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In this paper, we consider the problem of classification of misaligned multivariate functional data. We propose to use a model-based approach for the joint registration and classification of such data. The observed functional inputs are modeled as a functional nonlinear mixed effects model containing a nonlinear functional fixed effect constructed upon warping functions to account for curve alignment, and a nonlinear functional random effects component to address the variability among subjects. The warping functions are also modeled to accommodate common effect within groups and the variability between subjects. Then, a functional logistic regression model defined upon the representation of the aligned curves and scalar inputs is used to account for curve classification. EM-based algorithms are developed to perform maximum likelihood inference of the proposed models. The identifiability of the registration model and the asymptotical properties of the proposed method are established. The performance of the proposed procedure is illustrated via simulation studies and an analysis of a hyoid bone movement data application. The statistical developments proposed in this paper were motivated by the hyoid bone movement study, the methodology is designed and presented generality and can be applied to numerous areas of scientific research.

In many situations, it is common to have more than one observation per experimental unit, thus generating the experiments with repeated measures. In the modeling of such experiments, it is necessary to consider and model the intra-unit dependency structure. In the literature, there are several proposals to model positive continuous data with repeated measures. In this paper, we propose one more with the generalization of the beta prime regression model. We consider the possibility of dependence between observations of the same unit. Residuals and diagnostic tools also are discussed. To evaluate the finite-sample performance of the estimators, using different correlation matrices and distributions, we conducted a Monte Carlo simulation study. The methodology proposed is illustrated with an analysis of a real data set. Finally, we create an [Image: see text] package for easy access to publicly available the methodology described in this paper.

Aiming at the problem of fault detection in data collection in wireless sensor networks, this paper combines evolutionary computing and machine learning to propose a productive technical solution. We choose the classical particle swarm optimization (PSO) and improve it, including the introduction of a biological population model to control the population size, and the addition of a parallel mechanism for further tuning. The proposed RS-PPSO algorithm was successfully used to optimize the initial weights and biases of back propagation neural network (BPNN), shortening the training time and raising the prediction accuracy. Wireless sensor networks (WSN) has become the key supporting platform of Internet of Things (IoT). The correctness of the data collected by the sensor nodes has a great influence on the reliability, real-time performance and energy saving of the entire network. The optimized machine learning technology scheme given in this paper can effectively identify the fault data, so as to ensure the effective operation of WSN.

The [Image: see text] statistic, also known as the Cash statistic, is often used in astronomy for the analysis of low-count Poisson data. The main advantage of this statistic, compared to the more commonly used [Image: see text] statistic, is its applicability without the need to combine data points. This feature has made the [Image: see text] statistic a very useful method to analyze Poisson data that have small (or even null) counts in each resolution element. One of the challenges of the [Image: see text] statistic is that its probability distribution, under the null hypothesis that the data follow a parent model, is not known exactly. This paper presents an effort towards improving our understanding of the [Image: see text] statistic by studying (a) the distribution of [Image: see text] statistic for a fully specified model, (b) the distribution of C(min) resulting from a maximum-likelihood fit to a simple one-parameter constant model, i.e. a model that represents the sample mean of N Poisson measurements, and (c) the distribution of the associated [Image: see text] statistic that is used for parameter estimation. The results confirm the expectation that, in the high-count limit, both [Image: see text] statistic and C(min) have the same mean and variance as a [Image: see text] statistic with same number of degrees of freedom. It is also found that, in the low-count regime, the expectation of the [Image: see text] statistic and C(min) can be substantially lower than for a [Image: see text] distribution. The paper makes use of recent X-ray observations of the astronomical source PG 1116+215 to illustrate the application of the [Image: see text] statistic to Poisson data.

In this paper, we study the properties of a special class of frailty models when the frailty is common to several failure times. The models are closely linked to Archimedean copula models. We establish a useful formula for cumulative baseline hazard functions and develop a new estimator for cumulative baseline hazard functions in bivariate frailty regression models. Based on our proposed estimator, we present a graphical model checking procedure. We fit a leukemia data set using our model and end our paper with some discussions.

In this paper, a new bivariate discrete generalized exponential distribution, whose marginals are discrete generalized exponential distributions, is studied. It is observed that the proposed bivariate distribution is a flexible distribution whose cumulative distribution function has an analytical structure. In addition, a new bivariate geometric distribution can be obtained as a special case. We study different properties of this distribution and propose estimation of its parameters. We will see that the maximum of the variables involved in the proposed bivariate distribution defines some new classes of univariate discrete distributions, which are interesting in their own sake, and can be used to analyze some Reliability systems whose components are positive dependent. Some important futures of this new univariate family of discrete distributions are also studied in details. In addition, a general class of bivariate discrete distributions, whose marginals are exponentiated discrete distributions, is introduced. Moreover, the analysis of two real bivariate data sets is performed to indicate the effectiveness of the proposed models. Finally, we conclude the paper.

In this paper, a multiple step-stress model is designed and analyzed when the data are Type-I censored. Lifetime distributions of the experimental units at each stress level are assumed to follow a two-parameter Weibull distribution. Further, distributions under each of the stress levels are connected through a tampered failure-rate based model. In a step-stress experiment, as the stress level increases, the load on the experimental units increases and hence the mean lifetime is expected to be shortened. Taking this into account, the aim of this paper is to develop the order restricted inference of the model parameters of a multiple step-stress model based on the frequentist approach. An extensive simulation study has been carried out and two real data sets have been analyzed for illustrative purposes.

In clinical researches, various clinical scales with ordered categories are used to evaluate the efficacy and safety/toxicity of treatments. Such the clinical scales are sometimes summarized on the transition between the baseline and the study end point as a square contingency table. Also, clinical scales may be reclassified into three groups. However, the cutpoints can be varied depending on clinical researches or clinicians. Hence, this paper proposes a measure which is expressed by using same weights for collapsed tables and which can see the directionality for two kinds of asymmetries. Also, this paper shows an application of the proposed measure to clinical data, and that the proposed measure is a useful statistical method for analyzing ordered categorical data.

Among the models applied to analyze survival data, a standout is the inverse Gaussian distribution, which belongs to the class of models to analyze positive asymmetric data. However, the variance of this distribution depends on two parameters, which prevents establishing a functional relation with a linear predictor when the assumption of constant variance does not hold. In this context, the aim of this paper is to re-parameterize the inverse Gaussian distribution to enable establishing an association between a linear predictor and the variance. We propose deviance residuals to verify the model assumptions. Some simulations indicate that the distribution of these residuals approaches the standard normal distribution and the mean squared errors of the estimators are small for large samples. Further, we fit the new model to hospitalization times of COVID-19 patients in Piracicaba (Brazil) which indicates that men spend more time hospitalized than women, and this pattern is more pronounced for individuals older than 60 years. The re-parameterized inverse Gaussian model proved to be a good alternative to analyze censored data with non-constant variance.

In this paper, the inference of multicomponent stress-strength reliability has been derived using progressively censored samples from Topp-Leone distribution. Both stress and strength variables are assumed to follow Topp-Leone distributions with different shape parameters. The maximum likelihood estimate along with the asymptotic confidence interval are developed. Boot-p and Boot-t confidence intervals are also constructed. The Bayes estimates under generalized entropy loss function based on gamma priors using Lindley's, Tierney-Kadane's approximation and Markov chain Monte Carlo methods are derived. A simulation study is considered to check the performance of various estimation methods and different censoring schemes. A real data study shows the applicability of the proposed estimation methods.

In competitive business, such as insurance and telecommunications, customers can easily replace one provider for another, which leads to customer attrition. Keeping customer attrition rate low is crucial for companies, since retaining a customer is more profitable than recruiting a new one. As a main statistical process control (SPC) method, the CUSUM scheme is able to detect small and persistent shifts in customer attrition. However, customer attrition summaries are typically available on an uneven time scale (e.g. 4-week and 5-week ‘business month’), which may not satisfy the assumptions of traditional CUSUM designs. This paper mainly develops a latent CUSUM chart based on an exponential model for monitoring ‘monthly’ customer attrition, under varying time scales. Both maximum likelihood and least squares methods are studied, where the former mostly performs better and the latter is advantageous for quite small shifts. We apply a Markov chain algorithm to obtain the average run length (ARL), make calibrations for different combinations of parameters, and present reference tables of cutoffs. Three more complicated models are considered to test the robustness of deviations from the initial model. Furthermore, a real example of monitoring monthly customer attrition from a Chinese insurance company is used to illustrate the scheme.

In this paper, we introduce a new lifetime distribution as an alternative to generalized Gompertz, Gompertz distribution and its modified ones. This new distribution is a special case of the family of distributions introduced by Granzotto et al. [D.C.T. Granzotto, F. Louzada and N. Balakrishnan, Cubic rank transmuted distributions: inferential issues and applications., J. Stat. Comput. Simul. 87 (2017), pp. 2760–2778]. We obtain some characteristic properties of suggested distribution such as hazard function, ordinary moments, coefficient of skewness, coefficient of kurtosis, moment generating function, quantile function and median. We discuss three different methods of estimation to estimate the parameters of proposed distribution. A comprehensive Monte Carlo simulation study is performed in order to compare the performances of estimators according to mean square errors and biases. Finally, three real data applications are performed to illustrate usefulness of suggested distribution.

In this paper, monitoring the Weibull shape parameter arising from progressively censored competing risks data is investigated. The competing risks are assumed to be independent and not identically distributed from the Weibull distributions with different shape and scale parameters. Both the shape parameters can be monitored separately by the proposed control charts using censored and predicted observations. We also introduced a control chart for monitoring both shape parameters simultaneously to detect possible shifts in both opposite and the same directions. In addition, the problem of mask data is discussed and an efficient prediction method is proposed. The behavior of the average run length with and without mask data is investigated through extensive simulations. Furthermore, the effects of sample size, number of failures due to each risk, and censoring scheme on the charts' performance are also studied. Finally, an illustrative example is presented to demonstrate the application of the proposed control charts by investigating a real data set of the failure times of two-component ARC-1 VHF communication transmitter receivers of a single commercial airline. Although this data set has been widely investigated in reliability analysis studies, this is the first time it has been analyzed in a statistical process monitoring setting.

In this paper, by virtual of the inverse probability weighted technique, we considered the jump-preserving estimation on the nonparametric regression models with missing data on response variable. First, we used local piecewise-linear expansion respectively with left and right kernel to approximate the unknown regression function. Second, we obtained the left- and right-limit estimation of regression function at each observed points and then determinated the final estimators by residual sums of squares. Third, we presented the convergence rate of estimators and the residual sums of squares. Finally, we illustrated the performance of our proposed method through some simulation studies and a conjunctivitis example from The Affiliated Hospital of Hangzhou Normal University.

In this paper, we propose a new distribution, named unit log–log distribution, defined on the bounded (0,1) interval. Basic distributional properties such as model shapes, stochastic ordering, quantile function, moments, and order statistics of the newly defined unit distribution are studied. The maximum likelihood estimation method has been pointed out to estimate its model parameters. The new quantile regression model based on the proposed distribution is introduced and it has been derived estimations of its model parameters also. The Monte Carlo simulation studies have been given to see the performance of the estimation method based on the new unit distribution and its regression modeling. Applications of the newly defined distribution and its quantile regression model to real data sets show that the proposed models have better modeling abilities than competitive models. The proposed unit quantile regression model has targeted to explain linear relation between educational measurements of both OECD (Organization for Economic Co-operation and Development) countries and some non-members of OECD countries, and their Better Life Index. The existence of the significant covariates has been seen on the real data applications for the unit median response.

This paper presents a new method called the functional distributional clustering algorithm (FDCA) that seeks to identify spatially contiguous clusters and incorporate changes in temporal patterns across overcrowded networks. This method is motivated by a graph-based network composed of sensors arranged over space where recorded observations for each sensor represent a multi-modal distribution. The proposed method is fully non-parametric and generates clusters within an agglomerative hierarchical clustering approach based on a measure of distance that defines a cumulative distribution function over temporal changes for different locations in space. Traditional hierarchical clustering algorithms that are spatially adapted do not typically accommodate the temporal characteristics of the underlying data. The effectiveness of the FDCA is illustrated using an application to both empirical and simulated data from about 400 sensors in a 2.5 square miles network area in downtown San Francisco, California. The results demonstrate the superior ability of the the FDCA in identifying true clusters compared to functional only and distributional only algorithms and similar performance to a model-based clustering algorithm.

In this paper, we have introduced a new type of censoring scheme named the multiple interval type-I censoring scheme. Further, We have assumed that the test units are drawn from the Weibull population. We have also proposed the maximum product of spacing estimators for unknown parameters under the multiple interval type-I censoring scheme and compare them with the existing maximum likelihood estimators. In addition to this, the Bayes estimators for shape and scale parameters are also obtained under the squared error loss function. Their corresponding asymptotic confidence/credible intervals are also discussed. A real data set containing the breakdown time of insulating fluids are used to demonstrate the appropriateness of the proposed methodology.

Influenza virus strains undergo genetic mutations every year and these changes in genetic makeup pose difficulties for effective vaccine selection. To better understand the problem it is important to statistically quantify the amount of genetic change between circulating strains from different years. In this paper, we propose the nonparametric crossmatch test applied to phylogenetic trees to assess the level of discrepancy between circulating flu virus strains between two years; the viruses being represented by a phylogenetic tree. The crossmatch test has advantages compared to parametric tests in that it preserves more information in the data. The outcome of the test would indicate whether the circulating influenza virus has mutated sufficiently in the past year to be considered as a new population of virus, suggesting the need to consider a new vaccine. We validate the test on simulated phylogenetic tree samples with varying branch lengths, as well as with publicly available virus sequence data from the 'Global Initiative on Sharing All Influenza Data' (GISAID: https://www.gisaid.org/).

With the rapid development of modern sensor technology, high-dimensional data streams appear frequently nowadays, bringing urgent needs for effective statistical process control (SPC) tools. In such a context, the online monitoring problem of high-dimensional and correlated binary data streams is becoming very important. Conventional SPC methods for monitoring multivariate binary processes may fail when facing high-dimensional applications due to high computational complexity and the lack of efficiency. In this paper, motivated by an application in extreme weather surveillance, we propose a novel pairwise approach that considers the most informative pairwise correlation between any two data streams. The information is then integrated into an exponential weighted moving average (EWMA) charting scheme to monitor abnormal mean changes in high-dimensional binary data streams. Extensive simulation study together with a real-data analysis demonstrates the efficiency and applicability of the proposed control chart.

The classic censored regression model (tobit model) has been widely used in the economic literature. This model assumes normality for the error distribution and is not recommended for cases where positive skewness is present. Moreover, in regression analysis, it is well-known that a quantile regression approach allows us to study the influences of the explanatory variables on the dependent variable considering different quantiles. Therefore, we propose in this paper a quantile tobit regression model based on quantile-based log-symmetric distributions. The proposed methodology allows us to model data with positive skewness (which is not suitable for the classic tobit model), and to study the influence of the quantiles of interest, in addition to accommodating heteroscedasticity. The model parameters are estimated using the maximum likelihood method and an elaborate Monte Carlo study is performed to evaluate the performance of the estimates. Finally, the proposed methodology is illustrated using two female labor supply data sets. The results show that the proposed log-symmetric quantile tobit model has a better fit than the classic tobit model., 23 pages, 2 figures

International audience; Exponentially weighted moving average (EWMA) control charts for time-between-events (TBE) are commonly suggested to monitor high-quality manufacturing processes for the early detection of process deteriorations. In this study, an enhanced one-sided EWMA TBE control chart is developed for rapid detection of increases or decreases in the process mean. The use of the truncation method helps to improve the sensitivity of the proposed scheme in the process mean detection. Moreover, by taking the effects of parameter estimation into account, the proposed scheme with estimated parameters is also investigated in this paper. Both the average run length (ARL) and standard deviation of run length (SDRL) performances of the proposed scheme with known and estimated parameters are studied using the Markov chain method, respectively. Furthermore, an optimal design procedure is developed for the recommended one-sided EWMA TBE chart based on ARL. Numerical results show that the proposed optimal one-sided EWMA TBE chart is more sensitive than the existing optimal one-sided exponential EWMA chart in monitoring both upward and downward mean shifts. Meanwhile, it also performs better than the existing comparative scheme in resisting the effect of the parameter estimation. Finally, two illustrative examples are considered to show the implementation of the recommended one-sided EWMA TBE scheme for simulated and real datasets. For the real dataset of F-16 aircraft, the accident occurrences of F-16 are very low, in which case monitoring the time between two successive F-16 accidents is more efficient than the traditional monitoring schemes. Moreover, the usage of the truncation method makes the proposed one-sided EWMA TBE chart more appropriate for monitoring those two datasets with known shift directions, and the operation of the proposed scheme is simple which does not need to predetermine the reflecting boundary of the existing comparative scheme.

In this study, we consider different poverty indexes in a dynamic framework where individuals change their rate of income randomly in time. The primary objective of this paper is to assess the accuracy of the approximation of the indexes that can be obtained by applying the strong law of large numbers to an economic system composed of an infinite number of agents. The main result is a multivariate central limit theorem for dynamic poverty measures, which is obtained applying the theory of U-statistics. We also show how to get the confidence sets for the considered dynamic indexes, which show the appropriateness of the model. An application to the Italian income data from 1998 to 2012 confirms the effectiveness of the considered approach and the possibility to determine the evolution of poverty and inequality in real economies.

This paper introduces a new class of distributions by compounding the inverse Lindley distribution and power series distributions which is called compound inverse Lindley power series (CILPS) distributions. An important feature of this distribution is that the lifetime of the component associated with a particular risk is not observable, rather only the minimum lifetime value among all risks is observable. Further, these distributions exhibit an unimodal failure rate. Various properties of the distribution are derived. Besides, two special models of the new family are investigated. The model parameters of the two sub-models of the new family are obtained by the methods of maximum likelihood, least square, weighted least square and maximum product of spacing and compared them using the Monte Carlo simulation study. Besides, the log compound inverse Lindley regression model for censored data is proposed. Three real data sets are analyzed to illustrate the flexibility and importance of the proposed models.

It is well known that financial data frequently contain outlying observations. Almost all methods and techniques used to estimate GARCH models are likelihood-based and thus generally non-robust against outliers. Minimum distance method, as an important tool for statistical inferences and a competitive alternative for achieving robustness, has surprisingly not been well explored for GARCH models. In this paper, we proposed a minimum Hellinger distance estimator (MHDE) and a minimum profile Hellinger distance estimator (MPHDE), depending on whether the innovation distribution is specified or not, for estimating the parameters in GARCH models. The construction and investigation of the two estimators are quite involved due to the non-i.i.d. nature of data. We proved that the MHDE is a consistent estimator and derived its bias in explicit expression. For both of the proposed estimators, we demonstrated their finite-sample performance through simulation studies and compared with the well-established methods including MLE, Gaussian Quasi-MLE, Non-Gaussian Quasi-MLE and Least Absolute Deviation estimator. Our numerical results showed that MHDE and MPHDE have much better performance than MLE-based methods when data are contaminated while simultaneously they are very competitive when data is clean, which testified to the robustness and efficiency of the two proposed MHD-type estimations.

Bimodal data sets are very common in different areas of knowledge. The crude birth rates data, fish length data, egg diameter data, the eruption and interruption times of the Old Faithful geyser, are examples of this type of data. In this paper, a new class of symmetric density functions for modeling bimodal data as described above are presented. From density functions with support on [Image: see text] , the symmetry is getting by reflecting the density function in the negative semi-axis with their respective normalization. In this way, if the primitive density function is unimodal, then the resulting density will be bimodal. We introduce asymmetry parameters and study their behavior, in particular the values of their modes and some other statistical values of interest. The cases for densities generated by Gamma, Weibull, Log-normal, and Birnbaum-Saunders densities, among others are studied. Statistical inference is performed from a classical perspective. A small simulation study to evaluate the benefits and limitations of the new proposal. In addition, an application to a data set related to the fetal weight in grams obtained through ultrasound in a sample of 500 units is also presented; the results show the great usefulness of the model in practical situations.

Cox model and traditional frailty models assume that all individuals will eventually experience the event of interest. This assumption is often overlooked, and situations will arise where it is not realistic. We introduce Compound Poisson frailty model for survival analysis to deal with populations in which some of the individuals will not experience the event of interest. This model assumes that the target population is a mixture of individuals with zero frailty and those with positive frailty. In this paper, we consider a compound Poisson frailty model for right-censored event times from a Bayesian perspective and compute the Bayesian estimator using the Markov Chain Monte Carlo method, where a Gamma process prior is adopted for the baseline hazard function. Furthermore, we evaluate the approach using simulation studies and demonstrate the methodology by analyzing the data from achalasia patient cohort.

In this paper, we consider a two-stage sequential estimation procedure to estimate the parameters of a cumulative exposure model under an accelerated testing scenario. In particular, we focus on a step-stress model where the stress level changes after a pre-specified number of failures occur, which is also random. This is termed as a 'random stress change time' in the literature. We further aim to estimate these parameters using maximum precision and hence use a certain variance optimality criteria. Our proposed two-stage estimation procedures follow interesting efficiency properties and their applicability is seen through extensive simulation analyses and a pseudo-real data example from reliability studies.

Discriminative subspace clustering (DSC) can make full use of linear discriminant analysis (LDA) to reduce the dimension of data and achieve effective clustering high-dimension data by clustering low-dimension data in discriminant subspace. However, most existing DSC algorithms do not consider the noise and outliers that may be contained in data sets, and when they are applied to the data sets with noise or outliers, and they often obtain poor performance due to the influence of noise and outliers. In this paper, we address the problem of the sensitivity of DSC to noise and outlier. Replacing the Euclidean distance in the objective function of LDA by an exponential non-Euclidean distance, we first develop a noise-insensitive LDA (NILDA) algorithm. Then, combining the proposed NILDA and a noise-insensitive fuzzy clustering algorithm: AFKM, we propose a noise-insensitive discriminative subspace fuzzy clustering (NIDSFC) algorithm. Experiments on some benchmark data sets show the effectiveness of the proposed NIDSFC algorithm.

The increasing inequality of private income and wealth requires the redistribution of financial resources. Thus, several financial support schemes allocate budget across countries or regions. This work shows how to estimate private wealth at low regional levels by means of a modified Fay-Herriot approach that deals with (a) unit and item non-response, especially with used multiple imputation, (b) the skewness of the wealth distribution, and (c) inconsistencies of the regional estimates with the national direct estimate. One compelling example for financial redistribution is the promoted catching-up process of East Germany after the German reunification. This work shows that 25 years after the reunification differences are more diverse than just between the East and the West by estimating private wealth at two regional levels in Germany. The analysis is based on the Household Finance and Consumption Survey (HFCS) that the European Central Bank launched for all euro area countries in 2010. Although the application in this paper focuses particularly on Germany, the approach proposed is applicable to the other countries participating in the HFCS as well as to other surveys that make use of multiple imputation.

This paper deals with the statistical inference of the unknown parameters of three-parameter exponentiated power Lindley distribution under adaptive progressive type-II censored samples. The maximum likelihood estimator (MLE) cannot be expressed explicitly, hence approximate MLEs are conducted using the Newton-Raphson method. Bayesian estimation is studied and the Markov Chain Monte Carlo method is used for computing the Bayes estimation. For Bayesian estimation, we consider two loss functions, namely: squared error and linear exponential (LINEX) loss functions, furthermore, we perform asymptotic confidence intervals and the credible intervals for the unknown parameters. A comparison between Bayes estimation and the MLE is observed using simulation analysis and we perform an optimally criterion for some suggested censoring schemes by minimizing bias and mean square error for the point estimation of the parameters. Finally, a real data example is used for the illustration of the goodness of fit for this model.

The relationship between the response variable and one or more independent variables refers to the quality characteristic in some statistical quality control applications, which is called profile. Most research dealt with the monitoring of profiles in single-stage processes considering a basic assumption of normality. However, some processes are made up of several sub-processes; thus, the effect of cascade property in multistage processes should be considered. Moreover, sometimes in practice, the assumption of normally distributed data does not hold. This paper first examines the effect of non-normal data to monitor simple linear profiles in two-stage processes in Phase II. We study non-normal distributions such as the skewed gamma distribution and the heavy-tailed symmetric t-distribution to measure the non-normality effect using the average run length criterion. Next, generalized linear models have been used and a monitoring approach based on generalized likelihood ratio (GLR) has been developed for gamma-distributed responses as a remedial measure to reduce the detrimental effects of non-normality. The results of simulation studies reveal that the performance of the GLR procedure is satisfactory for the multistage non-normal linear profiles. Finally, the simulated and real case studies with gamma-distributed data have been provided to show the application of the competing monitoring approaches.

This paper presents methods of estimation of the parameters and acceleration factor for Nadarajah–Haghighi distribution based on constant-stress partially accelerated life tests. Based on progressive Type-II censoring, Maximum likelihood and Bayes estimates of the model parameters and acceleration factor are established, respectively. In addition, approximate confidence interval are constructed via asymptotic variance and covariance matrix, and Bayesian credible intervals are obtained based on importance sampling procedure. For comparison purpose, alternative bootstrap confidence intervals for unknown parameters and acceleration factor are also presented. Finally, extensive simulation studies are conducted for investigating the performance of the our results, and two data sets are analyzed to show the applicabilities of the proposed methods.

In this paper, we propose a new kind of multivariate t distribution by allowing different degrees of freedom for each univariate component. Compared with the classical multivariate t distribution, it is more flexible in the model specification that can be used to deal with the variant amounts of tail weights on marginals in multivariate data modeling. In particular, it could include components following the multivariate normal distribution, and it contains the product of independent t-distributions as a special case. Subsequently, it is extended to the regression model as the joint distribution of the error terms. Important distributional properties are explored and useful statistical methods are developed. The flexibility of the specified structure in better capturing the characteristic of data is exemplified by both simulation studies and real data analyses.

Geyser eruption is one of the most popular signature attractions at the Yellowstone National Park. The interdependence of geyser eruptions and impacts of covariates are of interest to researchers in geyser studies. In this paper, we propose a parametric covariate-adjusted recurrent event model for estimating the eruption gap time. We describe a general bivariate recurrent event process, where a bivariate lognormal distribution and a Gumbel copula with different marginal distributions are used to model an interdependent dual-type event system. The maximum likelihood approach is used to estimate model parameters. The proposed method is applied to analyzing the Yellowstone geyser eruption data for a bivariate geyser system and offers a deeper understanding of the event occurrence mechanism of individual events as well as the system as a whole. A comprehensive simulation study is conducted to evaluate the performance of the proposed method., Comment: 29 pages

Linear regression models are useful statistical tools to analyze data sets in different fields. There are several methods to estimate the parameters of a linear regression model. These methods usually perform under normally distributed and uncorrelated errors. If error terms are correlated the Conditional Maximum Likelihood (CML) estimation method under normality assumption is often used to estimate the parameters of interest. The CML estimation method is required a distributional assumption on error terms. However, in practice, such distributional assumptions on error terms may not be plausible. In this paper, we propose to estimate the parameters of a linear regression model with autoregressive error term using Empirical Likelihood (EL) method, which is a distribution free estimation method. A small simulation study is provided to evaluate the performance of the proposed estimation method over the CML method. The results of the simulation study show that the proposed estimators based on EL method are remarkably better than the estimators obtained from CML method in terms of mean squared errors (MSE) and bias in almost all the simulation configurations. These findings are also confirmed by the results of the numerical and real data examples.

In this paper, we develop a variable selection framework with the spike-and-slab prior distribution via the hazard function of the Cox model. Specifically, we consider the transformation of the score and information functions for the partial likelihood function evaluated at the given data from the parameter space into the space generated by the logarithm of the hazard ratio. Thereby, we reduce the nonlinear complexity of the estimation equation for the Cox model and allow the utilization of a wider variety of stable variable selection methods. Then, we use a stochastic variable search Gibbs sampling approach via the spike-and-slab prior distribution to obtain the sparsity structure of the covariates associated with the survival outcome. Additionally, we conduct numerical simulations to evaluate the finite-sample performance of our proposed method. Finally, we apply this novel framework on lung adenocarcinoma data to find important genes associated with decreased survival in subjects with the disease.

The widely used Fellegi–Sunter model for probabilistic record linkage does not leverage information contained in field values and consequently leads to identical classification of match status regardless of whether records agree on rare or common values. Since agreement on rare values is less likely to occur by chance than agreement on common values, records agreeing on rare values are more likely to be matches. Existing frequency-based methods typically rely on knowledge of error probabilities associated with field values and frequencies of agreed field values among matches, often derived using prior studies or training data. When such information is unavailable, applications of these methods are challenging. In this paper, we propose a simple two-step procedure for frequency-based matching using the Fellegi–Sunter framework to overcome these challenges. Matching weights are adjusted based on frequency distributions of the agreed field values among matches and non-matches, estimated by the Fellegi–Sunter model without relying on prior studies or training data. Through a real-world application and simulation, our method is found to produce comparable or better performance than the unadjusted method. Furthermore, frequency-based matching provides greater improvement in matching accuracy when using poorly discriminating fields with diminished benefit as the discriminating power of matching fields increases.

In this paper, we introduced a new probability distribution named as inverse power Maxwell distribution. The proposal distribution can be seen as an extension of the Maxwell distribution with more flexibility in modeling upside-down lifetime data. Some statistical properties of this distribution are derived. In estimation viewpoint, five methods are used for estimating the unknown parameters of the distribution and these methods are performed through the simulation study. Finally, two real data sets were analyzed to illustrate the applicability of the proposed distribution, proving that it fits each real data set much better than some other existing distributions.

Analysis with principal points is a useful statistical tool for summarizing large data. In this paper, we propose a subgradient-based algorithm to calculate a set of principal points for multivariate binary data by the formulating it as a p-median problem. This enables us to find a globally optimal set of principal points or an ε-optimal solution in the middle of the calculation by combining an upper bound found using the greedy method. This algorithm is an iterative procedure where each iteration can be calculated in an efficient manner. We investigate the applicability of the proposed framework with questionnaire data and arXiv co-authors data.

Modeling cyber threats, such as the computer malicious software (malware) propagation dynamics in cyberspace, is an important research problem because models can deepen our understanding of dynamical cyber threats. In this paper, we study the statistical modeling of the macro-level evolution of dynamical cyber attacks. Specifically, we propose a Bayesian structural time series approach for modeling the computer malware propagation dynamics in cyberspace. Our model not only possesses the parsimony property (i.e. using few model parameters) but also can provide the predictive distribution of the dynamics by accommodating uncertainty. Our simulation study shows that the proposed model can fit and predict the computer malware propagation dynamics accurately, without requiring to know the information about the underlying attack-defense interaction mechanism and the underlying network topology. We use the model to study the propagation of two particular kinds of computer malware, namely the Conficker and Code Red worms, and show that our model has very satisfactory fitting and prediction accuracies.

Regression analyses are commonly performed with doubly limited continuous dependent variables; for instance, when modeling the behavior of rates, proportions and income concentration indices. Several models are available in the literature for use with such variables, one of them being the unit gamma regression model. In all such models, parameter estimation is typically performed using the maximum likelihood method and testing inferences on the model's parameters are usually based on the likelihood ratio test. Such a test can, however, deliver quite imprecise inferences when the sample size is small. In this paper, we propose two modified likelihood ratio test statistics for use with the unit gamma regressions that deliver much more accurate inferences when the number of data points in small. Numerical (i.e. simulation) evidence is presented for both fixed dispersion and varying dispersion models, and also for tests that involve nonnested models. We also present and discuss two empirical applications.

Partially paired data, either with incompleteness in one or both arms, are common in practice. For testing equality of means of two arms, practitioners often use only the portion of data with complete pairs and perform paired tests. Although such tests (referred as ‘naive paired tests’) are legitimate, their powers might be low as only partial data are utilized. The recently proposed ‘P-value pooling methods’, based on combining P-values from two tests, use all data, have reasonable type-I error control and good power property. While it is generally believed that ‘P-value pooling methods’ are superior to ‘naive paired tests’ in terms of power as the former use more data than the latter, no detailed power comparison has been done. This paper aims to compare powers of ‘naive paired tests’ and ‘P-value pooling methods’ analytically and our findings are counterintuitive, i.e. the ‘P-value pooling methods’ do not always outperform the naive paired tests in terms of power. Based on these results, we present guidance on how to select the best test for testing equality of means with partially paired data.

In many applications such as case-control studies with contaminated controls, or the test of a treatment effect in the presence of nonresponders in biological experiments or clinical trials, a two-sample problem with one of the samples having a mixture structure often arises. Due to the importance and wide applications of scale mixtures and location mixtures, we consider in this paper the case that the component densities differ only in scale parameters and the case that the component densities differ only in location parameters, and further construct an EM-test for the two-sample problem under each case. We show that both the EM-tests possess a chi-squared null limiting distribution. The local power analysis and sample size calculations are also investigated. Finally, the simulation studies and real data analysis demonstrate that the proposed EM-tests have better performance than the existing methods.

Extropy, a complementary dual of entropy, is considered in this paper. A Bayesian approach based on the Dirichlet process is proposed for the estimation of extropy. A goodness of fit test is also developed. Many theoretical properties of the procedure are derived. Several examples are discussed to illustrate the approach.

Providing reliable estimates of subpopulation/area parameters has attracted increased attention due to their importance in applications such as policymaking. Due to low or even no samples from some areas, we must adopt indirect model approaches. Existing indirect small area estimation methods often assume that a single nested error regression model is suitable for all the small areas. In particular, the effects of the auxiliary variables are either fixed or have a single attraction center. In some applications, it can be more appropriate to cluster the small areas so that the effects of the auxiliary variables are fixed but have multiple centers in the nested error regression model. In this paper, we examine an extended nested error regression model in which the auxiliary variables have mixed effects with multiple centers. We use a penalty approach to identify these centers and estimate the model parameters simultaneously. We then propose two new small area mean estimators and construct estimators of their mean square errors. Simulations based on artificial and realistic finite populations show that the new estimators can be efficient. Furthermore, the confidence intervals based on the new methods have accurate coverage probabilities. We illustrate the proposed methods with the Survey of Labour and Income Dynamics conducted in Canada.

In this paper, we propose the MulticlusterKDE algorithm applied to classify elements of a database into categories based on their similarity. MulticlusterKDE is centered on the multiple optimization of the kernel density estimator function with multivariate Gaussian kernel. One of the main features of the proposed algorithm is that the number of clusters is an optional input parameter. Furthermore, it is very simple, easy to implement, well defined and stops at a finite number of steps and it always converges regardless of the data set. We illustrate our findings by implementing the algorithm in R software. The results indicate that the MulticlusterKDE algorithm is competitive when compared to K-means, K-medoids, CLARA, DBSCAN and PdfCluster algorithms. Features such as simplicity and efficiency make the proposed algorithm an attractive and promising research field that can be used as basis for its improvement and also for the development of new density-based clustering algorithms.

In this paper, we propose two multimodal circular distributions which are suitable for modeling circular data sets with two or more modes. Both distributions belong to the regular exponential family of distributions and are considered as extensions of the von Mises distribution. Hence, they possess the highly desirable properties, such as the existence of non-trivial sufficient statistics and optimal inferences for their parameters. Fine particulates (PM2.5) are generally emitted from activities such as industrial and residential combustion and from vehicle exhaust. We illustrate the utility of our proposed models using a real data set consisting of fine particulates (PM2.5) pollutant levels in Houston region during Fall season in 2019. Our results provide a strong evidence that its diurnal pattern exhibits four modes; two peaks during morning and evening rush hours and two peaks in between.

In a ground-breaking paper published in 1990 by the Journal of the Royal Statistical Society, J.R.M. Hosking defined the L-moment of a random variable as an expectation of certain linear combinations of order statistics. L-moments are an alternative to conventional moments and recently they have been used often in inferential statistics. L-moments have several advantages over the conventional moments, including robustness to the the presence of outliers, which may lead to more accurate estimates in some cases as the characteristics of distributions. In this contribution, asymptotic theory and L-moments are used to derive confidence intervals of the population parameters and quantiles of the three-parametric generalized Pareto and extreme-value distributions. Computer simulations are performed to determine the performance of confidence intervals for the population quantiles based on L-moments and to compare them to those obtained by traditional estimation techniques. The results obtained show that they perform well in comparison to the moments and maximum likelihood methods when the interest is in higher quantiles, or even best. L-moments are especially recommended when the tail of the distribution is rather heavier and the sample size is small. The derived intervals are applied to real economic data, and specifically to market-opening asset prices.

Modern science frequently involves the analysis of large amount of quantitative information and the simultaneous testing of thousands or even hundreds of thousands null hypotheses. In this context, sometimes, naive deductions derived from the statistical reports substitute the rational thinking. The reproducibility crisis is a direct consequence of the misleading statistical conclusions. In this paper, the authors revisit some of the controversies on the implications derived from the statistical hypothesis testing. They focus on the role of the p-value on the massive multitesting problem and the loss of its standard probabilistic interpretation. The analogy between the hypothesis tests and the usual diagnostic process (both involve a decision-making) is used to point out some limitations in the probabilistic p-value interpretation and to introduce the receiver-operating characteristic, ROC, curve as a useful tool in the large-scale multitesting context. The analysis of the well-known Hedenfalk data illustrates the problem.

In this paper, we study the performance of a soccer player based on analysing an incomplete data set. To achieve this aim, we fit the bivariate Rayleigh distribution to the soccer dataset by the maximum likelihood method. In this way, the missing data and right censoring problems, that usually happen in such studies, are considered. Our aim is to inference about the performance of a soccer player by considering the stress and strength components. The first goal of the player of interest in a match is assumed as the stress component and the second goal of the match is assumed as the strength component. We propose some methods to overcome incomplete data problem and we use these methods to inference about the performance of a soccer player.