Mostrando recursos 1 - 20 de 52

  1. On Hilbert’s 8th problem

    Polson, Nicholas G.
    A Hadamard factorisation of the Riemann $\xi$-function is constructed to characterize the zeros of the zeta function.

  2. Weighted sampling without replacement

    Ben-Hamou, Anna; Peres, Yuval; Salez, Justin
    Comparing concentration properties of uniform sampling with and without replacement has a long history which can be traced back to the pioneer work of Hoeffding (1963). The goal of this note is to extend this comparison to the case of non-uniform weights, using a coupling between samples drawn with and without replacement. When the items’ weights are arranged in the same order as their values, we show that the induced coupling for the cumulative values is a submartingale coupling. As a consequence, the powerful Chernoff-type upper-tail estimates known for sampling with replacement automatically transfer to the case of sampling without...

  3. Semiparametric quantile estimation for varying coefficient partially linear measurement errors models

    Zhang, Jun; Zhou, Yan; Cui, Xia; Xu, Wangli
    We study varying coefficient partially linear models when some linear covariates are error-prone, but their ancillary variables are available. After calibrating the error-prone covariates, we study quantile regression estimates for parametric coefficients and nonparametric varying coefficient functions, and we develop a semiparametric composite quantile estimation procedure. Asymptotic properties of the proposed estimators are established, and the estimators achieve their best convergence rate with proper bandwidth conditions. Simulation studies are conducted to evaluate the performance of the proposed method, and a real data set is analyzed as an illustration.

  4. A note on weak convergence results for infinite causal triangulations

    Sisko, Valentin; Yambartsev, Anatoly; Zohren, Stefan
    We discuss infinite causal triangulations and equivalence to the size biased branching process measure—the critical Galton–Watson branching process distribution conditioned on non-extinction. Using known results from the theory of branching processes, this relation is used to prove a novel weak convergence result of the joint length-area process of a infinite causal triangulations to a limiting diffusion. The diffusion equation enables us to determine the physical Hamiltonian and Green’s function from the Feynman–Kac procedure, providing us with a mathematical rigorous proof of certain scaling limits of causal dynamical triangulations.

  5. Sums of possibly associated multivariate indicator functions: The Conway–Maxwell-Multinomial distribution

    Kadane, Joseph B.; Wang, Zhi
    The Conway–Maxwell-Multinomial distribution is studied in this paper. Its properties are demonstrated, including sufficient statistics and conditions for the propriety of posterior distributions derived from it. An application is given using data from Mendel’s ground-breaking genetic studies.

  6. A Bayesian approach to errors-in-variables beta regression

    Figueroa-Zúñiga, Jorge; Carrasco, Jalmar M. F.; Arellano-Valle, Reinaldo; Ferrari, Silvia L. P.
    Beta regression models have been widely used for the analysis of limited-range continuous variables. Here, we consider an extension of the beta regression models that allows for explanatory variables to be measured with error. Then we propose a Bayesian treatment for errors-in-variables beta regression models. The specification of prior distributions is discussed, computational implementation via Gibbs sampling is provided, and two real data applications are presented. Additionally, Monte Carlo simulations are used to evaluate the performance of the proposed approach.

  7. Parameter estimation for discretely observed non-ergodic fractional Ornstein–Uhlenbeck processes of the second kind

    El Onsy, Brahim; Es-Sebaiy, Khalifa; Ndiaye, Djibril
    We use the least squares type estimation to estimate the drift parameter $\theta>0$ of a non-ergodic fractional Ornstein–Uhlenbeck process of the second kind defined as $dX_{t}=\theta X_{t}\,dt+dY_{t}^{(1)},X_{0}=0$, $t\geq0$, where $Y_{t}^{(1)}=\int_{0}^{t}e^{-s}\,dB_{a_{s}}$ with $a_{t}=He^{\frac{t}{H}}$, and $\{B_{t},t\geq0\}$ is a fractional Brownian motion of Hurst parameter $H\in(\frac{1}{2},1)$. We assume that the process $\{X_{t},t\geq0\}$ is observed at discrete time instants $t_{1}=\Delta_{n},\ldots,t_{n}=n\Delta_{n}$. We construct two estimators $\hat{\theta}_{n}$ and $\check{\theta}_{n}$ of $\theta$ which are strongly consistent and we prove that these estimators are $\sqrt{n\Delta_{n}}$-consistent, in the sense that the sequences $\sqrt{n\Delta_{n}}(\hat{\theta}_{n}-\theta)$ and $\sqrt{n\Delta_{n}}(\check{\theta}_{n}-\theta)$ are tight.

  8. Diagnostics analysis for skew-normal linear regression models: Applications to a quality of life dataset

    Ferreira, Clécio da Silva; Vilca, Filidor; Bolfarine, Heleno
    The skew-normal distribution has been used successfully in various statistical applications. The main purpose of this paper is to consider local influence analysis, which is recognized as an important step of data analysis. Motivated to simplify expressions of the conditional expectation of the complete-data log-likelihood function, used in the EM algorithm, diagnostic measures are derived from the case-deletion approach and the local influence approach inspired by Zhu et al. [Biometrika 88 (2001) 727–737] and Zhu and Lee [J. R. Stat. Soc. Ser. B. Stat. Methodol. 63 (2001) 111–126]. Finally, the results obtained are applied to a dataset from a study...

  9. A large class of new bivariate copulas and their properties

    Sharifonnasabi, Zahra; Alamatsaz, Mohammad Hossein; Kazemi, Iraj
    In this paper, we shall construct a large class of new bivariate copulas. This class happens to contain several known classes of copulas, such as Farlie–Gumbel–Morgenstern, Ali–Mikhail–Haq and Barnett–Gumbel, as its especial members. It is shown that the proposed copulas improve the range of values of correlation coefficient and thus they are more applicable in data modeling. We shall also reveal that the dependent properties of the base copula are preserved by the generated copula under certain conditions. Several members of the new class are introduced as instances and their range of correlation coefficients are computed.

  10. Improving mean estimation in ranked set sampling using the Rao regression-type estimator

    Pelle, Elvira; Perri, Pier Francesco
    Ranked set sampling is a statistical technique usually used for a variable of interest that may be difficult or expensive to measure, but whose units are simple to rank according to a cheap sorting criterion. In this paper, we revisit the Rao regression-type estimator in the context of the ranked set sampling. The expression of the minimum mean squared error is given and a comparative study, based on simulated and real data, is carried out to clearly show that the considered estimator outperforms some competitive estimators discussed in the recent literature.

  11. Products of normal, beta and gamma random variables: Stein operators and distributional theory

    Gaunt, Robert E.
    In this paper, we extend Stein’s method to products of independent beta, gamma, generalised gamma and mean zero normal random variables. In particular, we obtain Stein operators for mixed products of these distributions, which include the classical beta, gamma and normal Stein operators as special cases. These operators lead us to closed-form expressions involving the Meijer $G$-function for the probability density function and characteristic function of the mixed product of independent beta, gamma and central normal random variables.

  12. Some unified results on stochastic properties of residual lifetimes at random times

    Misra, Neeraj; Naqvi, Sameen
    The residual life of a random variable $X$ at random time $\Theta$ is defined to be a random variable $X_{\Theta}$ having the same distribution as the conditional distribution of $X-\Theta$ given $X>\Theta$ (denoted by $X_{\Theta}=(X-\Theta|X>\Theta)$). Let $(X,\Theta_{1})$ and $(Y,\Theta_{2})$ be two pairs of jointly distributed random variables, where $X$ and $\Theta_{1}$ (and, $Y$ and $\Theta_{2}$) are not necessarily independent. In this paper, we compare random variables $X_{\Theta_{1}}$ and $Y_{\Theta_{2}}$ by providing sufficient conditions under which $X_{\Theta_{1}}$ and $Y_{\Theta_{2}}$ are stochastically ordered with respect to various stochastic orderings. These comparisons have been made with respect to hazard rate, likelihood ratio and...

  13. Nonlinear filtering with correlated Lévy noise characterized by copulas

    Fernando, B. P. W.; Hausenblas, E.
    The objective in stochastic filtering is to reconstruct the information about an unobserved (random) process, called the signal process, given the current available observations of a certain noisy transformation of that process. ¶ Usually $X$ and $Y$ are modeled by stochastic differential equations driven by a Brownian motion or a jump (or Lévy) process. We are interested in the situation where both the state process $X$ and the observation process $Y$ are perturbed by coupled Lévy processes. More precisely, $L=(L_{1},L_{2})$ is a $2$-dimensional Lévy process in which the structure of dependence is described by a Lévy copula. We derive the associated...

  14. Identifiability of structural characteristics: How relevant is it for the Bayesian approach?

    San Martín, Ernesto
    The role of identification in the Bayesian approach is still debatable. Since Lindley [Bayesian Statistics. A Review (1971) Philadelphia], most Bayesian statisticians pretend that unidentifiabiity causes no real difficulty in their approach. Recently, Wechsler, Izbicki and Esteves [Amer. Statist. 67 (2013) 90–93] provide a simple example illustrating this perspective. By critically reading Wechsler, Izbicki and Esteves [Amer. Statist. 67 (2013) 90–93], we intend to show that the Bayesian approach is far from being free of the identification problems, provided that the interest is focused on the interpretation of the parameters. It is written using a rather ancient style, the so-called...

  15. Mixture models applied to heterogeneous populations

    Cavalcante, Carolina V.; Gonçalves, Kelly C. M.
    Mixture models provide a flexible representation of heterogeneity in a finite number of latent classes. From the Bayesian point of view, Markov Chain Monte Carlo methods provide a way to draw inferences from these models. In particular, when the number of subpopulations is considered unknown, more sophisticated methods are required to perform Bayesian analysis. The Reversible Jump Markov Chain Monte Carlo is an alternative method for computing the posterior distribution by simulation in this case. Some problems associated with the Bayesian analysis of these class of models are frequent, such as the so-called “label-switching” problem. However, as the level of...

  16. On the number of unobserved and observed categories when sampling from a multivariate hypergeometric population

    Kim, Sungsu; Park, Chong Jin
    Consider taking a random sample of size $n$ from a finite population that consists of $N$ categories with $M_{i}$ copies in the $i$th category for $i=1,\dots,N$. Each observed unit in a sample is presumed to have a probability $1-p$ ($0

  17. The exponentiated logarithmic generated family of distributions and the evaluation of the confidence intervals by percentile bootstrap

    Marinho, Pedro Rafael Diniz; Cordeiro, Gauss M.; Peña Ramírez, Fernando; Alizadeh, Morad; Bourguignon, Marcelo
    We study some mathematical properties of a new generator of continuous distributions with three additional parameters, called the exponentiated logarithmic generated family, to extend the normal, Weibull, gamma and Gumbel distributions, among other well-known models. Some special models are discussed. Many properties of this family are studied, some inference procedures developed and a simulation study performed to verify the adequacy of the estimators of the model parameters. We prove empirically the potentiality of the new family by means of two real data sets. The simulation study for different samples sizes assesses the performance of the maximum likelihood estimates obtained by...

  18. Poisson–Lindley INAR(1) model with applications

    Mohammadpour, M.; Bakouch, Hassan S.; Shirozhan, M.
    The paper focuses on a new stationary integer-valued autoregressive model of first order with Poisson–Lindley marginal distribution. Several statistical properties of the model are established, like spectral density function, multi-step ahead conditional measures, stationarity, ergodicity and irreducibility. We consider several methods for estimating the unknown parameters of the model and investigate properties of the estimators. The performances of these estimators are compared via simulation. The model is motivated by some applications to two real count time series data.

  19. Bayesian analysis of multiple-inflation Poisson models and its application to infection data

    Ryu, Duchwan; Bilgili, Devrim; Ergönül, Önder; Ebrahimi, Nader
    In this article we propose a multiple-inflation Poisson regression to model count response data containing excessive frequencies at more than one non-negative integer values. To handle multiple excessive count responses, we generalize the zero-inflated Poisson regression by replacing its binary regression with the multinomial regression, while Su et al. [Statist. Sinica 23 (2013) 1071–1090] proposed a multiple-inflation Poisson model for consecutive count responses with excessive frequencies. We give several properties of our proposed model, and do statistical inference under the fully Bayesian framework. We perform simulation studies and also analyze the data related to the number of infections collected in...

  20. Truncated sequential Monte Carlo test with exact power

    Silva, Ivair; Assunção, Renato
    Monte Carlo hypothesis testing is extensively used for statistical inference. Surprisingly, despite the many theoretical advances in the field, statistical power performance of Monte Carlo tests remains an open question. Because the last assertion may sound questionable for some, the first goal in this paper is to show that the power performance of truncated Monte Carlo tests is still an unsolved question. The second goal here is to present a solution for this issue, that is, we introduce a truncated sequential Monte Carlo procedure with statistical power arbitrarily close to the power of the theoretical exact test. The most significant...

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