Lattice point problems and the central limit theorem in Euclidean spaces.
Limit distribution of the integrated squared error of trigonometric series regression estimator.
Limit distribution of the mean square deviation of the Gasser-Müller nonparametric estimate of the regression function.
Limit distributions of quantiles for a random sample of random length
Limit theorems for rank statistics detecting gradual changes
The purpose of the paper is to investigate weak asymptotic behaviour of rank statistics proposed for detection of gradual changes, linear trends in particular. The considered statistics can be used for various test procedures. The fundaments of the proofs are formed by results of Hušková [4] and Jarušková [5].
Limit theorems for self-normalized large deviation.
Limiting behavior of the perturbed empirical distribution functions evaluated at -statistics for strongly mixing sequences of random variables.
Limiting spectral distribution of circulant type matrices with dependent inputs.
Limiting spectral distribution of XX' matrices
The methods to establish the limiting spectral distribution (LSD) of large dimensional random matrices includes the well-known moment method which invokes the trace formula. Its success has been demonstrated in several types of matrices such as the Wigner matrix and the sample covariance matrix. In a recent article Bryc, Dembo and Jiang [Ann. Probab.34 (2006) 1–38] establish the LSD for random Toeplitz and Hankel matrices using the moment method. They perform the necessary counting of terms in the...
Linear rescaling of the stochastic process
Discussion on the limits in distribution of processes under joint rescaling of space and time is presented in this paper. The results due to Lamperti (1962), Weissman (1975), Hudson Mason (1982) and Laha Rohatgi (1982) are improved here.
Local asymptotic normality for normal inverse gaussian Lévy processes with high-frequency sampling
We prove the local asymptotic normality for the full parameters of the normal inverse Gaussian Lévy process X, when we observe high-frequency data XΔn,X2Δn,...,XnΔn with sampling mesh Δn → 0 and the terminal sampling time nΔn → ∞. The rate of convergence turns out to be (√nΔn, √nΔn, √n, √n) for the dominating parameter (α,β,δ,μ), where α stands for the heaviness of the tails, β the degree of skewness, δ the scale, and μ the location. The essential feature in our study is that the suitably normalized...
Local degeneracy of Markov chain Monte Carlo methods
We study asymptotic behavior of Markov chain Monte Carlo (MCMC) procedures. Sometimes the performances of MCMC procedures are poor and there are great importance for the study of such behavior. In this paper we call degeneracy for a particular type of poor performances. We show some equivalent conditions for degeneracy. As an application, we consider the cumulative probit model. It is well known that the natural data augmentation (DA) procedure does not work well for this model and the so-called...
Lois empiriques et distance de Prokhorov
Matrices aléatoires : statistique asymptotique des valeurs propres
Max-type rank tests in the two-sample problem
Medida de asociación propia entre variables aleatorias discretas.
En este trabajo estudiamos la asociación entre dos variables aleatorias discretas (no cardinales) definiendo una nueva medida [de] asociación, la cual está basada en la velocidad de convergencia del vector de probabilidad correspondiente a la cadena de Markov asociada a la distribución de probabilidad conjunta de las variables en estudio. Ponemos especial énfasis en el estudio muestral y propiedades de los estimadores de dicha medida, calculando sus distribuciones asintóticas bajo el muestreo multinomial...
Minimum disparity estimators for discrete and continuous models
Disparities of discrete distributions are introduced as a natural and useful extension of the information-theoretic divergences. The minimum disparity point estimators are studied in regular discrete models with i.i.d. observations and their asymptotic efficiency of the first order, in the sense of Rao, is proved. These estimators are applied to continuous models with i.i.d. observations when the observation space is quantized by fixed points, or at random, by the sample quantiles of fixed orders....
Model and method for analysis of categorical data with relations [Abstract of thesis]
Modeling snow crystal growth. I: Rigorous results for Packard's digital snowflakes.
Moments of order statistics