We consider the estimation of the slope function in functional linear regression, where scalar responses are modeled in dependence of random functions. Cardot and Johannes [2010] have shown that a thresholded projection estimator can attain up to a constant minimax-rates of convergence in a general framework which allows to cover the prediction problem with respect to the mean squared predictio...

We consider high-dimensional sparse regression problems in which we observe y = Xβ + z,where X is an n × p design matrix and z is an n-dimensional vector of independent Gaussianerrors, each with variance σ. Our focus is on the recently introduced SLOPE estimator [15],which regularizes the least-squares estimates with the rank-dependent penalty∑1≤i≤p λi|β̂|(i),where<lb...

Interest in variance estimation in nonparametric regression has grown greatly in the past several decades. Among the existing methods, the least squares estimator in Tong and Wang (2005) is shown to have nice statistical properties and is also easy to implement. Nevertheless, their method only applies to regression models with homoscedastic errors. In this paper, we propose two least squares es...

Time-space fluctuations of chlorophyll-a (Chl-a) within the region off central-southern Chile (33–42°S), and their association with meteorological-oceanographic conditions, were analyzed using satellite time series data (2002–2012). The mean distribution of moderate values of Chl-a (~0.5 mg∙m −3 ) in the northern section (33–38°S) extended out to ~200 km of the coast whereas they were restricte...

A non-parametric statistical method of tracking rapidly changing dynamical systems is introduced. The method implements the non-linear wavelet thresholding estimator to estimate the evolutionary transfer function of the system. The consistency and optimality of the resulting estimate of our method on rapidly changing systems are stated, while no linear estimator can achieve the same optimality....

ABSTRACT This paper studies the performance of the unrestricted estimator (UE) and preliminary test estimator (PTE) of the slope parameter of simple linear regression model under linex loss function. The risk functions of both the UE and PTE are derived. The moment generating function (MGF) of the PTE is derived which turns out to be a component of the risk function. From the MGF the first two ...

Abstract. More than thirty years ago Halbert White inaugurated a “modelrobust” form of statistical inference based on the “sandwich estimator” of standard error. This estimator is known to be “heteroskedasticityconsistent”, but it is less well-known to be “nonlinearity-consistent” as well. Nonlinearity, however, raises fundamental issues because regressors are no longer ancillary, hence can’t b...

Current models for the microwave polarimetric brightness temperature of the sea surface are reviewed. Results from the physical optics (PO), composite surface, and small slope approximation (SSA) theories are illustrated and compared with an empirical model. All models are shown to predict both first and second harmonic azimuthal variations of sea brightnesses, but the physical effects captured...