Abstract The occurrence of economic policies and other sudden and large shocks often bring out jumps in financial data, which can be characterized through continuous-time jump-diffusion model. In this paper, we will adopt convoluted smoothed approach to estimate unknown drift function of the potentially nonstationary diffusion models with jumps under high frequency sampling data. With Gaussian approximation

Abstract In this paper, we study the semi-functional partial linear regression for spatial data with considering a both parametric and nonparametric modeling. In this case we obtain the asymptotic normality of the parametric component, and probability convergence with rate of the nonparametric component under spatial dependency. Finally, the performance of the parametric and nonparametric estimators

Abstract Based on the approach of left and right kernel smoothing with unilateral kernel function, we, in this paper, define estimators of change point and jump size in nonparametric regression model with response missing at random. It is shown that the change point estimator is n-consistent and converges to the smallest maximizer of one-dimensional bilateral compound Poisson process, the jump size

Abstract Longitudinal count and time to event (TTE) data are often associated in some ways. Hence, using joint models for analyzing these data constitutes an attractive modeling framework which is applied in many different fields of statistics and clinical studies. Also, Accelerated Failure Time (AFT) models can be used for the analysis of TTE data to estimate the effects of covariates on acceleration/deceleration

Abstract The modified exponentially weighted moving average (MEWMA) control chart has been proposed in the literature in an effort to improve the performance of the classical EWMA chart. In this article, we study in more detail the MEWMA chart using various values of its additional design parameter and we also propose the double MEWMA (DMEWMA) chart for monitoring shifts in the process mean, under

Abstract We look into the nonparametric regression estimation with additive and multiplicative noise and construct adaptive thresholding estimators based on Laguerre series. The proposed approach achieves asymptotically near-optimal convergence rates when the unknown function belongs to Laguerre–Sobolev space. We consider the problem under two noise structures; (1) i.i.d. Gaussian errors and (2) long-memory

Abstract In mixture experiments, sometimes, there are some so-called collapse phenomena among its mixture components. In view of these collapse phenomena, we present a detailed discussion of the influence thereof on the response models and the structures of the corresponding optimal designs. In this paper, we first propose a set of concepts related to the collapse phenomena, including collapsed mixture

Abstract In this paper we propose a novel clustering method for functional data based on the principal curve clustering approach. By this method functional data are approximated using functional principal component analysis (FPCA) and the principal curve clustering is then performed on the principal scores. The proposed method makes use of the nonparametric principal curves to summarize the features

Abstract Repeated measurements designs (RMDs) are always economical but there may arise carry over effects which become the cause of biasedness. Carry over effects can be balanced out through balanced or strongly balanced RMDs. In this article, some new generators are presented to obtain some classes of efficient circular balanced RMDs which can also be converted into efficient circular strongly and

Abstract Nonignorable missing data presents a great challenge in statistical applications, since the observed likelihood is not identifiable without any further restrictions. In this paper, we make inference about the differences between the corresponding parameters of two independent samples with nonignorable missing renponse. To address the identifiability issue, we consider a parametric propensity

Abstract A single outlier sequence in which the distribution of the first observation differs from the others is considered and the properties of record statistics extracted from such sequence are studied. The problem of estimating the model parameters is discussed in the proportional hazard rate model. The maximum likelihood estimator and the uniformly minimum variance unbiased estimator are obtained

Abstract This paper explores possibilities of applying multiple comparison tests (MCTs) that are commonly used in statistics to group the means once the analysis of variance (ANOVA) procedure rejects the hypothesis that all the means are equal. It is proposed here to apply MCT procedure to perform clustering when the data are repetitive and multidimensional. Since MCT procedure may result in overlapping

Abstract In this paper, when the population is composed of several strata, we deal with the problem of stratified estimation for sensitive attribute by applying the stratified random sampling to the Yennum, Sedory, and Singh (2020 Yennum, N. , S. A.Sedory, and S.Singh . 2020. Improved strategy to collect sensitive data by using negative binomial and negative hypergeometric distribution as randomization

Abstract In this paper, we study the asymptotic distribution of the plug-in kernel density estimator of the Matusita's overlapping measure. By utilizing the convergence of functional of stochastic processes, we show, under certain conditions, that the asymptotic distribution of the plug-in kernel density estimator (KDE) of Matusita's overlapping measure is normal distribution. Also, a small simulation

Abstract Stripe truncation in the normal distribution is introduced such that the variable is truncated when it is located on several intervals like stripes. This truncation includes single, double and elliptical truncation as special cases. Then, the moments and absolute moments of arbitrary orders for the deviation of the truncated variable from an arbitrary reference point are derived using closed-form

Abstract This paper is concerned with the consistency of nonparametric regression model. For the weighted estimator of unknown regression function, the strong consistency, the complete consistency and the convergence rate of the complete consistency are investigated under some mild conditions. These results extend or improve the corresponding ones of Yang et al. (2018) for extended negatively dependent

Abstract In this article, we proved the almost sure central limit theorem for the maxima of two types of functions of stationary Gaussian sequence including chi-random sequence and Gaussian order statistics sequence, where the covariance function rn of the Gaussian sequence satisfies the condition r n   log   n (   log     log   n ) 1 + ε = O ( 1 ) for some ε > 0 .

Abstract The paper proves the Strong Law of Large Numbers for integral functionals of random fields with unboundedly increasing covariances. The case of functional data and increasing domain asymptotics is studied. Conditions to guarantee that the Strong Law of Large Numbers holds true are provided. The considered scenarios include wide classes of non stationary random fields. The discussion about

Abstract Sampling plans using the coefficient of variation (CV) attract increasing attention by many authors in the literature due to its importance to measure the product quality. A generalized multiple dependent state (GMDS) sampling plan for accepting a lot is proposed based on the coefficient of variation when a quality characteristic comes from a normal distribution. The optimal plan parameters

Abstract We introduce and study a local linear nonparametric regression estimator for censorship model. The main goal of this paper is, to establish the uniform almost sure consistency result with rate over a compact set for the new estimate. To support our theoretical result, a simulation study has been done to make comparison with the classical regression estimator.

Abstract The ratio, product, difference estimators, and unbiased estimator under systematic sampling scheme has been studied in the presence of measurement error. The methods of estimation have been proposed for the estimation of the finite population mean. To exhibit the effect of measurement error, the study variable and auxiliary variable are supposed to be observed with measurement error. The properties

Abstract This article considers an one-unit multi-state system with a general α-series process and an order-replacement policy. It is supposed that the working times of the system after repair become shorter and shorter, while the repair times of the system become longer and longer. Further, an ordering policy N − 1 and a replacement policy N is adopted. After the Nth repair, the system is replaced

Abstract Dual Response Surface Methodology is a powerful tool for simultaneously optimizing the mean and the variance of a quality characteristic in the field of quality engineering. The optimization of dual response systems to achieve better quality has played a major role in the design of industrial products and processes. In this paper we suggest using a process capability index - Cpk - as the objective

Abstract We introduce the global recovery time of Gaver’s parallel system supervised by a safety unit. The entire system is attended by two heterogeneous repairmen. Our methodology is based on the theory of sectionally holomorphic functions combined with the notion of dual transforms. As an application, we consider the particular case of Coxian distributions.

Abstract In this article, we propose several statistics to conduct goodness-of-fit tests for Rayleigh distribution based on progressively Type-II censored data, where a cumulative entropy and its upper and lower bounds as well as the sample spacings are used respectively, and the corresponding statistics are denoted by TE , TU , TL and TS . Especially, the null distribution of TS test statistic is

Abstract In addition to entropy, extropy - the complementary dual of entropy has also gained importance as a measure of information in many areas. Extropy of order statistics, record values and mixed systems, residual extropy properties of k record values, past extropy have been extensively studied in literature. In this paper, we propose length (size) biased shift dependent measures of uncertainty

Abstract The main purpose of this work is to introduce and examine the concept of (λ,f)-statistical boundedness of order α and give the relations between some known concepts and (λ,f)-statistical boundedness of order α.

Abstract We consider a stochastic differential equation of the form d r t = ( a − b r t ) d t + σ r t d W t , where a, b and σ are positive constants. The solution corresponds to the Cox–Ingersoll–Ross process. We study the estimation of an unknown drift parameter (a, b) by continuous observations of a sample path { r t , t ∈ [ 0 , T ] } . First, we prove the strong consistency of the maximum likelihood

Abstract We consider estimation of the scale parameter of an exponential distribution with unknown location under an arbitrary strictly convex loss function when samples are progressive type II censored. Stein-type procedures, improving upon the minimum risk equivariant (MRE) estimator, are obtained and illustrated upon using quadratic and entropy loss functions. We also study a class of improving

Abstract In this paper, we introduce the concept of l-order and conjecture that the l-order of hazard rate vectors of components implies the likelihood ratio order of parallel systems. We prove this conjecture when the number of components is no more than 5.

Abstract Predicting the future contagion of infectious diseases depends on the ability to estimate the current number of cases of infection. In this paper, a full smoothing method is proposed to evaluate the number of daily new cases of infection during the epidemic period. Under mild regularity assumptions, we obtain the consistency and asymptotic normality of the resulting estimator. Both simulated

Abstract In this paper, the uniformly asymptotic normality for sample quantiles of associated random variables is investigated under some conditions on the decay of the covariances. We obtain the rate of normal approximation of order O ( n − 1 / 2   log   2 n ) if the covariances decrease exponentially to 0. The best rate is shown as O ( n − 1 / 3 ) under a polynomial decay of the covariances.

Abstract In this study, a quasi-renewal process model with δ-shock is analyzed for a degenerative repairable supply chain with a single supplier source. The supplier of the supply chain system encounters shocks due to crisis events and, as a consequence, tends to fail if the interarrival time between two successive shocks is less than a random threshold. The non negligible repair time of the supplier

Abstract Motivated by the works of Irwin and Rodríguez-Avi et al., a destructive Waring regression cure model is developed here. This model enables the patients to be protagonists for the treatment and also facilitates an understanding of the nature of overdispersion of competing risk factors to prevent higher risk of the event of interest. The cure rate and the destructive mechanism (immune system)

Abstract In this paper, we study the hypothesis test for regression coefficients of partially linear models when the number of covariates in the linear part diverges. We propose a U-type test statistic. Asymptotic properties of the proposed test statistic are derived under null and local alternative on mild conditions. Extensive numerical examples are presented to demonstrate the advantages of the

Abstract In this paper, we explore the optimal insurance problem where the exclusion clause is taken into account. Assume that the insurable loss is mutually exclusive from another loss that is denied in the insurance coverage. Our objective is to characterize the optimal insurance strategy by minimizing the risk-adjusted value of a policyholder’s liability, where the unexpected loss is calculated

Abstract This paper develops a method to calculate the moments of statistical ratios as functionals of Bernoulli random variables via inverse moments of binomial distributions. We derive exact expressions for the mean, bias and variance formulas of several statistics, including the “modified” versions of the odds ratio and relative risk as well as the (positive) false discovery proportion (FDP), in

(2021). Statement of Retraction. Communications in Statistics - Theory and Methods: Vol. 50, No. 1, pp. 249-249.

Abstract In this article, we study the optimal investment and reinsurance problem involving a defaultable security for a group which holds shares of both an insurance company and a reinsurance company. Assuming that the claim process is described by a Brownian motion with drift, and the insurer can purchase proportional reinsurance and invest in a financial market consisting of a risk-free asset, a

Abstract A control chart is used to monitor longitudinal measurements of a quality characteristic and detects undesirable causes of variability. In practice, measurement error may exist and deteriorate the detection capability of a control chart. This paper focuses on the effect of measurement errors on the performance of a joint monitoring scheme for mean and coefficient of variation (CV), which is

Abstract The probability distributions that statistical methods use to represent uncertainty fail to capture all of the uncertainty that may be relevant to decision making. A simple way to adjust probability distributions for the uncertainty not represented in their models is to average the distributions with a uniform distribution or another distribution of maximum uncertainty. A decision-theoretic

Abstract This study investigates the process for estimating the mean number of individuals having rare sensitive attribute in stratified random sampling as well as in stratified random double sampling using Poisson distribution. The properties of the suggested estimation procedures are deeply examined. Empirical studies are performed to support the theoretical results, which show the dominance of the

Abstract The variance of the log-likelihood function, which is called varentropy, is a measure of the concentration of information content around the Shannon entropy. This measure is widely applied in finite blocklength information theory and data compression. On the other hand, in the field of statistics, this measure has been used as an alternative of the kurtosis measure for continuous density functions

Abstract Prakasa Rao (Sankhya, Series A (1987) 49 199–206) studied characterization of probability distributions by linear functions of independent random variables defined on a homogeneous Markov chain. These results are now extended to Q-independent random variables. It is known that independence implies Q-independence but the converse is not true.

Abstract We consider the Jeffreys-Lindley paradox from an objective Bayesian perspective by attempting to find priors representing complete indifference to sample size in the problem. This means that we ensure that the prior for the unknown mean and the prior predictive for the t-statistic are independent of the sample size. If successful, this would lead to Bayesian model comparison that was independent

Abstract In this paper, we model the daily volatility curve as a realization of functional data. We implement the spline technique to estimate the mean and covariance functions. Uniform convergence of the estimated mean and covariance functions are established. Simulation and real data studies justify that our estimation of the mean and covariance functions is accurate.

Abstract In this paper, a survival study across regions is designed by considering the relationship between the hazard time and the treatment effect with unrecognized heterogeneity which interacts with treatment. The log-rank test is employed for the unrecognized heterogeneity and its interaction with the treatment effect. The test statistic for the overall treatment effect is used to calculate the

Abstract A new method for constructing absolutely continuous two-dimensional copulas by differential equations is presented. The copulas are symmetric with respect to reflection in the opposite diagonal. The support of the copula density may be prescribed to arbitrary opposite symmetric hypographs of invertible functions, containing the diagonal. The method is applied to toxicological probit modeling

Abstract Zero-inflated models have become a popular tool for assessing relationships between explanatory variables and a zero-inflated count outcome. In these models, regression coefficients have latent class interpretations, where latent classes correspond to a susceptible subpopulation with observations generated from a count distribution and a non susceptible subpopulation that provides only zeros

Abstract This paper considers the change-point problem for finite sequences of networks. To avoid the difficulty of computing the normalization coefficient in the models such as Exponential Random Graphical Model (ERGM) and Markov networks, we construct a finite measure space with measure ratio statistics. A new performance measure of detection delay is proposed to detect the changes in distribution

Abstract In this paper, we propose a nonparametric Bayesian approach for Lindsey and penalized Gaussian mixtures methods. We compare these methods with the Dirichlet process mixture model. Our approach is a Bayesian nonparametric method not based solely on a parametric family of probability distributions. Thus, the fitted models are more robust to model misspecification. Also, with the Bayesian approach

Abstract Due to its flexibility, a partially linear single-index model arises in many contemporary scientific endeavors. In this paper, we set foot on its inference under settings of panel data and a serially correlated error component structure. By combining the local polynomial technique with the bias-corrected generalized estimating equations, we propose a feasible weighted generalized estimating

Abstract Record linkage is the process of matching together records from different data sources that belong to the same entity. Record linkage is increasingly being used by many organizations including statistical, health, government etc. to link administrative, survey, and other files to create a robust file for more comprehensive analysis. Therefore, it becomes necessary to assess the ability of

Abstract The extropy is a measure of information introduced as dual to entropy. It is a shift-independent information measure just as the entropy. We introduce here the notion of weighted extropy, a shift-dependent information measure which gives higher weights to larger values of random variables. We also study the weighted residual and past extropies as weighted versions of extropy for residual and

Abstract We introduce a new model for sums of exchangeable binary random variables. The proposed distribution is an approximation to the exact distributional form, and relies on the theory of completely monotone functions and the Laplace transform of a gamma distribution function. Using Monte Carlo methods, we show that this new model compares favorably to the beta-binomial model with respect to estimating

Abstract In this paper, we propose a non parametric functional estimator for diffusion coefficient in integrated stochastic diffusion process. The asymptotic bias of the kernel type estimator and the new proposed non parametric estimator for diffusion coefficient are developed when the time span is fixed, and we can see that the new non parametric estimator has a smaller asymptotic bias than the kernel

Abstract We consider n risks X 1 , X 2 , … , X n insured by a layer coverage with deductibles and limits given by ( d 1 , l 1 ) , … , ( d n , l n ) , respectively. We investigate the optimal allocation of insurance layers from the viewpoint of the insurer. We derive lower and upper bounds for the survival function of the smallest and largest claim amounts using the first stochastic dominance order

Abstract In this article, we compare the efficiency of the traditional Mean-Variance (MV) portfolio model proposed by Markowitz with the models which incorporate diverse information theoretic measures such as Shannon entropy, Renyi entropy, Tsallis entropy, and two-parameter Varma entropy. We put these measures as the objective function of the portfolio optimization problem with constraints derived

Abstract The binomial formula which was given by Cox et al. is a tool for valuating the European call option. We know that it converges to the Black–Scholes formula which was given by Black and Scholes as the number of periods (n) converges to infinity. In 1988, Boyle introduced the trinomial formula to be another tool for calculating the European call option. In 2013, Entit et al. considered the trinomial

Abstract Cumulative probability models are standard tools for analyzing ordinal response data. The cumulative probability models can however be very restrictive in practice because of the inherent homogeneous assumption. In this work we propose a new Bayesian model to analyze ordinal data collected in statistically designed experiments. In the proposed model, we assume that the intercepts on the latent