Estimation of the Parameters of the Weibull Distribution for the Censored Samples.
Estimation of variances in a heteroscedastic RCA(1) model
The paper concerns with a heteroscedastic random coefficient autoregressive model (RCA) of the form . Two different procedures for estimating or , respectively, are described under the special seasonal behaviour of . For both types of estimators strong consistency and asymptotic normality are proved.
Estimation paramétrique d'un processus de diffusion avec retards
Estimation variances for parameterized marked Poisson processes and for parameterized Poisson segment processes
A complete and sufficient statistic is found for stationary marked Poisson processes with a parametric distribution of marks. Then this statistic is used to derive the uniformly best unbiased estimator for the length density of a Poisson or Cox segment process with a parametric primary grain distribution. It is the number of segments with reference point within the sampling window divided by the window volume and multiplied by the uniformly best unbiased estimator of the mean segment length.
Estimators for epidemic alternatives
We introduce and study the behavior of estimators of changes in the mean value of a sequence of independent random variables in the case of so called epidemic alternatives which is one of the variants of the change point problem. The consistency and the limit distribution of the estimators developed for this situation are shown. Moreover, the classical estimators used for `at most change' are examined for the studied situation.
Estimators in the location model with gradual changes
A number of papers has been published on the estimation problem in location models with abrupt changes (e.g., Cs" orgő and Horváth (1996)). In the present paper we focus on estimators in location models with gradual changes. Estimators of the parameters are proposed and studied. It appears that the limit behavior (both the rate of consistency and limit distribution) of the estimators of the change point in location models with abrupt changes and gradual changes differ substantially.
Estimators of the asymptotic variance of stationary point processes - a comparison
We investigate estimators of the asymptotic variance of a –dimensional stationary point process which can be observed in convex and compact sampling window . Asymptotic variance of is defined by the asymptotic relation (as ) and its existence is guaranteed whenever the corresponding reduced covariance measure has finite total variation. The three estimators discussed in the paper are the kernel estimator, the estimator based on the second order intesity of the point process and the...
Evolutionary Pareto distributions
Exponential Convergence Properties of Linear Estimators under Exponential and Uniform Distribution.
Exponential rate of convergence of maximum likelihood estimators for inhomogeneous Wiener processes
Fixed-α and fixed-β efficiencies
Consider testing H0 : F ∈ ω0 against H1 : F ∈ ω1 for a random sample X1, ..., Xn from F, where ω0 and ω1 are two disjoint sets of cdfs on ℝ = (−∞, ∞). Two non-local types of efficiencies, referred to as the fixed-α and fixed-β efficiencies, are introduced for this two-hypothesis testing situation. Theoretical tools are developed to evaluate these efficiencies for some of the most usual goodness of fit tests (including the Kolmogorov–Smirnov tests). Numerical comparisons are provided using several...
Further discussion on second-order efficiency for estimation.
General -estimators in the presence of nuisance parameters. Skew projection technique.
Generalized Bayesian-type estimators. Robust and sensitivity analysis
Global information in statistical experiments and consistency of likelihood-based estimates and tests
In the framework of standard model of asymptotic statistics we introduce a global information in the statistical experiment about the occurrence of the true parameter in a given set. Basic properties of this information are established, including relations to the Kullback and Fisher information. Its applicability in point estimation and testing statistical hypotheses is demonstrated.
Hidden Markov model likelihoods and their derivatives behave like i.i.d. ones
How the initialization affects the stability of the қ-means algorithm
We investigate the role of the initialization for the stability of the қ-means clustering algorithm. As opposed to other papers, we consider the actual қ-means algorithm (also known as Lloyd algorithm). In particular we leverage on the property that this algorithm can get stuck in local optima of the қ-means objective function. We are interested in the actual clustering, not only in the costs of the solution. We analyze when different initializations lead to the same local optimum, and when they...
How the initialization affects the stability of the қ-means algorithm∗
We investigate the role of the initialization for the stability of the қ-means clustering algorithm. As opposed to other papers, we consider the actual қ-means algorithm (also known as Lloyd algorithm). In particular we leverage on the property that this algorithm can get stuck in local optima of the қ-means objective function. We are interested in the actual clustering, not only in the costs of the solution. We analyze when different initializations...
Hypothesis Testing and Parameter Estimation Based on M-Statistics in k Samples with Unequal Variances.
Introduction à la statistique mathématique. IV. Propriétés asymptotiques du modèle statistique