In this paper, we present an arithmetic short rate model based on generalized Langevin equations. The innovative feature of the model is that it accounts for memory effects in interest rate markets via the involved Langevin processes. In this setup, we provide a representation for the related zero-coupon bond price and infer its risk-neutral time dynamics. We also deduce the associated forward rate dynamics, the latter being of Heath–Jarrow–Morton type. We further establish a measure change to the risk-adjusted forward measure and propose a market-consistent calibration procedure. We finally derive a pricing formula for a European call option written on the zero-coupon bond by Fourier transform methods.

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.

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 CensMixReg.

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.

The functional law of the iterated logarithm is obtained for solutions of stochastic differential equations with random coefficients.From the conditions (2), (3) and ( 5), (6) it follows (see, for example, Gikhman and Skorokhod (2007), Chapter II, Theorem 3) that the equation (1) has a unique strong solution.We consider the space D[0, 1] of cdlg functions on the segment [0, 1] with uniform normand the metric generated by this norm.

The analysis of means (ANOM) is a method that can compare the mean of each treatment to the overall mean. According to the graphical result of a statistical data analysis, we can specify which one is different from another. One of the assumptions of the classical ANOM model is that the variances are equal. However, it is not always true for the practice. To solve unknown and unequal population variances, Nelson and Dudewicz (2002) proposed a two-stage sampling procedure. However, additional samples need to be added in the second stage of the two-stage sampling procedure, so it is not practical all the time due to limited time and insufficient budget. Thus, under heteroscedasticity, we applied Chen and Lam’s (1989) single-stage sampling procedure to solve the drawback of the two-stage sampling procedure. In addition, we also provided an illustrative example and critical values for practical uses. In order to make the procedure user-friendly, we built an interface by using R Shiny.

Three new mixed-effects regressions models using an extended Weibull distribution are defined for repeated measures, and their parameters are estimated by maximum likelihood. Monte Carlo simulations report the accuracy of the maximum likelihood estimators and the distribution of the quantile residuals in these regressions. The usefulness of the proposed regressions is illustrated in differential and integral class from the Exact Sciences Department at the University of São Paulo (Brazil) with the objective of showing a pedagogical alternative of learning diagnostic methodology as a game approach. The results indicate that the questions correctly answered by the students took less time to be solved than those incorrectly answered. In addition, the algebraic application and multiple representation questions has the lowest percentages of correct answers and, in general, the longest time to be solved. So, it is possible to note that the used game approach enables the identification of possible difficult points in a class and provides the teacher with the opportunity of search for different strategies to reduce these difficulties faced by differential and integral calculus students when entering higher education, which often result from basic education.

In this paper, we propose a log-symmetric survival model with cure fraction, considering that the distributions of lifetimes for susceptible individuals belong to the log-symmetric class of distributions. This class has continuous, strictly positive, and asymmetric distributions, including the log-normal, log-Student-t, Birnbaum–Saunders, log-logistic I, log-logistic II, contaminated log-normal, log-power-exponential, and log-slash distributions. The log-symmetric class is quite flexible and allows for including bimodal distributions and outliers. It has two parameters interpreted directly as location and scale, where the location is the median, which is a robust measure in the presence of outliers and quite informative in survival analysis. The proposed model includes explanatory variables through the parameter associated with the cure fraction. We evaluate the performance of such model through extensive simulation studies and consider a real data application to evaluate the effect of factors on the immunity to leprosy reactions in patients with Hansen’s disease.

The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors. Existing methods to estimate the model parameters may be sensitive to outlying observations, common in empirical applications. In addition, these methods may be severely affected by such observations, leading to undesirable estimation and prediction results. A robust estimation method, based on iteratively reweighted simple partial least squares, is introduced to improve the prediction accuracy of the function-on-function linear regression model in the presence of outliers. The performance of the proposed method is based on the number of partial least squares components used to estimate the function-on-function linear regression model. Thus, the optimum number of components is determined via a data-driven error criterion. The finite-sample performance of the proposed method is investigated via several Monte Carlo experiments and an empirical data analysis. In addition, a nonparametric bootstrap method is applied to construct pointwise prediction intervals for the response function. The results are compared with some of the existing methods to illustrate the improvement potentially gained by the proposed method.

We consider the Boolean model with random radii based on Cox point processes. Under a condition of stabilization for the random environment, we establish existence and non-existence of subcritical regimes for the size of the cluster at the origin in terms of volume, diameter and number of points. Further, we prove uniqueness of the infinite cluster for sufficiently connected environments.