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In this paper, we study the strong consistency and rates of convergence of the Lasso estimator. It is shown that when the error variables have a finite mean, the Lasso estimator is strongly consistent, provided the penalty parameter (say, λn) is of smaller order than the sample size (say n). We also show that this condition on λn cannot be relaxed. More specifically, we show that consistency...
The autoregressive moving average (ARMA) model is one of the most important models in time series analysis. We consider Bayesian estimation of an unknown spectral density in the ARMA model. In i.i.d. cases, it is known that Bayesian predictive densities based on a superharmonic prior asymptotically dominate those based on the Jeffreys prior. It was shown by using the asymptotic expansion of the risk...
In this paper, we study an L1-norm kernel estimator of the conditional quan- tile (CQ) of a scalar response variable Y given a random variable (rv) X taking values in a semi-metric space. The almost complete (a.co.) consis- tency and the asymptotic normality of this estimate are obtained when the sample is an α-mixing sequence. We illustrate our methodology by applying the estimator to...
The block bootstrap has been largely developed for weakly dependent time processes and, in this context, much research has focused on the large-sample properties of block bootstrap inference about sample means. This work validates the block bootstrap for distribution estimation with stationary, linear processes exhibiting strong dependence. For estimating the sample mean’s variance under long-memory,...
We define three types of nondegenerate Wiener-Poisson functionals. Then, for each type we show that the (weighted) characteristic function of nondegenerate functional is of polynomial decay. Our discussion is based on the analysis of Wiener-Poisson functional (Malliavin calculus) developed by Ishikawa and Kunita (2006). Then we apply the decay property to solutions of Itô’s SDE with jumps. We show...
This paper addresses the problem of estimating means of Hudson (1978) type exponential families, where the vector of means lies in a closed convex set with a piecewise smooth boundary. Instead of Stein (1981)-like integration-by-parts technique, the Gauss divergence theorem is used to provide an inequality for evaluation of the risk function with respect to a quadratic loss. The inequality shows that...
In the ranked set sampling algorithm a sample of size n2 is available. The data can be ranked without measurements. A subsample of size n is created using the information given by the ranks. The population mean is estimated by the subsample mean. In this paper, we investigate other ways for creating the subsample. To this end we introduce new sampling algorithms using the idea of antithetic variables...
Defining a location parameter as a generalization of the median, a robust test is proposed for (a) the nonparametric Behrens-Fisher problem, where the underlying distributions may have different scales and could be skewed, and (b) the generalized Behrens-Fisher problem, where the distributions may even have different shapes. We propose to bootstrap a signed rank statistic based on differences of sample...
Let Mnr be the rth largest of a random sample of size n from a distribution F of exponential power type on R. That is, 1-F(z) = O(xd exp(−x)) as x = (z/σ)α → ∞. For example, the exponential, gamma, chi-square, Laplace and normal distributions are of this type. We obtain an asymptotic expansion in powers of u1 = −log(1 − u) and u2 = log u1, for the quantile F−1(u) near u = 1. From this,...
There are various proposals for the selection of the so-called “objective” or “default” priors in Bayesian analysis. The paper introduces a new criterion, the moment matching criterion, which requires the matching of the posterior mean with the maximum likelihood estimator up to a high order of approximation. A complete characterization of such priors in the one or multi-parameter case is provided...
This paper deals with a model of possibly dependent competing risks in the presence of additional independent censoring. Under the assumption that the cumulative incidence functions are proportional or equivalently that the cause-specific cumulative hazard functions are proportional, we derive a maximum likelihood estimator for the cumulative incidence functions. Asymptotic results are derived for...
We consider the problem of estimating the unknown response function and its derivatives in the standard nonparametric regression model. Recently, Abramovich et al. (2010) applied a Bayesian testimation procedure in a wavelet context and proved asymptotical minimaxity of the resulting adaptive level-wise maximum a posteriori wavelet testimator of the unknown response function and its derivatives in...
In this paper, we study the method of moments estimation in a finite mixture where the mixing distribution is supported on [0, 1], and the number of support points is fixed. We prove the validity of the modification method proposed by Lindsay (1989). Further, we demonstrate that the modified estimator is weakly consistent and that its convergence rate is $N^{ - \tfrac{1} {2}} (\log \log N)^{\tfrac{1}...
We consider the model: Y = X + ε, where X and ε are independent random variables. The density of ε is known whereas the one of X is a finite mixture with unknown components. Considering the “ordinary smooth case” on the density of ε, we want to estimate a component of this mixture. To reach this goal, we develop two wavelet estimators: a nonadaptive based on a projection and an adaptive based on a...
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