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In this paper, we apply conformal prediction to time series data. Conformal prediction is a method that produces predictive regions given a confidence level. The regions outputs are always valid under the exchangeability assumption. However, this assumption does not hold for the time series data because there is a link among past, current, and future observations. Consequently, the challenge of applying conformal predictors to the problem of time series data lies in the fact that observations of a time series are dependent and therefore do not meet the exchangeability assumption. This paper aims to present a way of constructing reliable prediction intervals by using conformal predictors in the context of time series. We use the nearest neighbors method based on the fast parameters tuning technique in the weighted nearest neighbors (FPTO–WNN) approach as the underlying algorithm. Data analysis demonstrates the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The paper deals with the estimation methodology for the α-stable periodic autoregressive (PAR) models. For the classical (Gaussian) PAR time series is cyclostationary systems the periodicity is manifested in the model characteristics. One of the most common characteristics used in this context is the autocovariance function. One of the methods of the PAR model estimation utilizes the Yule-Walker equations that contain the autocovariance function of the given process. However, for the infinite variance version of the PAR model (i.e., α-stable-distributed) it is expected that the autocovariance function is not properly defined. Thus, alternative measures need to be used. In this paper, we present the general idea of the modified Yule-Walker equations for the considered model. It is proposed to replace the classical dependency measure by the dependency measures properly defined for infinite variance models. We demonstrate two possible modifications based on the covariation and fractional lower order covariance. The first approach was recently proposed in the literature while the latter is a novel algorithm. We compare the effectiveness of both estimation methods for the considered model. Finally, the results are compared with the classical Yule-Walker approach. We demonstrate the limitations of the classical method for the considered model. The possible application for real data analysis is demonstrated. [ABSTRACT FROM AUTHOR]

To avoid the expensive quadratic programming in the L2-loss support vector regression (SVR) model, smooth approximation and iteratively reweighted least square (IRLS) techniques were introduced in literature, resulting in smoothed SVR (SSVR) and IRLS-SVR. However, for nonlinear models, SSVR and IRLS-SVR both involve operations with matrices and vectors of the same size as the training set. Thus, as the training set becomes large, nonlinear SSVR and IRLS-SVR both need long training time and large memory. To further alleviate the training cost, this paper projects the original data into a low dimensional space via random Fourier feature. The inner product of the random Fourier features of two data points is approximately the same as the kernel function evaluated at these two data points. Hence, it is possible to use a linear model in the new low dimensional space to approximate the original nonlinear model, and consequently the time/memory efficient linear training algorithms could be applied. This paper applies the idea of random Fourier features to nonlinear SSVR and IRLS-SVR, and our testing results on real-world datasets show that, the introduction of random Fourier features makes SSVR and IRLS-SVR achieve similar prediction accuracy as the original nonlinear version with substantially higher time efficiency. [ABSTRACT FROM AUTHOR]

This paper investigates the availability of a system incorporating uncertainty in the inspection period, including multiple failure modes (FMs). We decrease or increase the inspection period depending on the occurrence or nonoccurrence of system failure during any particular inspection, i.e. if, during an inspection, a defect is detected, we reduce the inspection period for the next inspection, and if no defect is found, we increase the inspection period. Also, the proposed model is examined under a pre-defined critical repair time incorporating the Gumbel-Hougaard copula. This paper considers a repairable system having α number of FMs. Random failure times are associated with every single FM, and whenever the system collapses from the ath FM, a subsequent corrective repair is conducted, which requires a random amount of time ψ a (a = 1, 2,..., α). Then the point and long-run availability of the proposed model are derived, and a sensitivity analysis is done to examine how inspection time affects the system's availability. Additionally, the system's average long-run cost rate is analyzed, and the model is employed to determine the optimal inspection period that optimizes the system's ALRCR. Lastly, the results are verified via a numerical illustration of a power transformer. [ABSTRACT FROM AUTHOR]

The intraclass correlation coefficient ρ is used as a measure of the degree of resemblance among family members with respect to some biological or psychological attribute, such as blood pressure level or IQ. Many studies have been done in the area. However, a significant gap in the literature is that few statistics are available to test the significance ( H 0 : ρ = 0 against H A : ρ ≠ 0 ) of this important biological measure and no study is available as to the performance of these statistics with respect to level and power. In this paper we develop three large sample test statistics and compare these, in terms of level and power, using extensive simulation studies of these, the Wald test developed in this paper is found to have a very simple form and highest power while maintaining level well. [ABSTRACT FROM AUTHOR]

AbstractIn the present paper, we provide the density-mass functions of record times and values obtained from samples of independent and non-identically distributed random variables. By making use of these density-mass functions, we then present a record generation algorithm for the non-identical case. This algorithm was first proposed in the paper of S. A. Petukhov and A. V. Stepanov (2023) Generation of records obtained from sequences of independent and non-identically distributed random variables. Vestnik St. Petersburg University, Mathematics 56 (4):540–8 in a more complicated form. The algorithm applies the Markovian property of records, which is known in the case when the initial observations are independent and identically distributed and which extends to the non-identical case. Later in the paper, we test the proposed algorithm by conducting simulation experiments with exponential and normal variables. [ABSTRACT FROM AUTHOR]

In this paper we propose a new nonparametric regression technique under multiplicative distortion measurement errors settings. The unobservable variables are both distorted in a multiplicative fashion by an observed confounding variable. A bias reduction is proposed by choosing a function that is the projection of the unknown regression function onto the parametric family in a certain metric. We find that this new technique leads to substantial improvement in the performance of regression estimators in comparison with the direct one-step estimation, irrespective of the choice of a parametric model. We obtain asymptotic normality results for the estimated nonparametric kernel smoothers, and further discuss their estimation efficiency. We conduct Monte Carlo simulation experiments to examine the performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

Machine Learning Models are known to understand the intricacies of the data well, but native ML models cannot be used in time-to-event analysis due to censoring. In this paper, we explore the use of Machine Learning Models in the field of Survival Analysis using right censored Heart Failure Clinical Records Dataset. For this purpose, we first identify the top most important features responsible for death due to heart failure using Recursive Feature Elimination and then see how Machine Learning models can be adapted to improve the time-to-event analysis outcomes. To deal with this, Machine Learning Models are modified using the techniques Inverse Probability of Censoring Weighting (IPCW) and IPCW Bagging and are trained using the processed dataset alongside various survival analysis models. Area Under the time-dependent ROC (AUC) is used as a performance metric. The results reveal that the average AUC value for Survival Analysis Models is 0.51 while that of Machine Learning Models processed using IPCW increased to 0.80, and those processed using IPCW Bagging increased by 0.82. This reflects that Machine Learning models outperform Survival Analysis models in the case of time-to-event analysis of right censored dataset, and hence, are better indicators of risk of heart disease. [ABSTRACT FROM AUTHOR]

There have been some advances in multivariate control charts in recent years. This paper presents a new simultaneous scheme for monitoring both the mean and variability of a multivariate normal process in a single chart, which is developed by improving and modifying another recently proposed scheme. We not only propose a new control scheme but also make it adaptive by varying all control chart parameters. Our scheme, for the first time, considers the process variability in two forms: "covariance matrix" and "multivariate coefficient of variation (MCV)". This scheme, again for the first time, considers simultaneous monitoring of the MCV with another process parameter (in our case, the mean vector). In addition, we develop a Markov chain model to compute the average run length and average time to signal values. We conduct extensive numerical analyses to measure the performance of the proposed scheme in two scenarios of process variability. At last, we present a numerical example by using a real dataset from a healthcare process to illustrate how the scheme can be implemented in practice. [ABSTRACT FROM AUTHOR]

Linear Mixed Effects (LME) models have been widely applied in clustered data analysis in many areas including marketing research, clinical trials, and biomedical studies. Inference can be conducted using maximum likelihood approach if assuming Normal distributions on the random effects. However, in many applications of economy, business and medicine, it is often essential to impose constraints on the regression parameters after taking their real-world interpretations into account. Therefore, in this paper we extend the classical (unconstrained) LME models to allow for sign constraints on its overall coefficients. We propose to assume a symmetric doubly truncated Normal (SDTN) distribution on the random effects instead of the unconstrained Normal distribution which is often found in classical literature. With the aforementioned change, difficulty has dramatically increased as the exact distribution of the dependent variable becomes analytically intractable. We then develop likelihood-based approaches to estimate the unknown model parameters utilizing the approximation of its exact distribution. Simulation studies have shown that the proposed constrained model not only improves real-world interpretations of results, but also achieves satisfactory performance on model fits as compared to the existing model. [ABSTRACT FROM AUTHOR]

Clustered bivariate survival data arise in various fields, such as biology and medicine, when individuals in a dataset are clustered and exhibit two survival outcomes. Recently, the joint frailty-copula model was proposed to analyze clustered bivariate survival outcomes by accommodating the between-cluster heterogeneity via a shared frailty term. In this model, researchers fitted the baseline hazard functions via the nonparametric model, the spline model, or the Weibull model. However, when a population has extremely large survival time, the baseline hazard functions are better modeled by a heavy-tailed distribution. In this paper, we adopt the Pareto type I distribution for the joint frailty-copula model, which is one of the most popular heavy-tailed distributions. We show that the moments of the Pareto type I joint frailty copula model diverge to infinity owing to the heavy right-tail. We develop statistical inference methods based on three types of censoring schemes: (i) bivariate random censoring, (ii) semi-competing risks, and (iii) competing risks. We develop maximum likelihood estimation procedures, and make our computational tools available for users. Simulations are performed to check the accuracy of the proposed method. We finally analyze a real dataset for illustration. [ABSTRACT FROM AUTHOR]

Large-scale multiple testing with correlated tests and auxiliary statistics arises in a wide range of scientific fields. Conventional multiple testing procedures largely ignored auxiliary information, such as sparsity information, and the dependence structure among tests. This may result in loss of testing efficiency. In this paper, we propose a procedure, called multivariate local index of significance (mvLIS) procedure, for large-scale multiple testing. The mvLIS procedure can not only characterize local correlations among tests via a Markov chain but also incorporates auxiliary information via multivariate statistics. We present that the oracle mvLIS procedure is valid, namely, it controls false discovery rate (FDR) at the pre-specified level, and show that it yields the smallest false non-discovery rate (FNR) at the same FDR level. Then a data-driven mvLIS procedure is developed to mimic the oracle procedure. Comprehensive simulation studies and a real data analysis of schizophrenia (SCZ) data are performed to illustrate the superior performance of the mvLIS procedure. Moreover, as a byproduct that is of independent interest, we generalize the single-index modulated (SIM) multiple testing procedure, which embeds prior information via 2-dimensional p-values, to allow for d-dimensional ( d ≥ 3 ) statistics in multiple testing. The detailed extension is deferred to Discussion. [ABSTRACT FROM AUTHOR]

The coefficient of variation (CV) is one of the most important quality characteristics in industrial applications. There have been some control charts for monitoring this dimensionless and normalized characteristic. This paper presents three double exponentially weighted moving average (DEWMA) charts for monitoring the CV. Many numerical simulations are performed and the results are given in several tables to show the properties of the proposed DEWMA CV charts. Through comparisons with other existing exponentially weighted moving average (EWMA) CV charts using the average run length (ARL) metric, it is shown that the proposed DEWMA CV charts perform better than the existing EWMA CV charts for small shifts, especially when the smoothing parameter increases. In addition, a detailed comparison among the proposed three DEWMA CV charts is also presented. A real date example from industry is used to show the implementation of the proposed charts. [ABSTRACT FROM AUTHOR]

This paper is devoted to study several local asymptotic properties for fractional autoregressive models with strong mixing noises, we treat local asymptotic normality using Swensen's lemma, then we deal with local asymptotic minimaxity and local asymptotic linearity, these properties are fundamental and prepare the way for the construction of adaptive estimator. In order to measure the performance of our approach we deal with simulation study, it allows us to check the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

The minimum covariance determinant (MCD) estimate is an important subsample method in robust statistics. It is commonly used to estimate parameters of multivariate normal distributions when outliers exist because of its good robustness properties. However, MCD has some disadvantages including low efficiency when there is no outliers and poor performance when there are clustered outliers. This paper first introduces an adaptive subsample method, and shows that the adaptive MCD estimator can possess both full asymptotic efficiency and maximum breakdown value. We then propose a minimum distance subsample estimate to handle the situations where there are clustered outliers. Simulation results indicate that the adaptive version of the minimum distance subsample estimate has satisfactory performance for various types of outliers. [ABSTRACT FROM AUTHOR]

The two-parameter weighted Lindley distribution has become much popular due to its simplicity, attractive properties, and flexibility to fit data when compared with similar generalizations of the exponential model, such as gamma and Weibull, among others. In this paper, we introduce a regression model based on a weighted Lindley distribution, which is reparameterized in terms of mean and precision parameters. In this model, both the mean and precision parameters vary with the explanatory variable values and general link functions are used in order to account for these relationships. We developed and implemented local influence diagnostics to identify potential influential observations. Hessian and Fisher information matrices are computed on the closed-form as well as their inverses. Classical inference based on the maximum likelihood method is presented. Extensive Monte Carlo simulation studies are carried out for a special case of the regression model in order to verify the asymptotic properties of the maximum likelihood estimators. Finally, the usefulness of the proposed model is illustrated through an empirical analysis. [ABSTRACT FROM AUTHOR]

Calibration estimation is a popular method for making inference from probability samples and dealing with nonresponse problems. Calibration estimation, specially model-assisted calibration estimation, has been extensively explored for inference from non-probability samples in recent years. When there are rich covariates, the variable selection method such as Adaptive LASSO can be used to select important covariates and estimate model parameters for establishing appropriate models in model-assisted calibration estimation. In addition to the established model, distance functions also have an impact on calibration estimation. Different distance functions may produce different calibration estimators. In this paper, traditional calibration estimators, estimated-control model-assisted calibration estimators and estimated-control model-assisted calibration estimators with Adaptive LASSO under the chi-square distance and the modified backward Kullback-Leibler distance are proposed when the population information of covariates is unknown. The calibrated weights based on traditional calibration, model-assisted calibration and model-assisted calibration with Adaptive LASSO under the two distance functions are also derived. Results from a simulation study are presented to compare different calibration estimators. A real data set is also adopted to confirm the performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

Misclassified current status data arise when the failure time of interest is observed or known only to be either smaller or larger than an observation time rather than observed exactly, and the failure status is examined by a diagnostic test with testing error. Such data commonly occur in various scientific fields, including clinical trials, demographic studies and epidemiological surveys. This paper discusses regression analysis of such data with the focus on variable selection or identifying predictable and important covariates associated with the failure time of interest. For the problem, a penalized maximum likelihood approach is proposed under the Cox proportional hazards model and the smoothly clipped absolute deviation penalty. More specifically, we develop a penalized EM algorithm to relieve the computational burden in maximizing the resulting, complex penalized likelihood function. A simulation study is conducted to examine the empirical performance of the proposed approach in finite samples, and an illustration to a set of real data on chlamydia is also provided. [ABSTRACT FROM AUTHOR]

We consider two independent populations, N (μ 1 , σ 1 2) and N (μ 2 , σ 2 2) , with all four parameters assumed unknown, (μ 1 , μ 2) ∈ R 2 and (σ 1 , σ 2) ∈ R + 2 . In this paper, our goal is to revisit sequential minimum risk point estimation (MRPE) problems for the parameter μ 1 − μ 2 (≡ δ , say) under the squared error loss (SEL) plus linear cost of sampling in our quest for comparing two treatments. We explicitly consider two separate scenarios: (i) σ 1 = σ 2 = σ , but σ (∈ R +) is assumed unknown, and (ii) σ 1 , σ 2 are unknown and unequal. In defining the relevant purely sequential stopping rules, customarily one incorporates multiples of sample standard deviations to set up requisite boundary crossing conditions. We set out to replace the multiples of sample standard deviations used in defining requisite boundary crossing conditions with Gini's mean difference (GMD), mean absolute deviation (MAD), along with a number of combinations of the sample standard deviations, the GMD's, and the MAD's. We prove that the ensuing body of such newly developed purely sequential MRPE strategies have associated second-order regret expansions and that the GMD-based as well as the MAD-based strategies are better equipped to withstand occurrences of possible outlying observations. Our theory and methodologies are amply supported by both large-scale simulations and the illustrations with real data. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a parametric hypothesis test of the multiplicative distortion model under the exponentially distributed but unobserved random variable. The unobservable variable is distorted in a multiplicative fashion by an observed confounding variable. Firstly, some new test statistics are proposed to checking the exponential distribution assumption without distortion effects. Next, we proposed several test statistics when the variable is distorted in the multiplicative fashion. For the latter, the proposed test statistics automatically eliminate the distortion effects involved in the unobserved variable. The proposed test statistics with or without distortions are all asymptotical free, and the asymptotic null distribution of the test statistics are obtained with known asymptotic variances. We conduct Monte Carlo simulation experiments to examine the performance of the proposed test statistics. These methods are applied to analyze four real datasets for illustrations. [ABSTRACT FROM AUTHOR]

Cox regression model (CRM) with time-varying covariates is widely used in medical and health related studies to investigate the effects of longitudinal variables on survival. In this paper, tied survival refers to units in which different subjects have the same survival time, while the term interaction indicates the relationship between longitudinal covariate and survival time. Unlike previous studies, we calculate the statistical power of Wald χ 2 statistics to test the interaction term based on Monte Carlo (MC) simulations when Breslow, Efron, Discrete, and Exact approximation methods are used for handling tied survival times. A linear mixed effect model (LMM) is used to generate longitudinal covariate such as time-varying covariate in simulations. A numerical example is provided to illustrate the CRM with the interaction term between longitudinal covariate and survival time. Using extensive MC simulations under different conditions for censored proportion, type I error, and number of subjects, statistical power of Wald χ 2 statistics is calculated using four different methods in the CRM. Statistical power value calculated using Breslow method is usually lower than statistical power values calculated when the other three methods are used. The proportion of censored observations in survival analysis has an important effect on power calculations. [ABSTRACT FROM AUTHOR]

Performance capability indices are valuable measures to evaluate the quality of a product. In this paper, we consider inference on a lifetime performance index when the product's lifetime follows a gamma distribution with unknown parameters. The bias and mean square error of the maximum likelihood estimator and other proposed estimators are compared. Also, an asymptotic confidence interval using the maximum likelihood estimator, thirteen bootstrap confidence intervals, and four generalized pivotal quantities are derived for the performance capability index. A Monte Carlo simulation is provided to investigate the accuracy of expected lengths and coverage probabilities of the confidence intervals. An actual data set is used to illustrate the estimators and confidence intervals. [ABSTRACT FROM AUTHOR]

Numerous testing procedures for directional data have been proposed over the years and a natural question that springs is which to use and when. The aim of this paper is to answer this question, via a large scale Monte Carlo simulation study that covers circular and spherical data for the two mean directions problem. The results evidently signify that tests assuming equal concentration parameters should be avoided as they tend to inflate the test size, while the heterogeneous test that does not make this assumption is to be preferred, but unfortunately only with large sample sizes. Permutation calibration does not improve the performance of any testing procedure, whereas bootstrap does. Specifically, bootstrap calibrated tests exhibited superior performance; they attain the type I error in the vast majority of the case scenarios examined and possess nearly indistinguishable empirical power levels. Finally, examples with real data illustrate the performance of the bootstrap calibrated tests. [ABSTRACT FROM AUTHOR]

This paper introduces an alternative linear regression model for over-dispersed count responses with appropriate covariates. It is an extended work of univariate Poisson-Modification of the Quasi Lindley (PMQL) distribution via the generalized linear model approach. A re-parametrized PMQL distribution is considered to demonstrate the flexible properties of the distribution on its regression model. Further, the performance of its maximum likelihood estimation method is examined by a simulation study based on the asymptotic theory. The maximum likelihood estimator is used to estimate the parameters of the regression model. Finally, three simulated data sets and a real-world data set are taken to show the applicability of the PMQL regression model against the Poisson, Negative binomial (NB), Poisson-Quasi Lindley (PQL), and Generalized Poisson-Lindley (GPL) regression models. The results of applications show that the newly introduced model provides a better fit for over-dispersed count responses with covariates than the Poisson, NB, PQL, GPL regression models. [ABSTRACT FROM AUTHOR]

Fisher information is a fundamental concept of statistical inference and plays an important role in many areas of statistical analysis. In this paper, we obtain explicit expressions for the Fisher information matrix in ranked set sampling (RSS) from the simple linear regression model with replicated observations. It has been shown to be the sum of two matrices, one of which is the Fisher information matrix based on simple random sampling (SRS). The numerical results show that RSS provides more information than SRS when the same sample size is used. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, the marginal distribution of second-order concomitants of order statistics (SCOSs) from the Cambanis family is determined. An advantageous recurrence relation between single moments of SCOSs and concomitants of order statistics (COSs) is established based on the Cambanis family. We also use this family to derive an elegant beneficial recurrence relation between single moments of the SCOSs. Some information measures, such as Shannon differential entropy, differential extropy, and negative cumulative extropy (NCEX) of SCOSs based on this family, are investigated. Furthermore, we present some numerical examples to back up the theoretical findings. In addition, a set of bivariate data from the real world was examined. Finally, an estimate of a marginal variable’s scale parameter in the copula Cambanis family is obtained. [ABSTRACT FROM AUTHOR]

AbstractMost of existing methods for analyzing unreplicated two-level factorial designs need the assumption of effect sparsity and only perform well when the effectssparsity assumption holds. The effects-sparsity assumption is frequently true, but it is not always true. This paper proposes a new method that needs not the effects-sparsity assumption and has the potential for detecting up to m-1 active effects, in which m is the number of effects under study. The proposed method is illustrated by two unreplicated factorial designs appeared in the literature. An extensive Monte Carlo comparison study, based on 100,000 replications, is carried out to compare the proposed method with another four popular and powerful existing objective methods. The simulation study shows that the proposed method has more power than the remainder four compared methods in most of the conditions under study. [ABSTRACT FROM AUTHOR]

AbstractThe purpose of this paper is to study the parameter estimation of the Vasicek integrated diffusion process. Based on the contrast function, the parameter contrast estimators of the Vasicek integrated diffusion process are given, and the mean-square errors of drift parameter estimators are derived, so as to obtain the optimal sampling intervals for the parameter estimators. Then we prove the strong consistency of the contrast estimators by the tail probability exponential inequality of α-mixing long-span high-frequency data. In numerical simulation, we investigate the fitting effect of the estimates under different sampling intervals and different sample sizes. The results indicate that using optimal interval sampling can achieve good estimation performance. We use the daily closing price data of CSI 300 index to conduct an empirical analysis and give a logarithmic price prediction model. The analysis results show that the prediction model works well. [ABSTRACT FROM AUTHOR]

AbstractThe two-parameter strict arcsine distribution as a member of the natural exponential family with cubic variance function has been shown to be a viable candidate for statistical analysis of count data. Efficient methods of parameter estimation will be essential in practical applications of the distribution. In this paper we examine some methods of parameter estimation. Due to the simple expression of the probability generating function, a probability generating function-based estimation procedure is considered and compared with other estimation procedures. Since the accuracy of the parameter estimation procedure affects the probability of correct selection in choosing the correct probability distribution, we extend the investigation by examining the discrimination between strict arcsine and generalized Poisson distributions in which both have cubic variance functions. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, a new flexible count regression analysis is proposed. For this purpose, a new modification of the Poisson distribution is introduced which generalizes the Poisson, zero-inflated Poisson, zero-one inflated Poisson, and zero-one-two inflated Poisson distributions. Some distributional properties are discussed for the proposed distribution. The Fisher scoring and EM algorithms are derived to attain the maximum likelihood estimates of the unknown parameters. An expected Fisher information matrix is provided to construct an approximate confidence interval for the parameters. Using the modified Poisson distribution, an arbitrary multiply inflated counting regression model is proposed. The performance of the maximum likelihood methodology is investigated with a simulation study for the distribution and count regression model. Finally, two practical data sets are analyzed and the superiority of the proposed model is demonstrated among others. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, we deal with a Bayesian inference method for estimating the parameters of the queueing system with short- or long-tailed distributions based on the No-U-Turn Sampler (NUTS), a recently developed Hamilton Monte Carlo (HMC). We assume inter-arrival and service times to be either the short-tailed distributions or the long-tailed distributions since they are a better fit for real-world data. We illustrate our assumption using a number of simulated data sets, generated from distributions covering a wide range of cases. Then we estimate the parameters using the Bayesian approach based on No-U-Turn Sampler. As a result of comparing the No-U-Turn Sampler with the Gibbs sampler, the most common MCMC algorithm, we demonstrate that the NUTS outperforms Gibbs sampler for estimating parameters, which is especially significant for long-tailed distribution. We also investigate the influence of the size of observation data and the prior distributions on estimating these parameters. [ABSTRACT FROM AUTHOR]

AbstractOne of the major challenges in empirical studies is to construct an appropriate statistical model that accounts for the uncertainty of statistical methods and model specifications. An improperly specified model may bring the potential risk for the interpretation of conclusions and subsequent decision-making. In this paper, we introduce a Model Specification Test (MoST) inspired by the concept of model confidence bounds and variable selection deviation. To obtain the p-value of our proposed test, we develop an efficient single-layer bootstrap procedure. Our method can be readily applied to existing variable selection strategies without additional assumptions. Extensive numerical experiments demonstrate the feasibility and interpretability of our approach in various scenarios. [ABSTRACT FROM AUTHOR]

AbstractThis paper presents new simple lower and upper bounds for the cumulative normal distribution function, Φ(z). The accuracy and closeness of the proposed bounds to the exact Φ(z) are investigated based on the maximum absolute error and the mean absolute error. It is found that the maximum absolute error of the proposed lower bound is 8.55×10−3 and it is 4.1×10−4 for the upper bound. In addition, based on 5001 values between z=0 and z=5 with step 0.001, we found that the mean absolute error is 3.27×10−3 for the lower bound and it is 1.1×10−4 for the upper bound and these two values decrease with increasing the z value. [ABSTRACT FROM AUTHOR]

AbstractThe main objective of this paper is to propose a new general family of distributions, namely compound truncated Poisson log-normal distribution of which log-normal distribution is a special case. The proposed model has three unknown parameters, and it can take variety of shapes. It can be used effectively in analyzing maximum precipitation data during a particular period of time obtained from different stations. It is assumed that the number of stations operate follows a zero-truncated Poisson random variables, and the daily precipitation follows a log-normal random variable. The maximum likelihood estimators can be obtained quite conveniently using Expectation-Maximization (EM) algorithm. Approximate maximum likelihood estimators are also derived. The associated confidence intervals can also be obtained from the observed Fisher information matrix. Simulation results have been performed to check the performance of the EM algorithm, and it is observed that the EM algorithm works quite well in this case. When we analyze the precipitation data set using the proposed model it is observed that the proposed model provides better fit than some of the existing models. [ABSTRACT FROM AUTHOR]

AbstractThe matrix-variate normal distribution is a probability distribution that is a generalization of the multivariate normal distribution to matrix-valued random variables. In this paper, we introduce a wavelet shrinkage estimator based on Stein’s unbiased risk estimate (SURE) threshold for matrix-variate normal distribution. We find a new SURE threshold for soft thresholding wavelet shrinkage estimator under the reflected normal balanced loss function in low and high dimensional cases. Also, we obtain the restricted wavelet shrinkage estimator based on non-negative sub matrix of the mean matrix. Finally, we present a simulation study to test the validity of the wavelet shrinkage estimator and two real examples for low and high dimensional data sets. [ABSTRACT FROM AUTHOR]

Random execution of run sequences is employed in response surface designs to avoid bias in the response. Since the randomization of run sequences may induce frequent changes in the factor levels, which makes it difficult or expensive for the experimenter, especially when hard-to-change factors are involved in the experiment. Mostly, second order response surface designs (SORDs) are being used to explore the functional relationship between the response and the input variables. But when the lack of fit of the model becomes significant, it is desirable to explore the relationship with a polynomial model of order three. This requires third order rotatable designs (TORDs), which can be sequentially implemented by adding few more runs to the SORDs. In this paper, the construction of sequential TORDs with minimum level changes in the run sequences has been discussed. [ABSTRACT FROM AUTHOR]

Prediction of loss reserves corresponding to dependent lines of business is one of the most important problems in the actuarial sciences. In this paper, we propose a class of copula based multivariate distributions to model the losses with the heavy tailed distribution in the run-off triangles to predict unpaid losses. We set up ANOVA, ANCOVA, and state space models with four choices of copulas, Clayton, Frank, Gumbel, and Gaussian to provide a new procedure for analyzing run-off triangle tables. We use the Hamiltonian Monte Carlo sampler to perform a Bayesian analysis to estimate the parameters. We apply the proposed models to the data set consists of two lines of business of paid losses data from the Schedule P of the National Association of Insurance Commissioners (NAIC) database. Using some well known criteria, we compare the prediction accuracy of the mean models. As a result, the ANCOVA model with the Clayton copula dominates the other models. [ABSTRACT FROM AUTHOR]

In this paper a new bivariate lifetime distribution is introduced. Its marginal distribution functions follow two-parameter Chen distribution, which has a bathtub shaped or increasing hazard rate functions. The proposed distribution, which we call a bivariate Chen distribution (BCD), is of Marshall-Olkin type and it is a singular distribution. Several properties of this proposed distribution are discussed. The BCD distribution has four unknown parameters. The maximum likelihood (ML) method and the Bayes techniques are used to estimate the unknown parameters. The maximum likelihood estimators or the Bayes estimators cannot be obtained in closed form. Numerical methods have been used in both cases. A real data set is analyzed using the proposed distribution for illustrative and comparison purposes. An application to dependent competing risks data is discussed, and finally we have extended the BCD to the multivariate case. [ABSTRACT FROM AUTHOR]

Acceptance sampling is one of the most important tools in quality control, and it has been extensively used in the industry for inspecting received lots. As different situations and purposes could be encountered in real life, numerous approaches for sampling plans have been established. When the quality of the process is good and stable, Skip-lot sampling plans (SkSPs) are useful strategies of sampling and could be an advantageous examination scheme. Therefore, this paper aims to incorporate the process yield index for a first-order autoregressive process S p k ; A R (1) and the SkSP, when the quality characteristic follows a normal distribution with bilateral specification limits, to produce a variables Skip lot sampling plan of type 2 (SkSP-2) with a single sampling plan (SSP) based on S p k ; A R (1) as the reference plan. A non-linear optimization model is solved to decide the plan parameters, by fulfiling the quality and risk obligations identified by the manufacturer and buyer and minimizing the average sample number (ASN). We investigated the efficiency and performance of the suggested SkSP-2 S p k ; A R (1) -based, associated with the variables SSP in terms of average sample number curves and the operating characteristic. Furthermore, the plan parameters with particular conditions are delivered for reference as tables, and an industrial application is offered to prove the applicability of the proposed plan. [ABSTRACT FROM AUTHOR]

Traffic intensity is one of the most critical parameters of single-server Markovian queues. This paper deals with the Bayesian inference for the M/M/1 queue by sampling from the posterior distribution. The No-U-Turn Sampler (NUTS) is a recently developed Markov Chain Monte Carlo (MCMC) algorithm, which is proposed to compute the traffic intensity by observing the number of customers in the system at the departure epoch. Numerical results show that the NUTS outperforms the other algorithms in the literature. [ABSTRACT FROM AUTHOR]

Gompertz distribution is a significant and practical continuous lifetime distribution, which plays an important role in reliability engineering. A Gompertz distribution competing risks model is discussed and studied under general progressive censoring in this paper. When the lifetime model fails for different latent reasons, the maximum likelihood estimates are given for the unknown parameters. The approximate confidence intervals through Fisher information matrix and bootstrap confidence intervals are established, containing bootstrap-p and bootstrap-t techniques. In addition, the Bayes estimation of unknown parameters is investigated under the condition of squared error loss. Moreover, the Bayes credible interval is derived. Finally, a numerical simulation is conducted to evaluate the performances of the proposed methods and real-life data is analyzed by applying the proposed inference methods. [ABSTRACT FROM AUTHOR]

Control charts are very popular quality tools used to detect and control industrial process deviations in Statistical Process Control. In the current paper, we propose a new single memory-type control chart, called the maximum triple exponentially weighted moving average chart (referred as Max-TEWMA chart), that simultaneously detects both upward and downward shifts in the process mean and/or process dispersion. The run length performance and the diagnostic ability of the Max-TEWMA control chart are compared with that of the Max-EWMA, Max-DEWMA and Max-GWMA charts, through Monte-Carlo simulations. The comparisons reveal that the proposed chart is more efficient, than the competing ones, in detecting shifts in the process mean and variability simultaneously. Furthermore, the Max-TEWMA chart provides a satisfactory overall performance for identifying a wide range of shifts in the process mean and variability. Finally, two illustrative examples are presented to explain the application of the Max-TEWMA control chart. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the robustness of the estimation in the Zero-Inflated Poisson regression model, when varying the class membership model of the underlying mixture. We propose an estimation procedure based on the maximum likelihood estimator. Simulations are used to examine the performance of the MLE. The results suggest that maximum likelihood allows for accurate inference. Using simulated datasets, we show that the proposed alternative link functions are quite flexible and outperform the standard link function. Also, an application to a real dataset is provided. [ABSTRACT FROM AUTHOR]

This paper proposes a class of asymmetric kernels based on log-symmetric (LS) distributions for probability density function estimation in the context of strictly positive skewed data. Some asymptotic properties (bias, variance and mean integrated squared error) of the LS kernel density estimators are established. The choice of bandwidth is investigated by adapting the rule-of-thumb and cross-validation methods. A simulation study investigates the performance of the proposed LS kernel density estimators and compare their performances with the Kakizawa's LS kernel estimators [Nonparametric density estimation for nonnegative data, using symmetrical-based inverse and reciprocal inverse Gaussian kernels through dual transformation. Journal of Statistical Planning and Inference. 2018; 193:117–135]. Finally, an application on real data is analyzed. [ABSTRACT FROM AUTHOR]

The weighted exponential distribution is a distribution that introduce an extra shape parameter to the exponential distribution. It can be used quite effectively to analyze positively skewed data. In this paper, we study a change-point problem of this distribution. The procedures based on Likelihood ratio test, modified information criterion and Schwarz information criterion are studied. Simulations are conducted to indicate the performance of the proposed procedures under different scenarios. Applications on two sets of data are provided to illustrate the detection procedures. [ABSTRACT FROM AUTHOR]

In this paper, we concentrate on the European option pricing problem in incomplete markets by taking Vasicek stochastic interest rate model into account and expanding it in accordance with a Lévy process named Variance Gamma (VG) process. In doing so, first, we prove the existence and uniqueness of the solution to the stochastic differential equation of this model. Then, by the means of the hedging and replicating techniques, pricing formulas for the bond and, in succession, for European options are established. Finally, from a numerical point of view, we will analyze the value of a bond based on our consideration model and also, we will study a European call option bond price. All these results are reported through the Monte-Carlo simulation method. [ABSTRACT FROM AUTHOR]

Multivariate statistical process control (MSPC) was developed for the monitoring of variables that are either all numerical or all categorical. In the present paper, we describe a nonparametric control scheme that can be used to monitor a mixture of numerical and categorical variables simultaneously. It integrates Principal Component Analysis Mix (PCA Mix), a multivariate statistical tool, with the conventional Hotelling T2 chart. To estimate the control limit for the PCA Mix-based T2 statistic, two nonparametric approaches – kernel density estimation (KDE) and bootstrap – are employed, because of the unknown nature of the underlying distribution. The simulation results demonstrate that with an appropriate number of principal components, both bootstrap and KDE exhibit convincing performance in terms of generating the same, or nearly the same, number of false alarms (ARL0) as expected, and being able to detect process shifts efficiently (ARL1). Compared with bootstrap, KDE is shown to work better with small sample sizes (n < 800) and to be slightly more sensitive to small shifts. However, the results also show the instability of the estimated nonparametric control limit when highly imbalanced categorical variables are included, which indicates the need for further research on this topic. [ABSTRACT FROM AUTHOR]

A Shewhart control chart is highly effective for detecting large process shifts, however, it is relatively less sensitive to the small shifts. A CUSUM chart is more efficient than a Shewhart chart for detecting small process shifts but it is inferior to that for detecting the large ones. This paper proposes the nonparametric combined Shewhart-CUSUM (CSC) control charts based on the sign statistic. By appropriately choosing the design parameters, a CSC chart exhibits a trade-off statistical performance between that of the Shewhart and CUSUM sign charts. That is, its performance lies between the performances of the Shewhart and CUSUM sign charts for detecting a process shift of any size. The expressions for the zero-state and steady-state average run lengths of the CSC chart are obtained using a Markov chain approach. An example illustrating the implementation of this chart is provided. [ABSTRACT FROM AUTHOR]

In this paper, we first develop exact likelihood inference for Laplace distribution based on a generalized Type-I hybrid censored sample (Type-I HCS). We derive explicit expressions for the maximum likelihood estimators (MLEs) of the location and scale parameters. We then derive the joint moment generating function (MGF) of the MLEs, and use it to obtain the exact distributions and moments of the MLEs. Using an analogous approach, we extend the results to a generalized Type-II hybrid censored sample (Type-II HCS) next. Finally, we present a numerical example to illustrate all the results established here. [ABSTRACT FROM AUTHOR]

Existing negations are based on entropy. Recently, a new function called as extropy is developed, which can be seen as the dual concept of entropy. It is necessary to explore the negation with extropy. To address this issue, the negation method based on extropy is presented in this paper. In the proposed method, the change of the probability value and the corresponding extropy value during the iteration of the probability distribution is explored. Moreover, the extropy is proven to have the maximum value in this process. [ABSTRACT FROM AUTHOR]