Estimating a Multivariate Normal Mean with a Constraints Under Scaled Squared Error Lo
Abstract - For normal models with X ∼ Np (θ, σ2Ip ), S2∼ σ2χ2 , independent, we consider the problem of estimating the mean under scale invariant squared error loss, when it is known that the signal to noise ratio is bounded above by m. Risk analysis is achieved by making use of a conditional risk decomposition and we obtain in particular sufficient conditions for an estimator to dominate either the unbiased estimator X, or the maximum likelihood estimator, or both of these benchmark procedures. The given developments bring into play the pivotal role of the boundary Bayes estimator associated with a prior on (θ, σ2) such that θ|σ2 is uniformly distributed on the (boundary) sphere of radius mσ centered at the origin, and a non-informative 1/ σ2 prior measure is placed marginally on σ2. With a series of technical results related to the boundary Bayes estimator, which relate to particular ratios of confluent hypergeometric functions, we show that, the boundary Bayes estimator dominates both X and the maximum likelihood estimator under some conditions. The finding can be viewed as both a multivariate extension of p=1 result due to Kubokawa (2005) and an unknown variance extension of a similar dominance finding due to Marchand and Perron (2001). Various other dominance results are obtained, illustrations are provided and commented upon.
Randomly Censored Quantile Regression Estimation using Functional Stationary Ergodic Data.
Abstract - This paper investigates the conditional quantile estimation of a randomly censored scalar response variable given a functional random covariate (i.e. valued in some in_nite-dimensional space) whenever a stationary ergodic data are considered. A kernel type estimator of the conditional quantile function is introduced. Then, a strong consistency rate as well as the asymptotic distribution of the estimator are established under mild assumptions. A simulation study is considered to show the performance of the proposed estimator. An application to the electricity peak demand prediction using censored smart meter data is also provided.
An Extension of the Asymmetric Causality Tests for Dealing with Deterministic Trend Components
Abstract - This paper extends the asymmetric causality tests, as suggested by Hatemi-J (2012), for dealing with deterministic trend parts. It is shown how integrated variables up to three degrees with deterministic trend parts can be transformed into positive and negative cumulative components. These cumulative components can be used for implementing the asymmetric causality tests based on a Wald test statistic that is shown to follow a chi-square distribution asymptotically. Each solution is expressed as a proposition and a mathematical proof is provided for each underlying proposition. This issue is important because most economic or financial variables that are characterized by an asymmetric structure in the stochastic trend parts seem also to have deterministic trend parts.