Search results for "Mean squared error"
showing 10 items of 145 documents
A directional spectral mixture analysis method: application to multiangular airborne measurements
2006
This study aims at developing an operational approach-namely, directional spectral mixture analysis (DISMA)-for retrieving vegetation parameters like fractional vegetation cover (FVC) and leaf area index (LAI) from multispectral and multiangular data. The approach attempts to highlight the consistency of one-dimensional models and linear mixture approaches. DISMA combines spectral signatures of soil and vegetation components with an analytical approximation of the radiative transfer equation, giving rise to a fast invertible bidirectional reflectance distribution function (BRDF) model of discontinuous canopies. Both the forward model and its inversion using a simple technique based on looku…
Determination of total phenolic compounds in compost by infrared spectroscopy
2016
Abstract Middle and near infrared (MIR and NIR) were applied to determine the total phenolic compounds (TPC) content in compost samples based on models built by using partial least squares (PLS) regression. The multiplicative scatter correction, standard normal variate and first derivative were employed as spectra pretreatment, and the number of latent variable were optimized by leave-one-out cross-validation. The performance of PLS-ATR-MIR and PLS-DR-NIR models was evaluated according to root mean square error of cross validation and prediction (RMSECV and RMSEP), the coefficient of determination for prediction ( R pred 2 ) and residual predictive deviation (RPD) being obtained for this la…
Nondestructive Direct Determination of Heroin in Seized Illicit Street Drugs by Diffuse Reflectance near-Infrared Spectroscopy
2008
A new method has been developed for the fast and nondestructive direct determination of heroin in seized street illicit drugs using partial least-squares regression analysis of diffuse reflectance near-infrared spectra. Data were obtained from untreated samples placed in standard glass chromatography vials. A heterogeneous population of 31 samples, previously analyzed by a reference method, was employed to build the calibration model and to have a separated validation set. Based on the use of zero-order data for a calibration set of 21 samples, after standard normal variate and quadratic linear removed baseline correction (detrending), in the wavelength range from 1111 to 1647 nm, 8 PLS fac…
Variance Estimation and Asymptotic Confidence Bands for the Mean Estimator of Sampled Functional Data with High Entropy Unequal Probability Sampling …
2013
For fixed size sampling designs with high entropy it is well known that the variance of the Horvitz-Thompson estimator can be approximated by the Hajek formula. The interest of this asymptotic variance approximation is that it only involves the first order inclusion probabilities of the statistical units. We extend this variance formula when the variable under study is functional and we prove, under general conditions on the regularity of the individual trajectories and the sampling design, that it asymptotically provides a uniformly consistent estimator of the variance function of the Horvitz-Thompson estimator of the mean function. Rates of convergence to the true variance function are gi…
Comments on “Unobservable Selection and Coefficient Stability
2019
Abstract–: We establish a link between the approaches proposed by Oster (2019) and Pei, Pischke, and Schwandt (2019) which contribute to the development of inferential procedures for causal effects in the challenging and empirically relevant situation where the unknown data-generation process is not included in the set of models considered by the investigator. We use the general misspecification framework recently proposed by De Luca, Magnus, and Peracchi (2018) to analyze and understand the implications of the restrictions imposed by the two approaches.
Uniform convergence and asymptotic confidence bands for model-assisted estimators of the mean of sampled functional data
2013
When the study variable is functional and storage capacities are limited or transmission costs are high, selecting with survey sampling techniques a small fraction of the observations is an interesting alternative to signal compression techniques, particularly when the goal is the estimation of simple quantities such as means or totals. We extend, in this functional framework, model-assisted estimators with linear regression models that can take account of auxiliary variables whose totals over the population are known. We first show, under weak hypotheses on the sampling design and the regularity of the trajectories, that the estimator of the mean function as well as its variance estimator …
Efficiency Bounds for Product Designs in Linear Models
1999
We provide lower efficiency bounds for the best product design for an additive multifactor linear model. The A-optimality criterion is used to demonstrate that out bounds are better than the conventional bounds. Applications to other criteria, such as IMSE (integrated mean squared error) criterion are also indicated. In all the cases, the best product design appears to perform better when there are more levels in each factor but decreases when more factors are included. Explicit efficiency formulas for non-additive models are also constructed.
On the Ambiguous Consequences of Omitting Variables
2015
This paper studies what happens when we move from a short regression to a long regression (or vice versa), when the long regression is shorter than the data-generation process. In the special case where the long regression equals the data-generation process, the least-squares estimators have smaller bias (in fact zero bias) but larger variances in the long regression than in the short regression. But if the long regression is also misspecified, the bias may not be smaller. We provide bias and mean squared error comparisons and study the dependence of the differences on the misspecification parameter.
On the ambiguous consequences of omitting variables
2015
This paper studies what happens when we move from a short regression to a long regression (or vice versa), when the long regression is shorter than the data-generation process. In the special case where the long regression equals the data-generation process, the least-squares estimators have smaller bias (in fact zero bias) but larger variances in the long regression than in the short regression. But if the long regression is also misspecified, the bias may not be smaller. We provide bias and mean squared error comparisons and study the dependence of the differences on the misspecification parameter.
Multi-dimensional Function Approximation and Regression Estimation
2002
In this communication, we generalize the Support Vector Machines (SVM) for regression estimation and function approximation to multi-dimensional problems. We propose a multi-dimensional Support Vector Regressor (MSVR) that uses a cost function with a hyperspherical insensitive zone, capable of obtaining better predictions than using an SVM independently for each dimension. The resolution of the MSVR is achieved by an iterative procedure over the Karush-Kuhn-Tucker conditions. The proposed algorithm is illustrated by computers experiments.