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 Subjects -> MATHEMATICS (Total: 1040 journals)     - APPLIED MATHEMATICS (83 journals)    - GEOMETRY AND TOPOLOGY (23 journals)    - MATHEMATICS (770 journals)    - MATHEMATICS (GENERAL) (43 journals)    - NUMERICAL ANALYSIS (23 journals)    - PROBABILITIES AND MATH STATISTICS (98 journals) MATHEMATICS (770 journals)            First | 1 2 3 4
 Showing 401 - 538 of 538 Journals sorted alphabetically Journal of Humanistic Mathematics       (Followers: 1) Journal of Hyperbolic Differential Equations Journal of Indian Council of Philosophical Research Journal of Industrial Mathematics       (Followers: 2) Journal of Inequalities and Applications Journal of Infrared, Millimeter and Terahertz Waves       (Followers: 2) Journal of Integrable Systems       (Followers: 1) Journal of K-Theory Journal of Knot Theory and Its Ramifications       (Followers: 1) Journal of Kufa for Mathematics and Computer       (Followers: 1) Journal of Liquid Chromatography & Related Technologies       (Followers: 7) Journal of Logical and Algebraic Methods in Programming Journal of Manufacturing Systems       (Followers: 4) Journal of Mathematical Analysis and Applications       (Followers: 4) Journal of mathematical and computational science       (Followers: 7) Journal of Mathematical and Fundamental Sciences Journal of Mathematical Behavior       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North Carolina Journal of Mathematics and Statistics North-Holland Mathematical Library       (Followers: 1) North-Holland Mathematics Studies North-Holland Series in Applied Mathematics and Mechanics       (Followers: 1) Note di Matematica NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin       (Followers: 4) Numeracy : Advancing Education in Quantitative Literacy Numerical Analysis and Applications       (Followers: 1) Numerical Functional Analysis and Optimization       (Followers: 2) Numerical Linear Algebra with Applications       (Followers: 6) Numerical Mathematics : Theory, Methods and Applications Numerische Mathematik Open Journal of Discrete Mathematics       (Followers: 5) Open Journal of Modelling and Simulation       (Followers: 1) Open Mathematics       (Followers: 1) Operations Research Letters       (Followers: 11) Optimization Letters       (Followers: 2) Optimization Methods and Software       (Followers: 8) Opuscula Mathematica       (Followers: 108) Order ORiON P-Adic Numbers, Ultrametric Analysis, and Applications PAMM : Proceedings in Applied Mathematics and Mechanics       (Followers: 1) Parallel Processing Letters       (Followers: 3) Peking Mathematical Journal Periodica Mathematica Hungarica       (Followers: 1) Perspectivas da Educação Matemática Petroleum Science       (Followers: 1) Philosophia Mathematica       (Followers: 1) Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences       (Followers: 6) PNA. Revista de Investigación en Didáctica de la Matemática Polar Science       (Followers: 3) Positivity Prague Bulletin of Mathematical Linguistics, The

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Similar Journals
 Mathematical Methods of StatisticsJournal Prestige (SJR): 0.43 Number of Followers: 4      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1934-8045 - ISSN (Online) 1066-5307 Published by Springer-Verlag  [2574 journals]
• Maxiset Point of View for Signal Detection in Inverse Problems
• Abstract: 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 and indirect testing procedures.
PubDate: 2019-07-01

• Central Limit Theorems for Conditional Empirical and Conditional U
-Processes of Stationary Mixing Sequences
• Abstract: 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 or unbounded with envelope functions satisfying some moment conditions. We apply our results to introduce statistical tests for conditional independence that are multivariate conditional versions of the Kendall statistics.
PubDate: 2019-07-01

• Density Deconvolution with Small Berkson Errors
• Abstract: 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 small. By treating the former case as a kernel estimator with the zero bandwidth, we obtain the optimal expressions for the bandwidth. We show that the density of Berkson errors acts as a regularizer, so that the kernel estimator is unnecessary when the variance of Berkson errors lies above some threshold that depends on the shapes of the densities in the model and the number of observations.
PubDate: 2019-07-01

• The Empirical Process of Residuals from an Inverse Regression
• Abstract: 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 satisfies a functional central limit theorem.
PubDate: 2019-04-01

• On Predictive Density Estimation under α-Divergence Loss
• Abstract: Based on X ∼ Nd(θ, σ X 2 Id), we study the efficiency of predictive densities under α-divergence loss Lα for estimating the density of Y ∼ Nd(θ, σ Y 2 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 d, the variances σ X 2 and σ Y 2 , the choice of loss Lα; α ∈ (−1, 1). The findings also apply to a large number of plug-in densities, as well as for restricted parameter spaces with θ ∈ Θ ⊂ ℝd. The theoretical findings are accompanied by various observations, illustrations, and implications dealing for instance with robustness with respect to the model variances and simultaneous dominance with respect to the loss.
PubDate: 2019-04-01

• On the Asymptotic Power of Tests of Fit under Local Alternatives in
Autoregression
• Abstract: 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 local alternatives.
PubDate: 2019-04-01

• A Multiple Hypothesis Testing Approach to Detection Changes in
Distribution
• Abstract: 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 problem rely essentially on some prior information about θ. For instance, in the Bayes approach, it is assumed that θ is a random variable with a known probability distribution. In the methods related to hypothesis testing, this a priori information is hidden in the so-called average run length. The main goal in this paper is to construct stopping times that are free from a priori information about θ. More formally, we propose an approach to solving approximately the following minimization problem: $$\Delta(\theta;{\tau^\alpha})\rightarrow\min_{\tau^\alpha}\;\;\text{subject}\;\text{to}\;\;\alpha(\theta;{\tau^\alpha})\leq\alpha\;\text{for}\;\text{any}\;\theta\geq1,$$ where α(θ; τ) = Pθ{τ < θ} is the false alarm probability and Δ(θ; τ) = Eθ(τ − θ)+ is the average detection delay computed for a given stopping time τ. In contrast to the standard CUSUM algorithm based on the sequential maximum likelihood test, our approach is related to a multiple hypothesis testing methods and permits, in particular, to construct universal stopping times with nearly Bayes detection delays.
PubDate: 2019-04-01

• Asymptotic Theory for Longitudinal Data with Missing Responses Adjusted by
Inverse Probability Weights
• Abstract: 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, essentially under the some conditions on the marginal distribution and the surrogate correlation matrix as those presented in [15] in the case of complete data, and under minimal assumptions on the missingness probabilities. This method is applied to a real-life data set taken from [13], which examines the incidence of respiratory disease in a sample of 250 pre-school age Indonesian children which were examined every 3 months for 18 months, using as covariates the age, gender, and vitamin A deficiency.
PubDate: 2019-04-01

• On the Power of Pearson’s Test under Local Alternatives in
Autoregression with Outliers
• Abstract: 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. We obtain the asymptotic power of this test under local alternatives and establish its qualitative robustness under the hypothesis and alternatives.
PubDate: 2019-01-01

• A Large Deviation Approximation for Multivariate Density Functions
• Abstract: 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. Numerical comparisons are eventually provided for these two examples.
PubDate: 2019-01-01

• Bayesian Predictive Distribution for a Negative Binomial Model
• Abstract: 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 identity, a dominance property of a Bayesian predictive probability is studied when the parameter space is restricted.
PubDate: 2019-01-01

• Density Estimation for RWRE
• Abstract: 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 norm of these estimators that hold when the RWRE is recurrent or transient to the right. A simulation study supports our theoretical findings.
PubDate: 2019-01-01

• A Semi-Parametric Mode Regression with Censored Data
• Abstract: 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 that extends the classical least squares procedure for nonlinear regression. We also establish asymptotic properties for the proposed estimator under assumptions of the error density. We investigate the performance through a simulation study.
PubDate: 2019-01-01

• Outliers and the Ostensibly Heavy Tails
• Abstract: 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.
PubDate: 2019-01-01

• On Optimal Cardinal Interpolation
• Authors: B. Levit
Pages: 245 - 267
Abstract: 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 mean squared error of the optimal interpolant is evaluated explicitly, for all noise levels away from 0. A pivotal role is played by the interference effect, in which the oscillations exhibited by the interpolant’s bias and variance mutually cancel each other. In the limiting case β → ∞, the optimal interpolant converges to the well-knownNyquist–Shannon cardinal series.
PubDate: 2018-10-01
DOI: 10.3103/s1066530718040014
Issue No: Vol. 27, No. 4 (2018)

• Asymptotic Distribution of Least Squares Estimators for Linear Models with
Dependent Errors: Regular Designs
• Authors: E. Caron; S. Dede
Pages: 268 - 293
Abstract: We consider the usual linear regression model in the case where the error process is assumed strictly stationary.We use a result of Hannan, who proved a Central Limit Theorem for the usual least squares estimator under general conditions on the design and the error process.We show that for a large class of designs, the asymptotic covariance matrix is as simple as in the independent and identically distributed (i.i.d.) case.We then estimate the covariance matrix using an estimator of the spectral density whose consistency is proved under very mild conditions.
PubDate: 2018-10-01
DOI: 10.3103/s1066530718040026
Issue No: Vol. 27, No. 4 (2018)

• On the Empirical Distribution Function of Residuals in Autoregression with
Outliers and Pearson’s Chi-Square Type Tests
• Authors: M. V. Boldin; M. N. Petriev
Pages: 294 - 311
Abstract: We consider a stationary linear AR(p) model with observations subject to gross errors (outliers). The distribution of outliers is unknown and arbitrary, their intensity is γn−1/2 with an unknown γ, n is the sample size. The autoregression parameters are unknown, they are estimated by any estimator which is n1/2-consistent uniformly in γ ≤ Γ < ∞. Using the residuals from the estimated autoregression, we construct a kind of empirical distribution function (e.d.f.), which is a counterpart of the (inaccessible) e.d.f. of the autoregression innovations. We obtain a stochastic expansion of this e.d.f., which enables us to construct a test of Pearson’s chi-square type for testing hypotheses about the distribution of innovations. We establish qualitative robustness of this test in terms of uniform equicontinuity of the limiting level with respect to γ in a neighborhood of γ = 0.
PubDate: 2018-10-01
DOI: 10.3103/s1066530718040038
Issue No: Vol. 27, No. 4 (2018)

• On the Asymptotic Behavior of the Contaminated Sample Mean
• Authors: B. Berckmoes; G. Molenberghs
Pages: 312 - 323
Abstract: An observation of a cumulative distribution function F with finite variance is said to be contaminated according to the inflated variance model if it has a large probability of coming from the original target distribution F, but a small probability of coming from a contaminating distribution that has the same mean and shape as F, though a larger variance. It is well known that in the presence of data contamination, the ordinary sample mean looses many of its good properties, making it preferable to use more robust estimators. It is insightful to see to what extent an intuitive estimator such as the sample mean becomes less favorable in a contaminated setting. In this paper, we investigate under which conditions the sample mean, based on a finite number of independent observations of F which are contaminated according to the inflated variance model, is a valid estimator for the mean of F. In particular, we examine to what extent this estimator is weakly consistent for the mean of F and asymptotically normal. As classical central limit theory is generally inaccurate to copewith the asymptotic normality in this setting, we invokemore general approximate central limit theory as developed in [3]. Our theoretical results are illustrated by a specific example and a simulation study.
PubDate: 2018-10-01
DOI: 10.3103/s106653071804004x
Issue No: Vol. 27, No. 4 (2018)

• A Minimax Approach to Errors-in-Variables Linear Models
• Authors: Yu. Golubev
Pages: 205 - 225
Abstract: The paper considers a simple Errors-in-Variables (EiV) model Yi = a + bXi + εξi; Zi= Xi + σζi, where ξi, ζi are i.i.d. standard Gaussian random variables, Xi ∈ ℝ are unknown non-random regressors, and ε, σ are known noise levels. The goal is to estimates unknown parameters a, b ∈ ℝ based on the observations {Yi, Zi, i = 1, …, n}. It is well known [3] that the maximum likelihood estimates of these parameters have unbounded moments. In order to construct estimates with good statistical properties, we study EiV model in the large noise regime assuming that n → ∞, but $${\epsilon ^2} = \sqrt n \epsilon _ \circ ^2,{\sigma ^2} = \sqrt n \sigma _ \circ ^2$$ with some $$\epsilon_\circ^2, \sigma_\circ^2>0$$ . Under these assumptions, a minimax approach to estimating a, b is developed. It is shown that minimax estimates are solutions to a convex optimization problem and a fast algorithm for solving it is proposed.
PubDate: 2018-07-01
DOI: 10.3103/s1066530718030031
Issue No: Vol. 27, No. 3 (2018)

• Truncated Estimation of Ratio Statistics with Application to Heavy Tail
Distributions
• Authors: D. N. Politis; V. A. Vasiliev; S. E. Vorobeychikov
Pages: 226 - 243
Abstract: The problem of estimation of the heavy tail index is revisited from the point of view of truncated estimation. A class of novel estimators is introduced having guaranteed accuracy based on a sample of fixed size. The performance of these estimators is quantified both theoretically and in simulations over a host of relevant examples. It is also shown that in several cases the proposed estimators attain — within a logarithmic factor — the optimal parametric rate of convergence. The property of uniform asymptotic normality of the proposed estimators is established.
PubDate: 2018-07-01
DOI: 10.3103/s1066530718030043
Issue No: Vol. 27, No. 3 (2018)

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