Mostrando recursos 1 - 20 de 250

  1. Semimartingale properties of the lower Snell envelope in optimal stopping under model uncertainty

    Treviño Aguilar, Erick
    Optimal stopping under model uncertainty is a recent topic under research. The classical approach to characterize the solution of optimal stopping is based on the Snell envelope which can be seen as the value process as time runs. The analogous concept under model uncertainty is the so-called lower Snell envelope and in this paper, we investigate its structural properties. We give conditions under which it is a semimartingale with respect to one of the underlying probability measures and show how to identify the finite variation process by a limiting procedure. An example illustrates that without our conditions, the semimartingale property...

  2. Ranked set sampling with scrambled response model to subsample non-respondents

    Ahmed, Shakeel; Shabbir, Javid
    This paper considers use of the scrambled response model in Ranked Set Sampling (RSS) for collecting information on second call to estimate population mean when non-response is due to sensitivity of the study variable. It also uses Extreme Ranked Set Sampling (ERSS) and Median Ranked Set Sampling (MRSS) to sub-sample the non-respondents. Expressions for variances of different estimators are derived. A Monte Carlo experiment is carried out to observe the efficiency of proposed estimators.

  3. Calibration estimation of adjusted Kuk’s randomized response model for sensitive attribute

    Son, Chang-Kyoon; Kim, Jong-Min
    In this paper, we consider the calibration procedure for Su et al.’s [Sociol. Methods Res. 44 (2014) DOI:10.1177/0049124114554459] adjusted Kuk randomized response (RR) technique by using auxiliary information such as gender or age group of respondents associated with the variable of interest. Our proposed calibration method can overcome the problems such as noncoverage and nonresponse. From the efficiency comparison study, we show that the calibrated adjusted Kuk’s RR estimators are more efficient than that of Su et al. [Sociol. Methods Res. 44 (2014) DOI:10.1177/0049124114554459], when the known population cell and marginal counts of auxiliary information are used for the calibration...

  4. Multivariate versions of dimension walks and Schoenberg measures

    Alonso-Malaver, Carlos Eduardo; Porcu, Emilio; Giraldo Henao, Ramón
    This paper considers multivariate Gaussian fields with their associated matrix valued covariance functions. In particular, we characterize the class of stationary-isotropic matrix valued covariance functions on $d$-dimensional Euclidean spaces, as being the scale mixture of the characteristic function of a $d$ dimensional random vector being uniformly distributed on the spherical shell of $\mathbb{R}^{d}$, with a uniquely determined matrix valued and signed measure. This result is the analogue of celebrated Schoenberg theorem, which characterizes stationary and isotropic covariance functions associated to an univariate Gaussian fields. ¶ The elements $\mathbf{C}$, being matrix valued, radially symmetric and positive definite on $\mathbb{R}^{d}$, have a matrix valued...

  5. From heavy-tailed Boolean models to scale-free Gilbert graphs

    Hirsch, Christian
    Define the scale-free Gilbert graph based on a Boolean model with heavy-tailed radius distribution on the $d$-dimensional torus by connecting two centers of balls by an edge if at least one of the balls contains the center of the other. We investigate two asymptotic properties of this graph as the size of the torus tends to infinity. First, we determine the tail index associated with the asymptotic distribution of the sum of all power-weighted incoming and outgoing edge lengths at a randomly chosen vertex. Second, we study the behavior of chemical distances on scale-free Gilbert graphs and show the existence...

  6. Slash-elliptical nonlinear regression model

    Alcantara, Izabel Cristina; Cysneiros, Francisco José A.
    The aim of this paper is to develop nonlinear regression models with error distribution having the slash-elliptical family. A slash-elliptical random variable is defined as the quotient of two independent random variables, $Z$ and $U^{1/q}$, where $Z$ has an elliptical contoured distribution and $U$ has a uniform distribution. A key advantage of the slash-elliptical distribution is the simplicity by which the well-known elliptical contoured distribution can be modified to support increase in kurtosis. The main properties of the slash-elliptical distribution is symmetry, heavy tails and convergence to the elliptical contoured distribution as the limiting case of the shape parameter. One...

  7. A new stochastic model and its diffusion approximation

    Covo, Shai; Elalouf, Amir
    This paper considers a kind of queueing problem with a Poisson number of customers or, more generally, objects which may arrive in groups of random size. The focus is on the total quantity over time, called system size. The main result is that the process representing the system size, properly normalized, converges in finite-dimensional distributions to a centered Gaussian process (the diffusion approximation) with several attractive properties. Comparison with existing works (where the number of objects is assumed nonrandom) highlights the contribution of the present paper.

  8. Prediction of future failures for generalized exponential distribution under Type-I or Type-II hybrid censoring

    Valiollahi, R.; Asgharzadeh, A.; Kundu, D.
    In this paper, we consider the prediction of a future observation based on either Type-I or Type-II hybrid censored samples when the lifetime distribution of the experimental units is assumed to be a generalized exponential random variable. Different point and interval predictors are obtained using classical and Bayesian approaches. Monte Carlo simulations are performed to compare the performances of the different methods, and the analysis of one data set has been presented for illustrative purposes.

  9. Strong rate of tamed Euler–Maruyama approximation for stochastic differential equations with Hölder continuous diffusion coefficient

    Ngo, Hoang-Long; Luong, Duc-Trong
    We study the strong rate of convergence of the tamed Euler–Maruyama approximation for one-dimensional stochastic differential equations with superlinearly growing drift and Hölder continuous diffusion coefficients.

  10. Inference on dynamic models for non-Gaussian random fields using INLA

    Cortes, R. X.; Martins, T. G.; Prates, M. O.; Silva, B. A.
    Robust time series analysis is an important subject in statistical modeling. Models based on Gaussian distribution are sensitive to outliers, which may imply in a significant degradation in estimation performance as well as in prediction accuracy. State-space models, also referred as Dynamic Models, is a very useful way to describe the evolution of a time series variable through a structured latent evolution system. Integrated Nested Laplace Approximation (INLA) is a recent approach proposed to perform fast approximate Bayesian inference in Latent Gaussian Models which naturally comprises Dynamic Models. We present how to perform fast and accurate non-Gaussian dynamic modeling with...

  11. Consistency of hyper-$g$-prior-based Bayesian variable selection for generalized linear models

    Wu, Ho-Hsiang; Ferreira, Marco A. R.; Gompper, Matthew E.
    We study the consistency of a Bayesian variable selection procedure for generalized linear models. Specifically, we consider the consistency of a Bayes factor based on $g$-priors proposed by Sabanés Bové and Held [Bayesian Analysis 6 (2011) 387–410]. The integrals necessary for the computation of this Bayes factor are performed with Laplace approximation and Gaussian quadrature. We show that, under certain regularity conditions, the resulting Bayes factor is consistent. Furthermore, a simulation study confirms our theoretical results. Finally, we illustrate this model selection procedure with an application to a real ecological dataset.

  12. On the powers of polynomial logistic distributions

    Ostrovska, Sofiya
    Let $P(x)$ be a polynomial monotone increasing on $(-\infty,+\infty)$. The probability distribution possessing the distribution function ¶ \[F(x)=\frac{1}{1+\exp\{-P(x)\}}\] is called the polynomial logistic distribution associated with polynomial $P$ and denoted by PL($P$). It has recently been introduced, as a generalization of the logistic distribution, by V. M. Koutras, K. Drakos, and M. V. Koutras who have also demonstrated the importance of this distribution in modeling financial data. In the present paper, for a random variable $X\sim\mathrm{PL}(P)$, the analytical properties of its characteristic function are examined, the moment-(in)determinacy for the powers $X^{m},\;m\in\mathbb{N}$ and $|X|^{p},\;p\in(0,+\infty)$ depending on the values of $m$ and $p$ is...

  13. Spatio-temporal dynamic model and parallelized ensemble Kalman filter for precipitation data

    Sánchez, Luis; Infante, Saba; Griffin, Victor; Rey, Demetrio
    This paper presents a spatiotemporal dynamic model which allows Bayesian inference of precipitation states in some Venezuelan meteorological stations. One of the limitations that are reported in digital databases is the reliability of the records and the lack of information for certain days, weeks, or months. To complete the missing data, the Gibbs algorithm, a Markov Chain Monte Carlo (MCMC) procedure, was used. A feature of precipitation series is that their distribution contains discrete and continuous components implying complicated dynamics. A model is proposed based on a discrete representation of a stochastic integro-difference equation. Given the difficulty of obtaining explicit...

  14. Wavelet shrinkage for regression models with random design and correlated errors

    Porto, Rogério; Morettin, Pedro; Percival, Donald; Aubin, Elisete
    Extraction of a signal in the presence of stochastic noise via wavelet shrinkage has been studied under assumptions that the noise is independent and identically distributed (IID) and that the samples are equispaced (evenly spaced in time). Previous work has relaxed these assumptions either to allow for correlated observations or to allow for random sampling, but very few papers have relaxed both together. In this paper we relax both assumptions by assuming the noise to be a stationary Gaussian process and by assuming a random sampling scheme dictated either by a uniform distribution or by an evenly spaced design subject...

  15. On geometric ergodicity of additive and multiplicative transformation-based Markov Chain Monte Carlo in high dimensions

    Dey, Kushal Kr.; Bhattacharya, Sourabh
    Recently Dutta and Bhattacharya (Statistical Methodology 16 (2014) 100–116) introduced a novel Markov Chain Monte Carlo methodology that can simultaneously update all the components of high-dimensional parameters using simple deterministic transformations of a one-dimensional random variable drawn from any arbitrary distribution defined on a relevant support. The methodology, which the authors refer to as transformation-based Markov Chain Monte Carlo (TMCMC), greatly enhances computational speed and acceptance rate in high-dimensional problems. Two significant transformations associated with TMCMC are additive and multiplicative transformations. Combinations of additive and multiplicative transformations are also of much interest. In this work, we investigate geometric ergodicity associated...

  16. A note on the asymptotic law of the histogram without continuity assumptions

    Laloë, Thomas; Servien, Rémi
    Asymptotic normality of density estimates often requires the continuity of the underlying density and assumptions on its derivatives. Recently, these assumptions have been weakened for some estimates using the less restrictive notion of regularity index. However, the particular definition of this index makes it unusable for many estimates. In this paper, we define a more general regularity concept: the $r$-regularity. This concept is used to obtain asymptotic law of the histogram without hypothesis on the continuity of the underlying density. As expected, when it does exist, the limit distribution is a standard Gaussian. Then, to illustrate the new definition of...

  17. A Bayesian semi-parametric approach to extreme regime identification

    Ferraz do Nascimento, Fernando; Gamerman, Dani; Davis, Richard
    The limiting tail behaviour of distributions is known to follow one of three possible limiting distributions, depending on the domain of attraction of the observational model under suitable regularity conditions. This work proposes a new approach for identification and analysis of the shape parameter of the GPD as a mixture distribution over the three possible regimes. This estimation is based on evaluation of posterior probabilities for each regime. The model-based approach uses a mixture at the observational level where a Generalized Pareto distribution (GPD) is assumed above the threshold, and mixture of Gammas distributions is used under a threshold. The...

  18. Multiple imputation of unordered categorical missing data: A comparison of the multivariate normal imputation and multiple imputation by chained equations

    Karangwa, Innocent; Kotze, Danelle; Blignaut, Renette
    Missing data are common in survey data sets. Enrolled subjects do not often have data recorded for all variables of interest. The inappropriate handling of them may negatively affect the inferences drawn. Therefore, special attention is needed when analysing incomplete data. The multivariate normal imputation (MVNI) and the multiple imputation by chained equations (MICE) have emerged as the best techniques to deal with missing data. The former assumes a normal distribution of the variables in the imputation model and the latter fills in missing values taking into account the distributional form of the variables to be imputed. This study examines...

  19. Generalized backward stochastic variational inequalities driven by a fractional Brownian motion

    Borkowski, Dariusz; Jańczak-Borkowska, Katarzyna
    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.

  20. On modelling asymmetric data using two-piece sinh–arcsinh distributions

    Rubio, F. J.; Ogundimu, E. O.; Hutton, J. L.
    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.

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