This paper deals with beta regression models with a covariate that is not directly observed; instead, it is replaced by a surrogate covariate that underpredicts its actual value. We propose a multiplicative errors-in-variables model tailored for this situation and develop calibration regression and pseudo-likelihood-based inference for the unknown parameters. The impact of ignoring the measurement error and the performance of the inference methods are evaluated through simulations and a real data illustration.

In this paper, a new family of continuous random variables with positive support is introduced. Its density function has the capacity to incorporate features of unimodality and bimodality. Special attention is paid to the lognormal distribution which is included as a particular case. Its density function is given in closed-form, allowing probabilities, moments and other related measures such as skewness and kurtosis coefficients to be computed easily. In addition, a stochastic representation of the family that enables us to generate random variates of this model is also presented. Some properties related with the right tail and actuarial aspects of the distribution are also shown. This new family of distributions is numerically illustrated with data taken from the Medical Expenditure Panel Survey (MEPS), conducted by the US Agency of Health Research and Quality and with a well-known data set which has been studied widely in the actuarial literature.

In the framework of censored regression models, the distribution of the error term can depart significantly from normality, for instance, due to the presence of multimodality, skewness and/or atypical observations. In this paper we propose a novel censored linear regression model where the random errors follow a finite mixture of scale mixtures of normal (SMN) distribution. The SMN is an attractive class of symmetrical heavy-tailed densities that includes the normal, Student-t, slash and the contaminated normal distribution as special cases. This approach allows us to model data with great flexibility, accommodating simultaneously multimodality, heavy tails and skewness depending on the structure of the mixture components. We develop an analytically tractable and efficient EM-type algorithm for iteratively computing the maximum likelihood estimates of the parameters, with standard errors and prediction of the censored values as a by-products. The proposed algorithm has closed-form expressions at the E-step, that rely on formulas for the mean and variance of the truncated SMN distributions. The efficacy of the method is verified through the analysis of simulated and real datasets. The methodology addressed in this paper is implemented in the R package $\mathtt{CensMixReg}$.

This paper presents a procedure to calculate, in terms of analytic functions, the asymptotic covariance matrix of sample autocovariance differences of stationary autoregressive fractionally integrated moving average process with Gaussian and non-Gaussian errors. Furthermore, an application of minimum distance estimation of Gaussian autoregressive fractionally integrated moving average models is presented.

A multivariate mixed-effects model seems to be the most appropriate for gene expression data collected in a crossover trial. It is, however, difficult to obtain reliable results using standard statistical inference when some responses are missing. Particularly for crossover studies, missingness is a serious concern as the trial requires a small number of participants. A Monte Carlo EM (MCEM)-based technique was adopted to deal with this situation. In addition to estimation, MCEM likelihood ratio tests are developed to test fixed effects in crossover models with missing data. Intensive simulation studies were conducted prior to analyzing gene expression data.

This paper deals with maximum likelihood estimation for the drift of the reflected stochastic linear system with a large signal. The law of iterated logarithm, consistency, and the asymptotic distributions of the maximum likelihood estimators in both the stationary and the non-stationary cases are studied based on the continuous observation.

Motivated for a medical data about schizophrenia symptoms where an imbalanced binary response is observed, we introduce a broad class of link functions, called power and reverse power, as an alternative to analyse longitudinal binary data, particularly when it is imbalanced as is common in medical data. Bayesian estimation using an MCMC procedure through the No-U-Turn Sampler algorithm is proposed. Posterior predictive checks, Bayesian randomized quantile residuals, and a Bayesian influence measures are considered for model diagnostics. Different models are compared using selection model criteria. A simulation study is developed to analyse the prior sensitivity of the variance of the random effect and to assess the performance of the proposed model in the presence of imbalanced data. Finally, an application of the methodology studied in a set of medical data on the presence of schizophrenia symptom “thought disorder” is considered. In this data set, the presence of symptoms is much less than the absence, thus we show, in practice, the usefulness of using alternative link functions in imbalanced data.

Diagnostic analysis tools are studied for the censored power-normal Tobit regression model. We follow the Cook’s (J. R. Stat. Soc., Ser. B, Stat. Methodol. 48 (1986) 133–169) approach, and several perturbation schemes are considered to detect influential observations. In particular, closed-form expressions of the normal curvatures for studying local influence are obtained under some perturbation schemes. The approach pursued also considers separate analysis for regression and scale-asymmetry parameters. Further, we define residuals to identify departures from the model assumptions, as well as to assess the overall goodness-of-fit of the censored power-normal Tobit regression model. The diagnostic measures developed are applied in a real data set for illustrative purposes.

We consider a $\mathit{n}\times \mathit{d}$ random matrix ${\mathcal{X}}_{\mathit{n},\mathit{d}}$ whose entries are the spatial increments of the solution to the stochastic heat equation with space-time white noise. We analyze the limit behavior of the associated Wishart matrix, by showing that it converges almost surely to a diagonal matrix (with equal diagonal terms) and the renormalized Wishart matrix satisfies a central limit theorem. Our techniques are based on the analysis on Wiener chaos, Malliavin calculus and Stein’s method.

We consider a dependent percolation model on the square lattice ${\mathbb{Z}}^2$. The range of dependence is infinite in vertical and horizontal directions. In this context, we prove the existence of a phase transition. The proof exploits a multi-scale renormalization argument that is defined once the environment configuration is suitably good and, which, together with the main estimate for the induction step, comes from Kesten, Sidoravicius and Vares (Electronic Journal of Probability 27 (2022) 1–49). This paper is inspired by de Lima (Ph.D.Thesis, Informes de Matemática. IMPA, Série C-26/2004) where the simpler case of a deterministic environment was considered. It has various applications, including an alternative proof for the phase transition on the two dimensional random stretched lattice proved by Hoffman (Comm. Math. Phys. 254 (2005) 1–22).

In this short communication, we show that basic tools from Malliavin calculus can be applied to derive the two-point function of the slope of the one-dimensional KPZ equation, starting from a two-sided Brownian motion with an arbitrary diffusion parameter, in terms of the polymer end-point annealed distribution associated to the stochastic heat equation. We also prove that this distribution is given in terms of the derivative of the variance of the solution of the KPZ equation.