|
|
- Metropolis Algorithm Based Bayesian Analysis of a Competing Risk Data
Using Copula-Frailty Model-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract Competing risks can play a significant role in the design and analysis of critical intelligent systems which experience several risks of failure but actually fail due to a single cause that occurs first. The failure time of various components of these systems may be correlated as one failure may lead to another. In order to model such a dependence structure, copula models and frailty models have been developed for such competing risk data. The frailty term is used to describe the underlying heterogeneity among the units and the copula function is utilized to represent the dependence between the failure times. A Bayesian analysis using the Weibull distribution as the underlying failure time distribution to describe the competing risk data is carried out. The paper also considers some other models and compares them using a few standard Bayesian model comparison tools. Lastly, a real data set is studied to illustrate the proposed Bayesian approach.
PubDate: 2024-12-01
- Stochastic Comparisons for Series and Parallel Systems with Heterogeneous
Power Lomax Component Lifetimes-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract The present communication provides a comparison between the lifetimes of the series and the parallel systems with independent heterogeneous power Lomax ($$\mathcal{PL}$$) component lifetimes with respect to the usual stochastic ordering and the reversed hazard rate ordering. The sufficient conditions for the comparison of the lifetimes of two series systems have been developed when the heterogeneity is assumed in two model parameters. In addition, the reversed hazard rate ordering between the lifetimes of the parallel systems for multiple-outlier models have been established. Various examples and counterexamples have been presented to illustrate the theoretical establishments.
PubDate: 2024-12-01
- Polynomial Eulerian Shape Distributions
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract In this paper a new approach is derived in the context of shape analysis. The so called polynomial Eulerian shape theory solves an open problem proposed in [27] about the construction of certain shape density involving Euler hypergeometric functions of matrix arguments. The associated distribution is obtained by a connection between the required shape invariants and a known result on canonical correlations published in 1963. As usual in matrix variate statistical shape theory, the densities are expressed in terms of infinite series of zonal polynomials. However, if we consider certain parametric subspace for the parity of the number of landmarks, the computational problem can be solved analytically by deriving the Eulerian matrix relation of two matrix arguments. Under that restriction, the analysis of classical landmark data is based on polynomial distribution with small degree. Finally, a methodology to compare Eulerian shape and landmark discrimination under equivalent classes is proposed and applied in machine vision.
PubDate: 2024-12-01
- Nonparametric Predictive Inference for Two Future Observations with
Right-Censored Data-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract In reliability and survival analyses, right-censored observations are common. This type of data occurs when an event of interest is not fully observed during an experiment and there is no information provided about a random quantity, except that it exceeds a certain value. Nonparametric Predictive Inference (NPI) is a frequentist statistical method that relies on only few assumptions. It quantifies uncertainty by using imprecise probabilities based on Hill’s assumption $$A_{(n)}$$ and focuses specifically on future observations. NPI has been developed for various types of data, including right-censored data, for some inferences such as multiple group comparisons, uncertainty quantification of the survival function, and in the context of competing risks. However, NPI with right-censored data has only considered a single future observation. This paper aims to extend this method by considering two future observations and taking into account that in the NPI approach, such multiple future observations are not conditionally independent given the data. Specifically, we present NPI lower and upper probabilities for the event that both future observations are greater than a particular time. Examples are provided for illustration and an application to system reliability is presented.
PubDate: 2024-12-01
- The $$k$$-Nearest Neighbour Local Linear Estimation of the Conditional
Hazard Function in High-Dimensional Statistics-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract Local linear fitting has demonstrated several convincing statistical properties, especially in multivariate analysis. However, with the increasing importance of functional data analysis in the field of data science, local polynomials have become a significant focus in this research area. This paper focuses on estimating of the conditional hazard function of a scalar response variable with a functional random variable. A novel estimator is proposed by combining the $$k$$-nearest neighbors ($$k$$-NN) procedure with the local linear approach. The resulting estimator has many advantages from the two approaches (kNN and LLE methods). This is supported by the established asymptotic normality with explicit rates of the constructed estimator. As an application, the asymptotic con-fidence bands for the conditional hazard model based on the $$k$$-Nearest Neighbors Local Linear Estimator is presented. A simulation study, conducted to assess finite sample behavior, demonstrates the superiority of our new estimator than the classical kernel method.
PubDate: 2024-12-01
- Orderings Properties of Parallel Systems with Components Having Additive
Hazard Rates and Starting Devices-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract In this paper, we consider stochastic comparisons of parallel systems with additive hazard rate (AH) distributed components equipped with starting devices. By considering parallel systems with two components and starting devices, we prove the hazard rate and reversed hazard rate orders. These results are then generalized for such parallel systems with $$n$$ components in terms of usual stochastic order. The establish results are illustrated with some examples.
PubDate: 2024-12-01
- Inverse Problems to Estimate Market Price of Risk in Catastrophe Bonds
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract This research focuses on evaluating the market price of risk for catastrophe bonds (CAT bonds). Our approach involves constructing a model for CAT bonds that incorporates stochastic process interest rates and losses, followed by numerical methods. Recognizing the inherent challenge of directly obtaining the market price of risk from the market, we utilize inverse problems to derive it. Our assumptions include the CIR stochastic process model for the interest rates and the jump-diffusion stochastic process model for the loss. Through the analysis of a risk-free portfolio, we illustrate the alignment of CAT bonds with partial integral differential equations (PIDE). Employing inverse problems, we then estimate the market price of risk by solving the PIDE. Specifically, we implement Tikhonov regularization and propose a systematic method for determining the market price of risk.
PubDate: 2024-09-01
- On Estimation and Prediction in a Spatial Semi-Functional Linear
Regression Model with Derivatives-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract In this paper, we tackle estimation and prediction at non-vistedsites in a spatial semi-functional linear regression model withderivatives that combines a functional linear model with anonparametric regression one. The parametric part is estimated bya method of moments and the other one by a local linear estimator.We establish the convergence rate of the resulting estimators andpredictor. A simulation study and an application to ozonepollution prediction at non-visited sites are proposed toillustrate our results.
PubDate: 2024-09-01
- Doubly Generalized Yule Distribution of Order k and Its Applications
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract Recent statistical work has focused a lot on order k variations of discrete probability distributions and related generalizations. By referring to the generalized Yule distribution as the ‘‘doubly generalized Yule distribution’’ (DGYD), [19] obtained the distribution and described numerous uses for it. Through the development of an order k version of the DGYD and discussion of some of its key characteristics, including mean, variance, formulas for its probability generating function (p.g.f. ), recursion equations for its probabilities, raw moments, and factorial moments, we hope to advance the field. Additionally, we tried to estimate the parameters of this model using the maximum likelihood method. For the purpose of demonstrating the distribution’s applicability, it has been fitted to a few real-world data sets. A simulation study is done to assess the effectiveness of the maximum likelihood estimators, and the likelihood ratio test process is used to determine the relevance of the parameters.
PubDate: 2024-09-01
- Copula-Based Mutual Information Measures and Mutual Entropy: A Brief
Survey-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract The notion of divergence is often used to measure the separation between two parametric densities with possible applications on differential geometry to problems of parametric inference among others. Among them, in this paper, we discuss several popular divergence (alias pseudo-distance) measures such as the power divergence, Kullback–Leibler information, J-divergence, Hellinger distance, Bhattacharya divergence, $$\alpha$$-divergence, and so on. A wide range of discussion in terms of properties, relationship among these measures, and results related to distance between two probability distributions are derived via copula functions. In addition, several dependency concepts such as weak negative dependence etc. are visited in terms of copula based divergence measures and important inequalities are obtained.
PubDate: 2024-09-01
- Extensions of True Skewness for Unimodal Distributions
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract A 2022 paper [7] introduced the notion of true positive andnegative skewness for continuous random variables via Fréchet$$p$$-means. In this work, we find novel criteria for true skewnessand establish true skewness for the Weibull, Lévy, andskew-normal distributions. Furthermore, some relevant propertiesof the $$p$$-means of random variables are established.
PubDate: 2024-09-01
- Estimation of Multiple Delays in a Stochastic Dynamical System
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract The present study aims primarily to address the issue of estimating the delay parameters in a dynamical system that is subjected to small noise, using the maximum likelihood method. Our investigation focuses mainly on the asymptotic properties, namely consistency, asymptotic normality, and asymptotic efficiency, of the estimator utilized.
PubDate: 2024-09-01
- On Aggregation of Uncensored and Censored Observations
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract In survival analysis a random right-censoring partitions data into uncensored and censored observations of the lifetime of interest. The dominance of uncensored observations is a familiar methodology in nonparametric estimation motivated by the classical Kaplan–Meier product-limit and Cox partial likelihood estimators. Nonetheless, for high rate censoring it is of interest to understand what, if anything, can be done by aggregating uncensored and censored observations for the staple nonparametric problems of density and regression estimation. The oracle, who knows distribution of the censoring lifetime, can use each subsample for consistent estimation and hence may shed light on the aggregation. The oracle’s asymptotic theory reveals that density estimation, based on censored observations, is an ill-posed problem with slower rates of risk convergence, the ill-posedness occurs in frequency-domain, its severity increases with frequency, and accordingly a special aggregation on low frequencies may be beneficial. On the other hand, censored observations are not ill-posed for nonparametric regression and the aggregation is feasible. Based on these theoretical results, methodology of aggregation in frequency domain is developed and proposed estimators are tested on simulated and real examples.
PubDate: 2024-06-01
- Estimation of Parameters of Misclassified Size Biased Uniform Poisson
Distribution and Its Application-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract Statistical data analysis is of great interest in every field ofmanagement, business, engineering, medicine, etc. At the time ofclassification and analysis, errors may arise, like aclassification of observation in the other class instead of theactual class. All fields of science and economics have substantialproblems due to misclassification errors in the observed data. Dueto a misclassification error in the data, the sampling process maynot suggest an appropriate probability distribution, and in thatcase, inference is impaired. When these types of errors areidentified in variables, it is expected to consider the problem’ssolution regarding classification errors. This paper presents thesituation where specific counts are reported erroneously asbelonging to other counts in the context of size biased UniformPoisson distribution, the so-called misclassified size biasedUniform Poisson distribution. Further, we have estimated theparameters of misclassified size biased Uniform Poissondistribution by applying the method of moments, maximum likelihoodmethod, and approximate Bayes estimation method. A simulationstudy is carried out to assess the performance of estimationmethods. A real dataset is discussed to demonstrate thesuitability and applicability of the proposed distribution in themodeling count dataset. A Monte Carlo simulation study ispresented to compare the estimators. The simulation results showthat the ML estimates perform better than their correspondingmoment estimates and approximate Bayes estimates.
PubDate: 2024-06-01
- Asymptotic Properties of Extrema of Moving Sums of Independent
Non-identically Distributed Variables-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract In this work, we discuss the asymptotic behavior of minima and maxima of moving sums of independent and non-identically distributed random variables. We first establish some theoretical results associated with the asymptotic behavior of minima and maxima. Then, we apply these results to exponential and normal models. We also derive strong limit results for the minima and maxima of moving sums taken from these two models.
PubDate: 2024-06-01
- Rates of the Strong Uniform Consistency with Rates for Conditional
U-Statistics Estimators with General Kernels on Manifolds-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract $$U$$-statistics represent a fundamental class of statistics from modeling quantities of interest defined by multi-subject responses. $$U$$-statistics generalize the empirical mean of a random variable $$X$$ to sums over every $$m$$-tuple of distinct observations of $$X$$. Stute [103] introduced a class of so-called conditional $$U$$-statistics, which may be viewed as a generalization of the Nadaraya-Watson estimates of a regression function. Stute proved their strong pointwise consistency to: $$r^{(k)}(\varphi,\tilde{\mathbf{t}}):=\mathbb{E}[\varphi(Y_{1},\ldots,Y_{k}) (X_{1},\ldots,X_{k})=\tilde{\mathbf{t}}]\quad\textrm{for}\quad\tilde{\mathbf{t}}=\left(\mathbf{t}_{1},\ldots,\mathbf{t}_{k}\right)\in\mathbb{R}^{dk}.$$ In the analysis of modern machine learning algorithms, sometimes we need to manipulate kernel estimation within the nonconventional setting with intricate kernels that might even be irregular and asymmetric. In this general setting, we obtain the strong uniform consistency result for the general kernel on Riemannian manifolds with Riemann integrable kernels for the conditional $$U$$-processes. We treat both cases when the class of functions is bounded or unbounded, satisfying some moment conditions. These results are proved under some standard structural conditions on the classes of functions and some mild conditions on the model. Our findings are applied to the regression function, the set indexed conditional $$U$$-statistics, the generalized $$U$$-statistics, and the discrimination problem. The theoretical results established in this paper are (or will be) key tools for many further developments in manifold data analysis.
PubDate: 2024-06-01
- Stochastic Comparisons of the Smallest Claim Amounts from Two
Heterogeneous Portfolios Following Exponentiated Weibull Distribution-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract In actuarial science, it is often of interest to compare stochastically smallest claim amounts from heterogeneous portfolios. In this paper, we obtain the usual stochastic order between the smallest claim amounts when the matrix of parameters $$(\boldsymbol{\alpha}$$, $$\boldsymbol{\lambda})$$ changes to another matrix in terms of chain majorization order. By using the Archimedean copula and weak majorization conceptions, we also obtain some conditions for comparison of smallest claim amounts in terms of usual stochastic order.
PubDate: 2024-06-01
- Functional Uniform-in-Bandwidth Moderate Deviation Principle for the Local
Empirical Processes Involving Functional Data-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: 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-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: 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
- Assessing Monotonicity: An Approach Based on Transformed Order Statistics
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: 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
|
Hybrid journal (It can contain Open Access articles)
