Semiparametric estimation in autoregressive processes with Markov regime. (Estimación semiparamétrica en procesos autorregresivos con régimen de Markov.)
Semiparametric estimation of the parameters of multivariate copulas
In the paper we investigate properties of maximum pseudo-likelihood estimators for the copula density and minimum distance estimators for the copula. We derive statements on the consistency and the asymptotic normality of the estimators for the parameters.
Sequential estimation of survival functions with a neutral to the right process prior
In this work, a parametric sequential estimation method of survival functions is proposed in the Bayesian nonparametric context when neutral to the right processes are used. It is proved that the mentioned method is an 1-SLA rule when Dirichlet processes are used; furthermore, asymptotically pointwise optimal procedures are obtained. Finally, an example is given.
Set estimation under convexity type assumptions
Shape factor extremes for prolate spheroids
Microscopic prolate spheroids in a given volume of an opaque material are considered. The extremes of the shape factor of the spheroids are studied. The profiles of the spheroids are observed on a random planar section and based on these observations we want to estimate the distribution of the extremal shape factor of the spheroids. We show that under a tail uniformity condition the Maximum domain of attraction is stable. We discuss the normalising constants (n.c.) for the extremes of the spheroid...
Sharp bounds for expectations of spacings from decreasing density and failure rate families
We apply the method of projecting functions onto convex cones in Hilbert spaces to derive sharp upper bounds for the expectations of spacings from i.i.d. samples coming from restricted families of distributions. Two families are considered: distributions with decreasing density and with decreasing failure rate. We also characterize the distributions for which the bounds are attained.
Sharp bounds on quasiconvex moments of generalized order statistics.
Sharp upper bounds for the best predictor of future mean of some order statistics
We provide sharp upper bounds for the mean of the future order statistics based on observed r order statistics. These bounds are expressed in terms of various scale units. We also determine the probability distributions for which the bounds are attained.
Sign and Wilcoxon tests for quadratic versus cubic regression.
In this paper sign and Wilcoxon tests for testing the null hypothesis of quadratic regression versus the alternative, cubic regression are proposed. It is shown that in the case of a simple design consisting of multiple Y observations at each of the four levels of x, the proposed tests perform reasonably well as compared to their parametric competitors, while in the case of a general design consisting of a large number of levels of x, the loss in Pitman efficiency is considerable. However their...
Significance testing in exact logistic multiple regression.
Simple estimators of the parameters of generalized Tukey’s -family
Simple large sample estimators of scale and location parameters based on blocks of order statistics.
In this paper quite efficient large sample estimation procedures are derived for jointly estimating the parameters of the location-scale family of distributions. These estimators are linear combinations of the means of suitably chosen blocks of order statistics. For specific distributions, such as the extreme-value, normal, and logistic, little is to be gained by using more than three blocks. For these distributions we can obtain joint relative asymptotic efficiencies of 97-98% using the means of...
Simple random walk and rank order statistics
The distributions of rank order statistics are studied for the case of arbitrary sample sizes in the two sample problem. The method applied is a generalization of Dwass's method from his paper in Ann. Math. Statist. 38 (1967), based on the analogy of rank order statistics and functions on a simple random walk.
Simultaneous rank test procedures
Simultaneous rank test procedures are proposed for testing of randomness concerning some marginals. The considered test procedures are analogous to those introduced by Krishnaiah for classical normal theory (see Krishnaiah (1965) Ann. Inst. Statist. Math. 17, 35-53).
Size-robustness of tests based on order statistics and spacings for the exponential distribution
Smoothing and preservation of irregularities using local linear fitting
For nonparametric estimation of a smooth regression function, local linear fitting is a widely-used method. The goal of this paper is to briefly review how to use this method when the unknown curve possibly has some irregularities, such as jumps or peaks, at unknown locations. It is then explained how the same basic method can be used when estimating unsmooth probability densities and conditional variance functions.
Smoothing dichotomy in randomized fixed-design regression with strongly dependent errors based on a moving average
We consider a fixed-design regression model with errors which form a Borel measurable function of a long-range dependent moving average process. We introduce an artificial randomization of grid points at which observations are taken in order to diminish the impact of strong dependence. We show that the Priestley-Chao kernel estimator of the regression fuction exhibits a dichotomous asymptotic behaviour depending on the amount of smoothing employed. Moreover, the resulting estimator is shown to exhibit...
Smoothing Histograms by Means of Lattice- and Continuous Distributions.
Smoothness of Metropolis-Hastings algorithm and application to entropy estimation
The transition kernel of the well-known Metropolis-Hastings (MH) algorithm has a point mass at the chain’s current position, which prevent direct smoothness properties to be derived for the successive densities of marginals issued from this algorithm. We show here that under mild smoothness assumption on the MH algorithm “input” densities (the initial, proposal and target distributions), propagation of a Lipschitz condition for the iterative densities can be proved. This allows us to build a consistent...
Some adaptive estimators for slope parameter
An adaptive estimator (of a slope parameter) based on rank statistics is constructed and its asymptotic optimality is studied. A complete orthonormal system is incorporated in the adaptive determination of the score generating function. The proposed sequential procedure is based on a suitable stopping rule. Various properties of the sequential adaptive procedure and the stopping rule are studied. Asymptotic linearity results of linear rank statistics are also studied and some rates of the convergence...