We propose a two-step method for the analysis of copy number data. We first define the partitions of genome aberrations and conditional on the partitions we introduce a semiparametric Bayesian model for the analysis of multiple samples from patients with different subtypes of a disease. While the biological interest is to identify regions of differential copy numbers across disease subtypes, our model also includes sample-specific random effects that account for copy number alterations between different samples in the same disease subtype. We model the subtype and sample-specific effects using a random effects mixture model. The subtype’s main effects are characterized by a mixture distribution whose components are assigned Dirichlet process priors. The performance of the proposed model is examined using simulated data as well as a breast cancer genomic data set.

Fatigue is a structural damage which occurs when a material is exposed to stress and tension fluctuations. We propose and study the extended generalized half-normal distribution for modeling skewed fatigue life data. The new model contains as special cases the half-normal and generalized half-normal (Comm. Statist. Theory Methods 37 (2008) 1323–1337) distributions. Various of its structural properties are derived, including the density function, moments, quantile and generating functions, mean deviations and order statistics. We investigate maximum likelihood estimation of the model parameters. An application illustrates the potentiality of the new distribution.

In this paper, some bias correction methods are considered for parameter estimation of the complex Bingham distribution. The first method relies on the bias correction formula proposed by Cordeiro and Klein [Statistics & Probability Letters 19 (1994) 169–176]. The second method uses the formulas proposed by Kume and Wood [Statistics & Probability Letters 77 (2007) 832–837] for calculating the derivatives of the log likelihood function. The third method is based on the saddlepoint approximation proposed by Kume and Wood [Biometrika 92 (2005) 465–476]. Bootstrap bias correction methods due to Efron [The Annals of Statistics 7 (1979) 1–26] are also considered. Simulation experiments are used to compare the bias correction methods. In all cases, the analytical and bootstrap bias correction methods have smaller mean square errors. Since the dominant eigenvalue is used to obtain the mean shape, which has practical relevance, it is a key issue for comparing the estimators. The numerical results indicate that the bootstrap methods have a slightly better performance for the dominant eigenvalue.

We pursue the study of the Curie–Weiss model of self-organized criticality we designed in (Ann. Probab. 44 (2016) 444–478). We extend our results to more general interaction functions and we prove that, for a class of symmetric distributions satisfying a Cramér condition (C) and some integrability hypothesis, the sum $S_{n}$ of the random variables behaves as in the typical critical generalized Ising Curie–Weiss model. The fluctuations are of order $n^{3/4}$ and the limiting law is $k\exp(-\lambda x^{4})dx$ where $k$ and $\lambda$ are suitable positive constants. In (Ann. Probab. 44 (2016) 444–478), we obtained these results only for distributions having an even density.

We show that the family of Esscher-transformed Laplace distributions is a subclass of asymmetric Laplace laws.

We collect some applications of the variational formula established by Schroeder [J. Funct. Anal. 77 (1988) 60–87] and Rueß [ALEA Lat. Am. J. Probab. Math. Stat. 11 (2014) 679–709] for the quenched Lyapunov exponent of Brownian motion in stationary and ergodic nonnegative potential. We show, for example, that the Lyapunov exponent for nondeterministic potential is strictly lower than the Lyapunov exponent for the averaged potential. The behaviour of the Lyapunov exponent under independent perturbations of the underlying potential is examined. And with the help of counterexamples, we are able to give a detailed picture of the continuity properties of the Lyapunov exponent.

We consider statistical inference for linear regression models when some variables are distorted with errors by some unknown functions of commonly observable confounding variables. The proposed estimation procedure is designed to accommodate undistorted as well as distorted variables. To test a hypothesis on the parametric components, a restricted least squares estimator is proposed for unknown parameters under some restricted conditions. Asymptotic properties for the estimators are established. A test statistic based on the difference between the residual sums of squares under the null and alternative hypotheses is proposed, and we also obtain the asymptotic properties of the test statistic. A wild bootstrap procedure is proposed to calculate critical values. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analysed for an illustration.

We introduce the univariate two-piece sinh–arcsinh distribution, which contains two shape parameters that separately control skewness and kurtosis. We show that this new model can capture higher levels of asymmetry than the original sinh–arcsinh distribution [Biometrika 96 (2009) 761–780], in terms of some asymmetry measures, while keeping flexibility of the tails and tractability. We illustrate the performance of the proposed model with real data, and compare it to appropriate alternatives. Although we focus on the study of the univariate versions of the proposed distributions, we point out some multivariate extensions.

We study the existence and uniqueness of the generalized reflected backward stochastic differential equations driven by a fractional Brownian motion with Hurst parameter $H$ greater than $1/2$. The stochastic integral used throughout the paper is the divergence type integral.