Showing papers in "Sankhya in 2014"
TL;DR: In this paper, a new technique for monitoring shifts in covariance matrices of Gaussian processes is developed, which is asymptotically robust to the shifts in the mean.
Abstract: In this paper a new technique for monitoring shifts in covariance matrices of Gaussian processes is developed. The processes we monitor are obtained from the covariance matrices estimated using a single observation. These processes follow independent Gaussian distribution in the in-control state, thus allowing for application of standard control charts. Furthermore, in contrary to the existing literature, the suggested procedure is asymptotically robust to the shifts in the mean. The explicit out-of-control distribution for an arbitrary moment of the shift is derived. The performance of numerous multivariate control charts is evaluated in an extensive simulation study and applied to monitoring volatilities on financial markets.
5 citations
TL;DR: In this article, asymptotic theory for piecewise polynomial and spline regression with partially free knots and residuals exhibiting three types of dependence structures (long memory, short memory and anti-persistence) is considered.
Abstract: Motivated by the analysis of glomerular time series extracted from calcium-imaging data, asymptotic theory for piecewise polynomial and spline regression with partially free knots and residuals exhibiting three types of dependence structures (long memory, short memory and anti-persistence) is considered. Unified formulas based on fractional calculus are derived for subordinated residual processes in the domain of attraction of a Hermite process. The results are applied to testing for the effect of a neurotransmitter on the response of olfactory neurons in honeybees to odorant stimuli.
4 citations
TL;DR: In this article, the moments of statistic V used for testing sphericity for a general elliptical model were derived using the distribution of the trace of a generalized Wishart matrix based on elliptical models.
Abstract: In this second part of the paper, we make use of the distribution of the trace of a generalized Wishart matrix based on elliptical models to derive the moments of statistic V used for testing sphericity for a general elliptical model. From the general expressions, we derive specific expressions for the special case of the Kotz family, which includes the Gaussian subfamily. Finally, to illustrate the usefulness of the approach, the exact distribution of the statistic V is derived in terms of the G-function by using Mellin transform and complex integration techniques.
4 citations
TL;DR: In this article, Florens, Richard and Rolin proposed a specification test of a parametric hypothesis against a nonparametric one, in the framework of a Bayesian encompassing test.
Abstract: Florens, Richard and Rolin (2003) proposed a specification test of a parametric hypothesis against a nonparametric one, in the framework of a Bayesian encompassing test. Building on that work, this paper elaborates the procedure under a condition of partial observability. The general procedure is illustrated with the case where only the sign is observable, and more generally when the available data come from a binary reduction of a vector of latent variables. This example is also used to point out some difficulties when implementing the proposed procedure.
2 citations
TL;DR: This work proposes a new method to simultaneously select variables and favor a grouping effect, where strongly correlated predictors tend to be in or out of the model together, based on penalized least squares with a penalty function that combines the L1 and a Correlation based Penalty norms.
Abstract: La selection de variables peut etre difficile, en particulier dans les situations ou un grand nombre de variables explicatives est disponible, avec la presence possible de correlations elevees comme dans le cas des donnees d'expression genetique. Dans cet article, nous proposons une nouvelle methode de regression lineaire penalisee, appelee l'elastic corr-net, pour simultanement estimer les parametres inconnus et selectionner les variables importantes. De plus, elle encourage un effet de groupe: les variables fortement correlees ont tendance a etre toutes incluses ou toutes exclues du modele. La methode est fondee sur les moindres carres penalises avec une penalite qui, comme la penalite $L_{1}$, retrecit certains coefficients exactement vers zero. En outre, cette penalite contient un terme qui lie explicitement la force de penalisation a la correlation entre les variables explicatives. Pour montrer les avantages de notre approche par rapport aux methodes les plus concurrentes, une etude detaillee de simulation est realisee en moyenne et grande dimension. Enfin, nous appliquons la methodologie a trois ensembles de donnees reelles. Le resultat principal de notre methode est l'identification du cadre ou l'elastic-net est moins performante : en effet, en termes des erreurs de prediction et d'estimation, notre methode parait plus adaptee aux situations du type $p\leq n$ (le nombre de variables est inferieure a la taille de l'echantillon). Si $p\gg n,$ notre methode reste competive et elle permet aussi de selectionner plus que $n$ variables.
TL;DR: It is shown here that the Hajek estimator of the p.d.f., if properly centered and scaled, converges weakly to a Gaussian process with covariance kernel proportional to that of a Brownian bridge.
Abstract: The estimation of the distribution function of a population is an important problem in sampling finite populations. The existing literature focuses on the problem of estimating the population distribution function (p.f.d.) at a single point, or at a finite number of points. In this paper the main interest consists in estimating the whole p.d.f.. In many respects, the starting point is close to classical nonparametric statistics, although the approach to inference is based on sampling design. It is shown here that the Hajek estimator of the p.d.f., if properly centered and scaled, converges weakly to a Gaussian process with covariance kernel proportional to that of a Brownian bridge. The proportionality factor essentially depends on the sample design. Applications to (i) construction of a confidence band for the p.d.f., (i
i) comparison of the p.d.f.s of two populations, and (i
i
i) testing for independence of two characters are provided.