Modern science frequently involves the study of complex relationships among effects and factors. Flexible statistical tools are commonly used to visualize nonlinear associations. When our interest is to study the discrimination capacity of a multivariate marker on a binary outcome, the theoretical transformation leading to the optimal results in terms of sensitivity and specificity has already been

In a world that is increasingly connected on-line, cyber risks become critical. Cyber risk management is very difficult, as cyber loss data are typically not disclosed. To mitigate the reputational risks associated with their disclosure, loss data may be collected in terms of ordered severity levels. However, to date, there are no risk models for ordinal cyber data. We fill the gap, proposing a rank-based

Estimating conditional quantiles in the tail of a distribution is an important problem for several applications. However, data sparsity indicates that the predictions of tail behavior are more difficult compared with those for the mean or center quantiles, in particular, when a multivariate covariate is used. As additive models are known to be an efficient approach for multiple regression, this study

The receiver operating characteristic (ROC) curve is a graphical method commonly used to study the capacity of continuous variables (markers) to properly classify subjects into one of two groups. The decision made is ultimately endorsed by a classification subset on the space where the marker is defined. In this paper, we study graphical representations and propose visual forms to reflect those classification

In this paper, heteroscedastic nonlinear regression (HNLR) models under the flexible class of two–piece distributions based on the scale mixtures of normal (TP–SMN) family were examined. This novel class of nonlinear regression (NLR) models is a generalization of the well-known heteroscedastic symmetrical nonlinear regression models. The TP–SMN is a rich class of distributions that covers symmetric

Over the past 50 years, correspondence analysis (CA) has increasingly been used by data analysts to examine the association structure of categorical variables that are cross-classified to form a contingency table. However, the literature has paid little attention to the case where the variables are ordinal. Indeed, Pearson’s chi-squared statistic \(X^{2}\) can perform badly in studying the association

We show that the ordinary least squares (OLS) estimates of population parameters for Markov switching vector autoregressive (MS VAR) models coincide with the maximum likelihood estimates. Then, we propose an algorithm in matrix form for the estimation of model parameters, and derive an explicit expression in closed-form for the asymptotic covariance matrix of the OLS estimator of such models. The obtained

Integer-valued time series, seen as a collection of observations measured sequentially over time, have been studied with deep notoriety in recent years, with applications and new proposals of autoregressive models that broaden the field of study. This work proposes a new mixed integer-valued first-order autoregressive model with Poisson innovations, denoted POMINAR(1), mixing two operators known as

Inferring the most appropriate distribution (or distributions) to describe observed directional data is important in many applications of circular statistics. In particular, animal movement paths are typically analysed and modelled by considering the distribution of step lengths and turning (or absolute) angles. Here we demonstrate that a single-wrapped Cauchy distribution can appear to fit directional

In this article, we introduce a new random coefficients self-exciting threshold integer-valued autoregressive process. The autoregressive coefficients are driven by a logistic regression structure, so that the explanatory variables can be included. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares and conditional maximum likelihood estimators, as

Distance correlation and Hilbert-Schmidt independence criterion are widely used for independence testing, two-sample testing, and many inference tasks in statistics and machine learning. These two methods are tightly related, yet are treated as two different entities in the majority of existing literature. In this paper, we propose a simple and elegant bijection between metric and kernel. The bijective

Beta regressions are widely used for modeling random variables that assume values in the standard unit interval, (0, 1), such as rates, proportions, and income concentration indices. Parameter estimation is typically performed via maximum likelihood, and hypothesis testing inferences on the model parameters are commonly performed using the likelihood ratio test. Such a test, however, may deliver inaccurate

This study proposes a Bayesian structural equation model (SEM) to explore financial and economic sustainability indicators, considered by the Brazilian energy regulator (ANEEL), to evaluate the performance of energy distribution companies. The methodology applies confirmatory factor analysis for dimension reduction of the original multivariate data set into few representative latent variables (factors)

We introduce a new class of Poisson-exponential-Tweedie (PET) mixture in the framework of generalized linear models for ultra-overdispersed count data. The mean–variance relationship is of the form \(m+m^{2}+\phi m^{p}\), where \(\phi\) and p are the dispersion and Tweedie power parameters, respectively. The proposed model is equivalent to the exponential-Poisson–Tweedie models arising from geometric

For regression analysis of doubly truncated data, we propose two empirical likelihood (EL) inference approaches, called non-smooth EL and non-smooth Jackknife EL (JEL), to make inference about regression parameters based on the generalized estimating equations of existing weighted rank estimators. The limiting distributions of non-smooth log-EL and log-JEL ratios statistics are derived and non-smooth

In recent years, models incorporating heterogeneity among individuals have become increasingly popular in the analyses on subjective ordered choice data. However, there are rare previous studies that include individual heterogeneity in the multivariate ordered probit model. In this article, we describe the Bayesian multivariate ordered probit model introduced by Chen and Dey (in: Dey, Ghosh, Mallick

In this paper, we propose a geostatistical model for the counting process using a non-homogeneous Poisson model. This work aims to model the intensity function as the sum of two components: spatial and temporal. The spatial component is modeled using a Gaussian process in which the covariance structure is assumed to be anisotropic. Anisotropy is incorporated by applying a spatial deformation approach

This paper considers a situation in which cause–effect relationships among variables can be described by a linear structural equation model (linear SEM) and the corresponding directed acyclic graph (DAG). By considering a set of covariates that satisfies the back-door criterion, we formulate (1) the variances of the estimated mean response and (2) the mean squared error (MSE) of the predicted response

Assessing interventions applied to target populations is a matter of prime interest. Studies are usually undertaken to see whether an alternative intervention is superior (or at least equivalent) to a comparable standard intervention. This is typically achieved by comparing alternative and standard intervention within a given study, and the developed meta-analytic methodology is building on this assumption

In receiver operating characteristic (ROC) curve analysis, the area under the curve (AUC) is undoubtedly the most widely used index of diagnostic accuracy for the assessment of the utility of a biomarker or for the comparison of competing biomarkers. Along with the AUC, the maximum of the Youden index, J, is often used both as an index of diagnostic accuracy and as a tool useful for the estimation

In this article, we consider the problem of estimating cumulative distribution function (CDF) and a reliability parameter using moving extreme ranked set sampling (MERSS). Two different CDF estimators are described and compared with their competitors in simple random sampling (SRS) and ranked set sampling (RSS). It turns out the CDF estimators in MERSS can be more efficient than their competitors in

In this paper, we consider a general linear model where missing data occur in the response variable with a nonignorable mechanism. Also, to deal with missing data, we assume that the probability of missing data follows a logistic model. The main purpose of this paper is to construct some test functions to check the goodness of fit of the general linear model based on the score-type test. To achieve

In this paper, we study penalized empirical likelihood for parameter estimation and variable selection in partially linear models with measurement errors in possibly all the variables. By using adaptive Lasso penalty function, we show that penalized empirical likelihood has the oracle property. That is, with probability tending to one, penalized empirical likelihood identifies the true model and estimates

In many situations, it is crucial to estimate the variance properly. Ordinary variance estimators perform poorly in the presence of shifts in the mean. We investigate an approach based on non-overlapping blocks, which yields good results in change-point scenarios. We show the strong consistency and the asymptotic normality of such blocks-estimators of the variance under independence. Weak consistency

We introduce some new indexes to measure the departure of any multivariate continuous distribution on the nonnegative orthant of the corresponding space from a given reference distribution. The reference distribution may be an uncorrelated exponential model. The proposed multivariate variation indexes that are a continuous analogue to the relative Fisher dispersion indexes of multivariate count models

In multiple testing, the family-wise error rate can be bounded under some conditions by the copula of the test statistics. Assuming that this copula is Archimedean, we consider two nonparametric Archimedean generator estimators. More specifically, we use the nonparametric estimator from Genest et al. (Test 20(2):223–256, 2011) and a slight modification thereof. In simulations, we compare the resulting

Quantile regression models are typically used for modeling non-Gaussian outcomes, and such models allow quantile-specific inference. While there exists a vast literature on conditional quantile regression (where the model parameters are estimated precisely for one prefixed quantile level), relatively less work has been reported on joint quantile regression. The challenge in joint quantile regression

This paper studies an observation-driven model for time series of counts, in which the observations are supposed to follow a negative binomial distribution conditioned on past information with the form of the hysteretic autoregression. As an extension of the classical two-regime threshold process, the hysteretic autoregression enjoys a more flexible regime-switching mechanism. Stability properties

We consider six variants of (local) Whittle estimators of the fractional order of integration d. They follow a limiting normal distribution under stationarity as well as under (a certain degree of) nonstationarity. Experimentally, we observe a lack of continuity of the objective functions of the two fully extended versions at \(d=1/2\) that has not been reported before. It results in a pileup of the

Linear mixed-effects models are a class of models widely used for analyzing different types of data: longitudinal, clustered and panel data. Many fields, in which a statistical methodology is required, involve the employment of linear mixed models, such as biology, chemistry, medicine, finance and so forth. One of the most important processes, in a statistical analysis, is given by model selection

Bayesian sensitivity analysis of unmeasured confounding is proposed for observational data with misclassified outcome. The approach simultaneously corrects bias from error in the outcome and examines possible change in the exposure effect estimation assuming the presence of a binary unmeasured confounder. We assess the influence of unmeasured confounding on the exposure effect estimation through two

Pearson residuals are a widely used tool for model diagnostics of count time series. Despite their popularity, little is known about their distribution such that statistical inference is problematic. Squared Pearson residuals are considered for testing the conditional dispersion structure of the given count time series. For two popular types of Markov count processes, an asymptotic approximation for

The definition of multivariate quantiles has gained considerable attention in previous years as a tool for understanding the structure of a multivariate data cloud. Due to the lack of a natural ordering for multivariate data, many approaches have either considered geometric generalisations of univariate quantiles or data depths that measure centrality of data points. Both approaches provide a centre-outward

In this paper, we consider some statistical measures of deviation from the perfect ranking in the framework of ranked set sampling. We use nonparametric approach for testing the null hypothesis for perfect ranking. The distance-based Mallows’ models with appropriate distance on permutations are suggested in the case of imperfect ranking. Some asymptotic results for the corresponding error probability

If explanatory variables and a response variable of interest are simultaneously observed, then fitting a joint multivariate density to all variables would enable prediction via conditional distributions. Regular vines or vine copulas with arbitrary univariate margins provide a rich and flexible class of multivariate densities for Gaussian or non-Gaussian dependence structures. The density enables calculation

Common election poll reporting is often misleading as sample uncertainty is addressed insufficiently or not covered at all. Furthermore, main interest usually lies beyond the simple party shares. For a more comprehensive opinion poll and election coverage, we propose shifting the focus toward the reporting of survey-based probabilities for specific events of interest. We present such an approach for

A long-standing problem in the construction of asymptotically correct confidence bands for a regression function \(m(x)=E[Y|X=x]\), where Y is the response variable influenced by the covariate X, involves the situation where Y values may be missing at random, and where the selection probability, the density function f(x) of X, and the conditional variance of Y given X are all completely unknown. This

The problem of how to determine portfolio weights so that the variance of portfolio returns is minimized has been given considerable attention in the literature, and several methods have been proposed. Some properties of these estimators, however, remain unknown, and many of their relative strengths and weaknesses are therefore difficult to assess for users. This paper contributes to the field by comparing

We introduce a new class of regression models based on the geometric Tweedie models (GTMs) for analyzing both continuous and semicontinuous data, similar to the recent and standard Tweedie regression models. We also present a phenomenon of variation with respect to the equi-varied exponential distribution, where variance is equal to the squared mean. The corresponding power v-functions which characterize

Inference on impulse response functions from vector autoregressive models is commonly done using bootstrap methods. These methods can be inaccurate in small samples and for persistent processes. This article investigates the construction of skewness-adjusted confidence intervals and joint confidence bands for impulse responses with improved small sample performance. We suggest to adjust the skewness

Longitudinal studies often involve multiple mixed response variables measured repeatedly over time. Although separate modeling of these multiple mixed response variables can be easily performed, they may lead to inefficient estimates and consequently, misleading inferences. For obtaining correct inference, one needs to model multiple mixed responses jointly. In this paper, we use copula models for

In this paper, the repeated measures analysis for functional data is considered. The known testing procedures for this problem are based on test statistic being the integral of the difference between sample mean functions, which takes into account only “between group variability”. We modify this test statistic to use also information about “within group variability”. More precisely, we construct the

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We propose a new estimation procedure for estimating the unknown parameters and function in partial functional linear regression. The asymptotic distribution of the estimator of the vector of slope parameters is derived, and the global convergence rate of the estimator of unknown slope function is established under suitable norm. The convergence rate of the mean squared prediction error for the proposed

A unified testing framework is presented for large-dimensional mean vectors of one or several populations which may be non-normal with unequal covariance matrices. Beginning with one-sample case, the construction of tests, underlying assumptions and asymptotic theory, is systematically extended to multi-sample case. Tests are defined in terms of U-statistics-based consistent estimators, and their limits

Standard Poisson and negative binomial truncated regression models for count data include the regressors in the mean of the non-truncated distribution. In this paper, a new approach is proposed so that the explanatory variables determine directly the truncated mean. The main advantage is that the regression coefficients in the new models have a straightforward interpretation as the effect of a change

A scalar-response functional model describes the association between a scalar response and a set of functional covariates. An important problem in the functional data literature is to test nullity or linearity of the effect of the functional covariate in the context of scalar-on-function regression. This article provides an overview of the existing methods for testing both the null hypotheses that

The subjective assessment of quality of life, personal skills and the agreement with a certain opinion are common issues in clinical, social, behavioral and marketing research. A wide set of surveys providing ordinal data arises. Beside such variables, other common surveys generate responses on a continuous scale, where the variable actual point value cannot be observed since data belong to certain

We consider a problem of allocation of a sample in two- and three-stage sampling. We seek allocation which is both multi-domain and population efficient. Choudhry et al. (Survey Methods 38(1):23–29, 2012) recently considered such problem for one-stage stratified simple random sampling without replacement in domains. Their approach was through minimization of the sample size under constraints on relative

Complexity of longitudinal data lies in the inherent dependence among measurements from same subject over different time points. For multiple longitudinal responses, the problem is challenging due to inter-trait and intra-trait dependence. While linear mixed models are popularly used for analysing such data, appropriate inference on the shape of the population cannot be drawn for non-normal data sets

We introduce the novel notion of the integrated characteristic function and its empirical counterpart. Some basic properties of these new objects are mentioned and in turn utilized in order to construct new procedures for testing goodness of fit to parametric distributions, for testing symmetry and homogeneity, and for testing independence. Asymptotic results are obtained, while corresponding Monte

The problem of testing for the parametric form of the conditional variance is considered in a fully nonparametric regression model. A test statistic based on a weighted \(L_2\)-distance between the empirical characteristic functions of residuals constructed under the null hypothesis and under the alternative is proposed and studied theoretically. The null asymptotic distribution of the test statistic

The ordinary variable inspection plans rely on the normality of the underlying populations. However, this assumption is vague or even not satisfied. Moreover, ordinary variable sampling plans are sensitive against deviations from the distribution assumption. Nonconforming items occur in the tails of the distribution. They can be approximated by a generalized Pareto distribution (GPD). We investigate

Interval-censored data may arise in questionnaire surveys when, instead of being asked to provide an exact value, respondents are free to answer with any interval without having pre-specified ranges. In this context, the assumption of noninformative censoring is violated, and thus, the standard methods for interval-censored data are not appropriate. This paper explores two schemes for data collection

We consider the Bayesian inference of nonlinear, large-scale regression problems in which the parameters model the spatial distribution of some property. A homoscedastic Gaussian sampling distribution is supposed as well as certain assumptions about the regression function. Propriety of the posterior and the existence of its moments are explored when using improper prior distributions expressing different

Most model selection methods for time series models with many predictors are devised for the stationary processes. We consider the problem of selecting higher-order autoregressive (AR) models whose integration orders can be positive or zero, and hence both stationary and non-stationary cases are included. Combining the strengths of AIC and BIC, we propose a two-stage information criterion (TSIC), and

The performance of a product frequently relies on more than one quality characteristic. In such a setting, joint control schemes are used to determine whether or not we are in the presence of unfavorable disruptions in the location (\({\varvec{\mu }}\)) and spread (\({\varvec{\varSigma }}\)) of a vector of quality characteristics. A common joint scheme for multivariate output comprises two charts:

In this paper, case-deletion diagnostics in beta regression models are proposed. The diagnostics are based on the distance between the distributions of the maximum likelihood estimates of the model parameters resulting from the entire sample and after removing a sample case. Two metrics between probability distributions are considered: the Frèchet distance (Frèchet in Comptes Rendus hebdomadaires des

In nearly all papers on process control for time-dependent data, it is assumed that the underlying target process is stationary. In the present paper, the target process is modeled by a multivariate state-space model which may be non-stationary. Our aim is to monitor its mean behavior. The likelihood ratio method, the sequential probability ratio test and the Shiryaev–Roberts procedure are applied

It is well known that standard tests for a mean shift are invalid in long-range dependent time series. Therefore, several long-memory robust extensions of standard testing principles for a change-in-mean have been proposed in the literature. These can be divided into two groups: those that utilize consistent estimates of the long-run variance and self-normalized test statistics. Here, we review this