 Subjects -> STATISTICS (Total: 130 journals)
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- Exceedance Counts and GOD’s Order Statistics
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Abstract: Abstract In this paper we derive a characterization of the distribution of the number of exceedances among the components of a random vector in terms of order statistics of generators of D-norms (GOD). The computation of the fragility index is an immediate consequence.
PubDate: 2023-02-28
- Correction to: Local Linear Estimation of the Conditional Cumulative
Distribution Function: Censored Functional Data Case-
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PubDate: 2023-02-01
- On Moments of the Noncentral Chi Distribution
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Abstract: Abstract The mean of a noncentral chi random variable is usually expressed in terms a hypergeometric function. On a 17 pages paper, Lawrence [Sankhyā A. https://doi.org/10.1007/s13171-021-00262-3] derived simpler expressions for the mean, involving the modified Bessel function of the first kind and the error function. We show here that these expressions follow immediately from known relationships between the hypergeometric and modified Bessel / error functions.
PubDate: 2023-02-01
- Local linear estimation of the conditional cumulative distribution
function: Censored functional data case-
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Abstract: Abstract In this paper, we estimate the conditional cumulative distribution function of a randomly censored scalar response variable given a functional random variable using the local linear approach. Under this structure, we state the asymptotic normality with explicit rates of the constructed estimator. Moreover, the usefulness of our results is illustrated through a simulated study.
PubDate: 2023-02-01
- A Portmanteau Local Feature Discrimination Approach to the Classification
with High-dimensional Matrix-variate Data-
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Abstract: Abstract Matrix-variate data arise in many scientific fields such as face recognition, medical imaging, etc. Matrix data contain important structure information which can be ruined by vectorization. Methods incorporating the structure information into analysis have significant advantages over vectorization approaches. In this article, we consider the problem of two-class classification with high-dimensional matrix-variate data, and propose a novel portmanteau-local-feature discrimination (PLFD) method. This method first identifies local discrimination features of the matrix variate and then pools them together to construct a discrimination rule. We investigated the theoretical properties of the PLFD method and established its asymptotic optimality. We carried out extensive numerical studies including simulation and real data analysis to compare this method with other methods available in the literature, which demonstrate that the PLFD method has a great advantage over the other methods in terms of misclassification rate.
PubDate: 2023-02-01
- Cluster Correlations and Complexity in Binary Regression Analysis Using
Two-stage Cluster Samples-
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Abstract: Abstract In a two-stage cluster sampling setup for binary data, a sample of clusters such as hospitals is chosen at the first stage from a large number of clusters belonging to a finite population, and in the second stage a random sample of individuals such as nurses is chosen from the selected cluster and the binary responses along with covariates are collected from the selected individuals. Because the hypothetical binary responses from the individuals in a given cluster/hospital under the first stage sample are correlated (as they share a common cluster effect), this correlation plays a complex role in developing the second stage sample based estimating equations for the underlying regression parameters. Moreover, the correlation parameters have to be consistently estimated too. In this paper, unlike the existing studies, we demonstrate how to accommodate (1) the so-called inverse correlation weights arising from a finite population based generalized quasi-likelihood (GQL) estimating function, on top of (2) the sampling weights, to develop a survey sample based doubly weighted (SSDW) estimation approach, for consistent estimation of both regression and correlation parameters. For simplicity, we refer to this GQL cum SSDW approach as the SSDW approach only. The method of moments (MM) cum SSDW approach will be simpler but less efficient, which is not included in the paper. The estimating function involved in the proposed SSDW estimating equation has the form of a sample total, which unbiasedly estimate the corresponding finite population total that arises from the aforementioned generalized quasi-likelihood function for the targeted finite population parameter. The resulting SSDW estimators, thus, become consistent for the respective parameters. This consistency property for the SSDW estimator for both regression and cluster correlation parameters is studied in details.
PubDate: 2023-02-01
- On Compatibility/Incompatibility of Two Discrete Probability Distributions
in the Presence of Incomplete Specification-
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Abstract: Abstract Conditional specification of distributions is a developing area with several applications. In the finite discrete case, a variety of compatible conditions can be derived. In this paper, we revisit a rank–based criterion for identifying compatible distributions corresponding to complete conditional specification, including the case with zeros under the finite discrete set up. Based on this, we primarily focus on the compatibility of two conditionals (under the finite discrete set-up) in which incomplete specification on either or both the conditional matrices are present. Compatibility in the general case are also briefly discussed. The proposed methods are finally illustrated with several examples.
PubDate: 2023-02-01
- The Confidence Density for Correlation
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Abstract: Abstract Inference for correlation is central in statistics. From a Bayesian viewpoint, the final most complete outcome of inference for the correlation is the posterior distribution. An explicit formula for the posterior density for the correlation for the binormal is derived. This posterior is an optimal confidence distribution and corresponds to a standard objective prior. It coincides with the fiducial introduced by R.A. Fisher in 1930 in his first paper on fiducial inference. C.R. Rao derived an explicit elegant formula for this fiducial density, but the new formula using hypergeometric functions is better suited for numerical calculations. Several examples on real data are presented for illustration. A brief review of the connections between confidence distributions and Bayesian and fiducial inference is given in an Appendix.
PubDate: 2023-02-01
- Behaviour of the Monotone Single Index Model Under Repeated Measurements
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Abstract: Abstract The generalized linear model is an important method in the statistical toolkit. The isotonic single index model can be thought of as a further generalization whereby the link function is assumed to be monotone non-decreasing as opposed to known and fixed. Such a shape constraint is quite natural in many statistical problems, and is fulfilled by the usual generalized linear models. In this paper we consider inference in this model in the setting where repeated measurements of predictor values and associated responses are observed. This setting is encountered in medical studies and is very different from the one considered in the classical monotone single index model studied in the literature. Here, we use nonparametric maximum likelihood estimation to infer the unknown regression vector and link function. We present a detailed study of finite and asymptotic properties of this estimator and propose goodness-of-fit tests for the model. Through an extended simulation study, we show that the model has competitive predictive performance. We illustrate our estimation approach using a Leukemia data set.
PubDate: 2023-02-01
- Estimation Parameters for the Continuous q-Distributions
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Abstract: Abstract In this paper, we are basically interested in the issue of estimation parameters for continuous q-distributions. The parameters estimation and simulation studies of three classical continuous Lindley, gamma and exponential q-distributions are elaborated. For the parameters estimation problem the moment method is used. The effectiveness of the proposed models are highlighted through simulation studies for different q parameters values and samples sizes of the Lindley, gamma and exponential q-distributions.
PubDate: 2023-02-01
- A Skew-Normal Spatial Simultaneous Autoregressive Model and its
Implementation-
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Abstract: Abstract Abstract: We propose generalization of the spatial Simultaneous Autoregressive (SAR) model on a lattice towards modelling for asymmetry. Under the assumption of skew-normal error structure, expression for density and characteristic function for the induced distribution of response are obtained. Full-likelihood based implementation of the proposed model to a real data set is performed using Differential Evolution (DE). The relevant results are reported and compared with the results from existing models.
PubDate: 2023-02-01
- Classical and Bayesian Estimation of Entropy for Pareto Distribution in
Presence of Outliers with Application-
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Abstract: Abstract The measure of entropy has a pivotal role in the information theory area. In this paper, estimation of differential entropy for Pareto distribution in presence of r outliers is considered. In this regard, the classical and Bayesian estimation techniques of differential entropy are employed. In classical setup, we obtain the maximum likelihood estimators of the differential entropy as well as assessing their performance via a simulation study. The entropy Bayesian estimator is derived using squared error, linear exponential, weighted squared error and K loss functions. The Metropolis-Hastings algorithm is used to generate posterior random variables. Monte Carlo simulations are designed to implement the precision of estimates for different sample sizes and number of outliers. Furthermore, performance of estimates is planned by experiments with real data. Generally, we conclude that the entropy Bayesian estimates of simulated data tend to the true value as the number of outliers increases. Further, the entropy Bayesian estimate under weighted squared error loss function is preferable to the other estimates in majority of situations.
PubDate: 2023-02-01
- Maximum Likelihood Estimation of Parameters of a Random Variable Using
Monte Carlo Methods-
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Abstract: Abstract In a parametric estimation framework, this paper proposes different properties for the maximum likelihood estimators of unknown parameters of a given random variable having a known distribution, where different parameter estimation cases are studied. The Refined Descriptive Sampling (RDS) method is chosen to generate samples used for the estimation purpose. Then, we compare the RDS maximum likelihood estimators to their competitors provided by simple random samples with the same size and issued from the same distribution, through their Fisher information. Furthermore, the Maximum likelihood RDS mean is written as a function of its corresponding empirical estimator where the expression can be used to determine the estimator value when a refined descriptive sample is provided. All these results allow us to conclude that the proposed Maximum Likelihood Estimation (MLE) using refined descriptive samples is more efficient than that already obtained from simple random samples, which means that MLE using RDS has advantage in estimating parameters when the samples are not independent and identically distributed. Some Monte Carlo simulations are provided to validate the obtained theoretical results.
PubDate: 2023-02-01
- Stick-Breaking processes, Clumping, and Markov Chain Occupation Laws
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Abstract: Abstract We connect the empirical or ‘occupation’ laws of certain discrete space time-inhomogeneous Markov chains, related to simulated annealing, to a novel class of ‘stick-breaking’ processes, a ‘nonexchangeable’ generalization of the Dirichlet process used in nonparametric Bayesian statistics. To make this unexpected correspondence, we examine an intermediate ‘clumped’ structure in both the time-inhomogeneous Markov chains and the stick-breaking processes, perhaps of its own interest, which records the sequence of different states visited and the scaled proportions of time spent on them. By matching the associated intermediate structures, we identify the limits of the empirical measures of the time-inhomogeneous Markov chains as types of stick-breaking processes.
PubDate: 2023-02-01
- A General Theory of Three-Stage Estimation Strategy with Second-Order
Asymptotics and Its Applications-
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Abstract: Abstract We begin with a generic expression of an optimal fixed-sample-size n∗ which has an expression λg(ðœƒ) with λ > 0 and g(ðœƒ) > 0 where 𜃠is an unknown parameter. A consistent estimator of 𜃠is a sample mean of independent and identically distributed (i.i.d.) random variables. Under fairly relaxed set of conditions on g(.), we have developed a general theory of three-stage sampling strategy detailing requisite mathematical techniques for proving both asymptotic (as \(\lambda \rightarrow \infty \) ) first-order and second-order analyses. We believe that this theory is broad and rich especially since the technicalities developed are not tailored to fit a specific inference problem of choice. We have validated this sentiment with the help of illustrations which cannot be handled satisfactorily by improvising upon some of the existing methodologies. For example, (i) Illustration 1 proposes a three-stage strategy under Linex loss in a recently developed inference problem; (ii) Illustration 2 handles estimation of 𜃠in a Uniform(0,ðœƒ) distribution which obviously stays outside an exponential family; and (iii) Illustration 3 incorporates expressions of g(.) functions which no existing paper’s analyses could treat.
PubDate: 2023-02-01
- Nonparametric Recursive Estimation for Multivariate Derivative Functions
by Stochastic Approximation Method-
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Abstract: Abstract Important information concerning a multivariate data set, such as modal regions, is contained in the derivatives of the probability density or regression functions. Despite this importance, nonparametric estimation of higher order derivatives of the density or regression functions have received only relatively scant attention. The main purpose of the present work is to investigate general recursive kernel type estimators of function derivatives. We establish the central limit theorem for the proposed estimators. We discuss the optimal choice of the bandwidth by using the plug in methods. We obtain also the pointwise MDP of these estimators. Finally, we investigate the performance of the methodology for small samples through a short simulation study.
PubDate: 2023-02-01
- A Robust Bayesian Analysis of Variable Selection under Prior Ignorance
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Abstract: Abstract We propose a cautious Bayesian variable selection routine by investigating the sensitivity of a hierarchical model, where the regression coefficients are specified by spike and slab priors. We exploit the use of latent variables to understand the importance of the co-variates. These latent variables also allow us to obtain the size of the model space which is an important aspect of high dimensional problems. In our approach, instead of fixing a single prior, we adopt a specific type of robust Bayesian analysis, where we consider a set of priors within the same parametric family to specify the selection probabilities of these latent variables. We achieve that by considering a set of expected prior selection probabilities, which allows us to perform a sensitivity analysis to understand the effect of prior elicitation on the variable selection. The sensitivity analysis provides us sets of posteriors for the regression coefficients as well as the selection indicators and we show that the posterior odds of the model selection probabilities are monotone with respect to the prior expectations of the selection probabilities. We also analyse synthetic and real life datasets to illustrate our cautious variable selection method and compare it with other well known methods.
PubDate: 2023-02-01
- Correction to: The Pareto–Poisson Distribution: Characteristics,
Estimations and Engineering Applications-
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PubDate: 2023-01-12
- Families of Discrete Circular Distributions with Some Novel Applications
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Abstract: Abstract We give a unified treatment of constructing families of circular discrete distributions. Some of these families are deduced from established distributions such as von Mises and wrapped Cauchy. Some others are derived directly such as a flexible family based on trigonometric sums and the circular location family. Results interrelating these families are discussed. These distributions have been motivated by two examples of discrete circular data: casino roulette spins and smart health acrophase monitoring, and these data are analyzed using our proposed models. We discuss how using continuous circular models for circular discrete data can be misleading.
PubDate: 2022-11-22
DOI: 10.1007/s13171-022-00298-z
- Correction to: Inferences and Optimal Censoring Schemes for Progressively
First-Failure Censored Nadarajah-Haghighi Distribution-
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PubDate: 2022-10-06
DOI: 10.1007/s13171-022-00296-1
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