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  Subjects -> STATISTICS (Total: 130 journals)
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Mathematical Methods of Statistics
Journal Prestige (SJR): 0.43
Number of Followers: 4  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1934-8045 - ISSN (Online) 1066-5307
Published by Springer-Verlag Homepage  [2468 journals]
  • Assessing Monotonicity: An Approach Based on Transformed Order Statistics

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      Abstract: In a number of research areas, such as non-convex optimization and machine learning, determining and assessing regions of monotonicity of functions is pivotal. Numerically, it can be done using the proportion of positive (or negative) increments of transformed ordered inputs. When the number of inputs grows, the proportion tends to an index of increase (or decrease) of the underlying function. In this paper, we introduce a most general index of monotonicity and provide its interpretation in all practically relevant scenarios, including those that arise when the distribution of inputs has jumps and flat regions, and when the function is only piecewise differentiable. This enables us to assess monotonicity of very general functions under particularly mild conditions on the inputs.
      PubDate: 2024-03-01
       
  • Controlling Separation in Generating Samples for Logistic Regression
           Models

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      Abstract: Separation has a significant impact on parameter estimates for logistic regression models in frequentist approach and in Bayesian approach. When separation presents in a sample, the maximum likelihood estimation (MLE) does not exist through standard estimation methods. The existence of posterior means is affected by the presence of separation and also depended on the forms of prior distributions. Therefore, controlling the appearance of separation in generating samples from the logistic regression models has an important role for parameter estimation techniques. In this paper, we propose necessary and sufficient conditions for separation occurring in the logistic regression samples with two dimensional models and multiple dimensional models of independent variables. By using the technique of rotating Castesian coordinates of p dimensions, the characteristic of separation occurring in general cases is presented. Using these results, we propose algorithms to control the probability of separation appearance in generated samples for given sample sizes and multiple dimensional models of independent variables. The simulation studies show that the proposed algorithms can effectively generate the designed random samples with controlling the probability of separation appearance.
      PubDate: 2024-03-01
       
  • Truncated Estimators for a Precision Matrix

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      Abstract: In this paper, we estimate the precision matrix \({\Sigma}^{-1}\) of a Gaussian multivariate linear regression model through its canonical form \(({Z}^{T},{U}^{T})^{T}\) where \(Z\) and \(U\) are respectively an \(m\times p\) and an \(n\times p\) matrices. This problem is addressed under the data-based loss function \(\textrm{tr}\ [({\hat{\Sigma}}^{-1}-{\Sigma}^{-1})S]^{2}\) , where \({\hat{\Sigma}}^{-1}\) estimates \({\Sigma}^{-1}\) , for any ordering of \(m,n\) and \(p\) , in a unified approach. We derive estimators which, besides the information contained in the sample covariance matrix \(S={U}^{T}U\) , use the information contained in the sample mean \(Z\) . We provide conditions for which these estimators improve over the usual estimators \(a{S}^{+}\) where \(a\) is a positive constant and \({S}^{+}\) is the Moore-Penrose inverse of \(S\) . Thanks to the role of \(Z\) , such estimators are also improved by their truncated version.
      PubDate: 2024-03-01
       
  • Functional Uniform-in-Bandwidth Moderate Deviation Principle for the Local
           Empirical Processes Involving Functional Data

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      Abstract: Our research employs general empirical process methods to investigate and establish moderate deviation principles for kernel-type function estimators that rely on an infinite-dimensional covariate, subject to mild regularity conditions. In doing so, we introduce a valuable moderate deviation principle for a function-indexed process, utilizing intricate exponential contiguity arguments. The primary objective of this paper is to contribute to the existing literature on functional data analysis by establishing functional moderate deviation principles for both Nadaraya–Watson and conditional distribution processes. These principles serve as fundamental tools for analyzing and understanding the behavior of these processes in the context of functional data analysis. By extending the scope of moderate deviation principles to the realm of functional data analysis, we enhance our understanding of the statistical properties and limitations of kernel-type function estimators when dealing with infinite-dimensional covariates. Our findings provide valuable insights and contribute to the advancement of statistical methodology in functional data analysis.
      PubDate: 2024-03-01
       
  • Characterizing Existence and Location of the ML Estimate in the
           Conway–Maxwell–Poisson Model

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      Abstract: As a flexible extension of the common Poisson model, the Conway–Maxwell–Poisson distribution allows for describing under- and overdispersion in count data via an additional parameter. Estimation methods for two Conway–Maxwell–Poisson parameters are then required to specify the model. In this work, two characterization results are provided related to maximum likelihood estimation of the Conway–Maxwell–Poisson parameters. The first states that maximum likelihood estimation fails if and only if the range of the observations is less than two. Assuming that the maximum likelihood estimate exists, the second result then comprises a simple necessary and sufficient condition for the maximum likelihood estimate to be a solution of the likelihood equation; otherwise it lies on the boundary of the parameter set. A simulation study is carried out to investigate the accuracy of the maximum likelihood estimate in dependence of the range of the underlying observations.
      PubDate: 2024-03-01
       
  • Validation Data-Located Modification for the Multilevel Analysis of
           Miscategorized Nominal Response with Covariates Subject to Measurement
           Error

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      Abstract: In many longitudinal and hierarchical epidemiological frameworks, observations regarding to each individual are recorded repeatedly over time. In these follow-ups, accurate measurements of time-dependent covariates might be invalid or expensive to be obtained. In addition, in the recording process, or as a result of other undetected reasons, miscategorization of the response variable might occur, that does not demonstrate the true condition of the response process. In contrast with binary outcome by which classification error occurs between two categories, disorderliness in categorical outcome has more intricate impacts, as a result of the increased number of categories and asymmetric miscategorization matrix. When no modification is made, insensitivity of errors in either covariate or response variable, results in potentially incorrect conclusion, tends to bias the statistical inference and eventually degrades the efficiency of the decision-making procedure. In this article, we provide an approach to simultaneously adjust for misclassification in the correlated nominal response and measurement error in the covariates, incorporating validation data in the estimation of misclassification probabilities, using the multivariate Gauss–Hermite quadrature technique for the approximation of the likelihood function. Simulation results demonstrate the effects of modifying covariate measurement error and response misclassification on the estimation procedure.
      PubDate: 2023-12-01
      DOI: 10.3103/S1066530723040026
       
  • Estimating Sample Skewness from Sample Data Summaries and Associated
           Evaluation of Normality

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      Abstract: We propose a method to estimate a sample skewness from the given summary statistics and give explicit formulas for the most common scenarios. We show that our method provides a nearly unbiased estimator for the non-parametric skewness measure. We empirically evaluate the performance on real-life data sets of COVID-19 vaccination status. We also demonstrate how the method can be applied to detect the skewness of the underlying distribution.
      PubDate: 2023-12-01
      DOI: 10.3103/S106653072304004X
       
  • Statistical Inference in Marginalized Zero-inflated Poisson Regression
           Models with Missing Data in Covariates

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      Abstract: The marginalized zero-inflated poisson (MZIP) regression model quantifies the effects of an explanatory variable in the mixture population. Also, in practice the variables are usually partially observed. Thus, we first propose to study the maximum likelihood estimator when all variables are observed. Then, assuming that the probability of selection is modeled using mixed covariates (continuous, discrete and categorical), we propose a semiparametric inverse-probability weighted (SIPW) method for estimating the parameters of the MZIP model with covariates missing at random (MAR). The asymptotic properties (consistency, asymptotic normality) of the proposed estimators are established under certain regularity conditions. Through numerical studies, the performance of the proposed estimators was evaluated. Then the results of the SIPW are compared to the results obtained by semiparametric inverse-probability weighted kermel-based (SIPWK) estimator method. Finally, we apply our methodology to a dataset on health care demand in the United States.
      PubDate: 2023-12-01
      DOI: 10.3103/S1066530723040038
       
  • Sharp Lower Bound for Regression with Measurement Errors and Its
           Implication for Ill-Posedness of Functional Regression

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      Abstract: Nonparametric regression estimation with Gaussian measurement errors in predictors is a classical statistical problem. It is well known that the errors dramatically slow down the rate of regression estimation, and this paper complement that result by presenting a sharp constant. Then an interesting example of using this sharp constant to discover a new curse of dimensionality in functional nonparametric regression is presented, and analysis of real data complements the theory.
      PubDate: 2023-09-01
      DOI: 10.3103/S1066530723030031
       
  • Multivariate Doubly Truncated Moments for a Class of Multivariate
           Location-Scale Mixture of Elliptical Distributions

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      Abstract: In this paper, we investigate multivariate doubly truncated moments for a class of multivariate location-scale mixture of elliptical (LSME) distributions. This rich family includes some well-known distributions, such as location-scale mixture of normal, location-scale mixture of Student- \(t\) , location-scale mixture of logistic and location-scale mixture of Laplace distributions, as special cases. We first present general formulae for computing the first two moments of the LSME distributions under the double truncation. We then consider a special case for cross moment. As an application, we present the results of multivariate tail conditional expectation (MTCE) for generalized hyperbolic (MGH) distribution.
      PubDate: 2023-09-01
      DOI: 10.3103/S1066530723030043
       
  • Information Generating Function of $$\boldsymbol{k}$$ -Record Values and
           Its Applications

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      Abstract: In this paper, we study the information-generating (IG) measure of \(k\) -record values and examine some of its main properties. We establish some bounds for the IG measure of \(k\) -record values. In addition, we present some results related to the characterization of an exponential distribution by maximization (minimization) of the IG measure of record values under certain conditions. We also examine the relative information generating (RIG) measure between the distribution of record values and the corresponding underlying distribution and present some results in this regard. Several examples have been provided throughout the study to illustrate the results. We also consider the problem of estimation of the IG measure for a two-parameter Weibull distribution based on the upper \(k\) -record values.
      PubDate: 2023-09-01
      DOI: 10.3103/S106653072303002X
       
  • Numerical Solution of Stochastic Mixed Volterra–Fredholm Integral
           Equations Driven by Space-Time Brownian Motion via Two-Dimensional
           Triangular Functions

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      Abstract: The goal of this paper is to introduce an efficient method for solving problems formulated by stochastic mixed Volterra–Fredholm integral equations driven by space-time white noise. Two dimensional triangular functions and their operational matrix and stochastic operational matrix of integration are considered. This method has several benefits; in addition to validity and good degree of accuracy, arithmetic operations are carried out without the need to derivative or integration. Illustrative examples are included to demonstrate the efficiency and applicability of the operational matrices based on two dimensional triangular functions.
      PubDate: 2023-09-01
      DOI: 10.3103/S1066530723030055
       
  • Improved Estimators of Tail Index and Extreme Quantiles under Dependence
           Serials

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      Abstract: In this paper, we deal with the estimation problem for the extreme value parameters in the case of stationary \(\beta\) -mixing serials with heavy-tailed distributions. We first introduce two families of estimators generalizing the Hill’s estimator. And from those families, three asymptotically unbiased estimators of the extreme value index are established. Our reflection is based on the generalized Jackknife methodology which consists of taking any pair of three special cases of our family of estimators to cancel the bias term. The resulting estimators are also used to deduce three asymptotically unbiased estimators of the extreme quantiles. In a simulation survey, the performance of our proposed methods are compared to alternative estimators recently introduced in the literature. Finally, our methods are applied to high financial losses data in order to estimate the Value-at-Risk of the daily stock returns on the S&P500 index.
      PubDate: 2023-06-01
      DOI: 10.3103/S1066530723020011
       
  • Distributions Derived from the Continuous Iteration of the Hyperbolic Sine
           Function

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      Abstract: Families of distributions built from the fractional or continuous iteration of exponential-type functions are characterized by a wide range of tail-heaviness. The present paper aims to define classes of distributions supported on the whole real line based on the continuous iteration of the hyperbolic sine function sinh. This function has already been commonly employed in univariate transformations such as the Johnson’s \(S_{U}\) and sinh–arcsinh transforms. The tail versatility generated by a transformation based on the continuous iteration of sinh is highlighted based on an initial logistic distribution. It leads to the Hyperbolic Tetration distribution. The Double Hyperbolic Tetration distribution, defined from two successive hyperbolic transformations, is also introduced. It is among the first class of distributions with potential distinct tetration indices at plus and minus infinity. The distributions are applied to multiple data sets in hydrology.
      PubDate: 2023-06-01
      DOI: 10.3103/S1066530723020023
       
  • A Discrete Analogue of Terrell’s Characterization of Rectangular
           Distributions

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      Abstract: Terrell [18] showed that the Pearson coefficient of correlation of an ordered pair from a random sample of size two is at most one-half, and the equality is attained only for rectangular (uniform over some interval) distributions. In the present note it is proved that the same is true for the discrete case, in the sense that the correlation coefficient attains its maximal value only for discrete rectangular (uniform over some finite lattice) distributions.
      PubDate: 2023-06-01
      DOI: 10.3103/S1066530723020035
       
  • Quantile Based Geometric Vitality Function of Order Statistics

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      Abstract: In [1], the authors introduced the geometric vitality function that explains the failure pattern of components or systems based on the geometric mean of the remaining lifetime. Recently, studies based on quantile function played an essential role in the research domain because of its unique properties than the distribution function method. Based on this, we define geometric vitality function in terms of quantile function and established monotone, ordering properties for the proposed measure. In addition to this, we also introduce the proposed measure in the context of order statistics. Some important properties were discussed for the proposed measure. Finally, we provide an application of the new measure for some distributions useful in lifetime data analysis.
      PubDate: 2023-03-01
      DOI: 10.3103/S1066530723010040
       
  • Reliability Bounds of Dependent Circular Consecutive $$\boldsymbol{k}$$
           -out-of- $$\boldsymbol{n:G}$$ Systems

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      Abstract: Computation of reliability function of a coherent system is a difficult task especially when the system’s configuration is complex. Hence, sometimes, we should simply work with some approximations, as bounds reliability. The computation of these bounds has been widely studied in the case of coherent systems with independent and identically distributed (i.i.d) components. However, few results have been obtained in the case of heterogeneous (non i.d) dependent components. In this paper, we derive sharp bounds for the reliability of circular consecutive \(k\) -out-of- \(n:G\) systems consisting by dependent components with identical or arbitrary distribution functions. Also some stochastic comparisons are made. Illustrative examples are included.
      PubDate: 2023-03-01
      DOI: 10.3103/S1066530723010052
       
  • Rates of the Strong Uniform Consistency for the Kernel-Type Regression
           Function Estimators with General Kernels on Manifolds

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      Abstract: In the present paper, we develop strong uniform consistency results for the generic kernel (including the kernel density estimator) on Riemannian manifolds with Riemann integrable kernels in order to accomplish these difficult tasks. The kernels of the Vapnik-Chervonenkis class that are commonly utilized in statistical problems are different to the isotropic kernels we address in this paper. Moreover, we show, in the same context, the uniform consistency for nonparametric inverse probability of censoring weighted (IPCW) estimators of the regression function under random censorship. As an application, we present the strong uniform consistency for estimators of the Nadaray-Watson type, which is of independent interest.
      PubDate: 2023-03-01
      DOI: 10.3103/S1066530723010027
       
  • Gaussian Approximation for Penalized Wasserstein Barycenters

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      Abstract: In this work we consider regularized Wasserstein barycenters (average in Wasserstein distance) in Fourier basis. We prove that random Fourier parameters of the barycenter converge to some Gaussian random vector in distribution. The convergence rate has been derived in finite-sample case with explicit dependence on measures count ( \(n\) ) and the dimension of parameters ( \(p\) ).
      PubDate: 2023-03-01
      DOI: 10.3103/S1066530723010039
       
  • Tail and Quantile Estimation for Real-Valued $$\boldsymbol{\beta}$$
           -Mixing Spatial Data

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      Abstract: This paper deals with extreme-value index estimation of a heavy-tailed distribution of a spatial dependent process. We are particularly interested in spatial rare events of a \(\beta\) -mixing process. Given a stationary real-valued multidimensional spatial process \(\left\{X_{\mathbf{i}},\mathbf{i}\in{\mathbb{Z}}^{N}\right\}\) , we investigate its heavy-tail index estimation. Asymptotic properties of the corresponding estimator are established under mild mixing conditions. The particularity of the tail proposed estimator is based on the spatial nature of the sample and its unbiased and reduced variance properties compared to well known tail index estimators. Extreme quantile estimation is also deduced. A numerical study on synthetic and real datasets is conducted to assess the finite-sample behaviour of the proposed estimators.
      PubDate: 2022-12-01
      DOI: 10.3103/S1066530722040044
       
 
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  Subjects -> STATISTICS (Total: 130 journals)
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