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Consider a compound Poisson process which is discretely observed with sampling interval $$\Delta $$ Δ until exactly $$n$$ n nonzero increments are obtained. The jump density and the intensity of the Poisson process are unknown. In this paper, we build and study parametric estimators of appropriate functions of the intensity, and an adaptive nonparametric estimator of the jump size...
This article focuses on a recent concept of covariation for processes taking values in a separable Banach space $$B$$ B and a corresponding quadratic variation. The latter is more general than the classical one of Métivier and Pellaumail. Those notions are associated with some subspace $$\chi $$ χ of the dual of the projective tensor product of $$B$$ B with itself. We also...
This paper seeks to highlight two approaches to the solution of stochastic control and optimal stopping problems in continuous time. Each approach transforms the stochastic problem into a deterministic problem. Dynamic programming is a well-established technique that obtains a partial/ordinary differential equation, variational or quasi-variational inequality depending on the type of problem; the...
We review one method for estimating the modulus of continuity of a Schramm–Loewner evolution (SLE) curve in terms of the inverse Loewner map. Then we prove estimates about the distribution of the inverse Loewner map, which underpin the difficulty in bounding the modulus of continuity of SLE for $$\kappa =8$$ κ = 8 . The main idea in the proof of these estimates is applying the Girsanov theorem...
We focus on the asymptotic behavior of $$U$$ U -statistics of the type $$\begin{aligned} \sum _{1\le i\ne j\le n} h(X_i,X_j)\\ \end{aligned}$$ ∑ 1 ≤ i ≠ j ≤ n h ( X i , X j ) in the long-range dependence setting, where $$(X_i)_{i\ge 1}$$ ( X i ) i ≥ 1 is a stationary mean-zero Gaussian process. Since $$(X_i)_{i\ge 1}$$ ( X i ) i ≥ 1...
The purpose of this note is twofold. First, we survey the study of the percolation phase transition on the Hamming hypercube $$\{0,1\}^{m}$$ { 0 , 1 } m obtained in the series of papers (Borgs et al. in Random Struct Algorithms 27:137–184, 2005; Borgs et al. in Ann Probab 33:1886–1944, 2005; Borgs et al. in Combinatorica 26:395–410, 2006; van der Hofstad and Nachmias in Hypercube percolation,...
Tests for parametric nonhomogeneous and homogeneous Markov processes are given. Asymptotic distribution of test statistics is investigated. Tests for various well-known models are discussed as examples.
What are the face-probabilities of a cuboidal die, i.e. a die with different side-lengths? This paper introduces a model for these probabilities based on a Gibbs distribution. Experimental data produced in this work and drawn from the literature support the Gibbs model. The experiments also reveal that the physical conditions, such as the quality of the surface onto which the dice are dropped, can...
The single-index model is an important tool in multivariate nonparametric regression. This paper deals with M-estimators for the single-index model. Unlike the existing M-estimator for the single-index model, the unknown link function is approximated by B-spline and M-estimators for the parameter and the nonparametric component are obtained in one step. The proposed M-estimator of unknown function...
We consider estimation of the mean vector, $$\theta $$ , of a spherically symmetric distribution with known scale parameter under quadratic loss and when a residual vector is available. We show minimaxity of generalized Bayes estimators corresponding to superharmonic priors with a non decreasing Laplacian of the form $$\pi (\Vert \theta \Vert ^{2})$$ , under certain conditions on the generating...
This paper considers estimation of a functional partially quantile regression model whose parameters include the infinite dimensional function as well as the slope parameters. We show asymptotical normality of the estimator of the finite dimensional parameter, and derive the rate of convergence of the estimator of the infinite dimensional slope function. In addition, we show the rate of the mean squared...
In this paper, we propose the diagonal model (DM), a survey technique for multicategorical sensitive variables. The DM is a nonrandomized response method; that is, the DM avoids the use of any randomization device. Thus, both survey complexity and study costs are reduced. The DM does not require that at least one outcome of the sensitive variable is nonsensitive. Thus, the model can even be applied...
Simple transformations are given for reducing/stabilizing bias, skewness and kurtosis, including the first such transformations for kurtosis. The transformations are based on cumulant expansions and the effect of transformations on their main coefficients. The proposed transformations are compared to the most traditional Box–Cox transformations. They are shown to be more efficient.
Let $$\mathcal{M }_{\underline{i}}$$ be an exponential family of densities on $$[0,1]$$ pertaining to a vector of orthonormal functions $$b_{\underline{i}}=(b_{i_1}(x),\ldots ,b_{i_p}(x))^\mathbf{T}$$ and consider a problem of estimating a density $$f$$ belonging to such family for unknown set $${\underline{i}}\subset \{1,2,\ldots ,m\}$$ , based on a random sample $$X_1,\ldots...
Two-sided confidence intervals for a probability $$p$$ p under a prescribed confidence level $$\gamma $$ γ are an elementary tool of statistical data analysis. A confidence interval has two basic quality characteristics: i) exactness, i. e., whether the actual coverage probability equals or exceeds the prescribed level $$\gamma $$ γ ; ii) inferential precision, measured...
In this paper, a focused vector information criterion for model selection and model averaging is considered for the linear model with missing response. Based on the focused information criterion of Hjort and Claeskens (J Am Stat Assoc 98:879–945, 2003) and imputation idea, a frequentist model averaging estimator for a focused vector of a linear model is proposed, and the estimator is shown to be root-n...
In this paper, we investigate the effect of a single cold standby component on the performance of a coherent system. In particular, we focus on coherent systems which may fail at the time of the first component failure in the system. We obtain signature based expressions for the survival function and mean time to failure of the coherent systems satisfying the abovementioned property.
While identifiability of finite mixtures for a wide range of distributions has been studied by statisticians for decades, discussion on countably infinite mixtures is still limited. This article provides an sufficient condition by means of well-ordered sets and uniform convergence of series. It is then applied to revisit some examples for which the identifiability is well established and then explore...
In the linear regression model with heteroscedastic errors, we propose nonparametric tests for regression under nuisance heteroscedasticity, and tests for heteroscedasticity under nuisance regression. Both types of tests are based on suitable ancillary statistics for the nuisance parameters; hence they avoid their estimation, in contradistinction to tests proposed in the literature. A simulation study,...
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