Regression
    Math. Meth. Stat. Pub Date : 2019-08-05
    T. Kutta, N. Bissantz, J. Chown, H. Dette

    In this paper we investigate an indirect regression model characterized by the Radon transformation. This model is useful for recovery of medical images obtained by computed tomography scans. The indirect regression function is estimated using a series estimator motivated by a spectral cutoff technique. Further, we investigate the empirical process of residuals from this regression, and show that it

    更新日期:2019-08-05
  • On Predictive Density Estimation under α-Divergence Loss
    Math. Meth. Stat. Pub Date : 2019-08-05
    A. L’Moudden, È. Marchand

    Based on X ∼ Nd(θ, σ 2 X Id), we study the efficiency of predictive densities under α-divergence loss Lα for estimating the density of Y ∼ Nd(θ, σ 2 Y Id). We identify a large number of cases where improvement on a plug-in density are obtainable by expanding the variance, thus extending earlier findings applicable to Kullback-Leibler loss. The results and proofs are unified with respect to the dimension

    更新日期:2019-08-05
  • Asymptotic Theory for Longitudinal Data with Missing Responses Adjusted by Inverse Probability Weights
    Math. Meth. Stat. Pub Date : 2019-08-05
    R. M. Balan, D. Jankovic

    In this article, we propose a new method for analyzing longitudinal data which contain responses that are missing at random. This method consists in solving the generalized estimating equation (GEE) of [8] in which the incomplete responses are replaced by values adjusted using the inverse probability weights proposed in [17]. We show that the root estimator is consistent and asymptotically normal,

    更新日期:2019-08-05
  • A Multiple Hypothesis Testing Approach to Detection Changes in Distribution
    Math. Meth. Stat. Pub Date : 2019-08-05
    G. Golubev, M. Safarian

    Let X1, X2,... be independent random variables observed sequentially and such that X1,..., Xθ−1 have a common probability density p0, while Xθ, Xθ+1,... are all distributed according to p1 ≠ p0. It is assumed that p0 and p1 are known, but the time change θ ∈ ℤ+ is unknown and the goal is to construct a stopping time τ that detects the change-point θ as soon as possible. The standard approaches to this

    更新日期:2019-08-05
  • On the Asymptotic Power of Tests of Fit under Local Alternatives in Autoregression
    Math. Meth. Stat. Pub Date : 2019-08-05
    M. V. Boldin

    We consider a stationary AR(p) model. The autoregression parameters are unknown as well as the distribution of innovations. Based on the residuals from the parameter estimates, an analog of empirical distribution function is defined and the tests of Kolmogorov’s and ω2 type are constructed for testing hypotheses on the distribution of innovations. We obtain the asymptotic power of these tests under

    更新日期:2019-08-05
  • A Semi-Parametric Mode Regression with Censored Data
    Math. Meth. Stat. Pub Date : 2019-05-03
    S. Khardani

    In this work we suppose that the random vector (X, Y) satisfies the regression model Y = m(X) + ϵ, where m(·) belongs to some parametric class {\({m_\beta}(\cdot):\beta \in \mathbb{K}\)} and the error ϵ is independent of the covariate X. The response Y is subject to random right censoring. Using a nonlinear mode regression, a new estimation procedure for the true unknown parameter vector β0is proposed

    更新日期:2019-05-03
  • Density Estimation for RWRE
    Math. Meth. Stat. Pub Date : 2019-05-03
    A. Havet, M. Lerasle, É. Moulines

    We consider the problem of nonparametric density estimation of a random environment from the observation of a single trajectory of a random walk in this environment. We build several density estimators using the beta-moments of this distribution. Then we apply the Goldenschluger-Lepski method to select an estimator satisfying an oracle type inequality. We obtain non-asymptotic bounds for the supremum

    更新日期:2019-05-03
  • A Large Deviation Approximation for Multivariate Density Functions
    Math. Meth. Stat. Pub Date : 2019-05-03
    C. Joutard

    We establish a large deviation approximation for the density of an arbitrary sequence of random vectors, by assuming several assumptions on the normalized cumulant generating function and its derivatives. We give two statistical applications to illustrate the result, the first one dealing with a vector of independent sample variances and the second one with a Gaussian multiple linear regression model

    更新日期:2019-05-03
  • Bayesian Predictive Distribution for a Negative Binomial Model
    Math. Meth. Stat. Pub Date : 2019-05-03
    Y. Hamura, T. Kubokawa

    Estimation of the predictive probability function of a negative binomial distribution is addressed under the Kullback—Leibler risk. An identity that relates Bayesian predictive probability estimation to Bayesian point estimation is derived. Such identities are known in the cases of normal and Poisson distributions, and the paper extends the result to the negative binomial case. By using the derived

    更新日期:2019-05-03
  • Outliers and the Ostensibly Heavy Tails
    Math. Meth. Stat. Pub Date : 2019-05-03
    L. Klebanov, I. Volchenkova

    The aim of the paper is to show that the presence of one possible type of outliers is not connected to that of heavy tails of the distribution. In contrary, typical situation for outliers appearance is the case of compactly supported distributions.

    更新日期:2019-05-03
  • On the Power of Pearson’s Test under Local Alternatives in Autoregression with Outliers
    Math. Meth. Stat. Pub Date : 2019-05-03
    M. V. Boldin

    We consider a stationary linear AR(p) model with contamination (gross errors in the observations). The autoregression parameters are unknown, as well as the distribution of innovations. Based on the residuals from the parameter estimates, an analog of the empirical distribution function is defined and a test of Pearson’s chi-square type is constructed for testing hypotheses on the distribution of innovations

    更新日期:2019-05-03
  • On Optimal Cardinal Interpolation
    Math. Meth. Stat. Pub Date : 2019-02-05
    B. Levit

    For the Hardy classes of functions analytic in the strip around real axis of a size 2β, an optimal method of cardinal interpolation has been proposed within the framework of Optimal Recovery [12]. Below this method, based on the Jacobi elliptic functions, is shown to be optimal according to the criteria of Nonparametric Regression and Optimal Design. In a stochastic non-asymptotic setting, the maximal

    更新日期:2019-02-05
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