Search results for "Equal probability"

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 H\'ajek 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 we can get a uniformly convergent estimator of the variance function of the Horvitz-Thompson estimator of the mean function. Rates of convergence to the true variance function are given for the re…

Event-related potentials to unattended changes in facial expressions: detection of regularity violations or encoding of emotions?

2013

Visual mismatch negativity (vMMN), a component in event-related potentials (ERPs), can be elicited when rarely presented “deviant” facial expressions violate regularity formed by repeated “standard” faces. vMMN is observed as differential ERPs elicited between the deviant and standard faces. It is not clear, however, whether differential ERPs to rare emotional faces interspersed with repeated neutral ones reflect true vMMN (i.e., detection of regularity violation) or merely encoding of the emotional content in the faces. Furthermore, a face-sensitive N170 response, which reflects structural encoding of facial features, can be modulated by emotional expressions. Owing to its similar latency …

N1 and P2 components of auditory event-related potentials in children with and without reading disabilities.

2007

Abstract Objective The effects of within stimulus presentation rate and rise time on basic auditory processing were investigated in children with reading disabilities and typically reading children. Methods Children with reading disabilities (RD; N =19) and control children ( N =20) were studied using event-related potentials (ERPs). Paired stimuli were used with two different within-pair-intervals (WPI; 10 and 255ms) and two different rise times (10 and 130ms). Each stimulus was presented with equal probability and long between-pair inter-stimulus intervals (1–5s). The study focused on N1 and P2 components. Results The P2 responses to the first tone in the pair showed differences between c…

Variance Estimation for the Horvitz-Thompson Total Estimator in Unequal Probability Sampling Designs

Separating mismatch negativity (MMN) response from auditory obligatory brain responses in school-aged children

2013

Mismatch negativity (MMN) overlaps with other auditory event-related potential (ERP) components. We examined the ERPs of 50 9- to 11-year-old children for vowels /i/, /y/ and equivalent complex tones. The goal was to separate MMN from obligatory ERP components using principal component analysis and equal probability control condition. In addition to the contrast of the deviant minus standard response, we employed the contrast of the deviant minus control response, to see whether the obligatory processing contributes to MMN in children. When looking for differences in speech deviant minus standard contrast, MMN starts around 112 ms. However, when both contrasts are examined, MMN emerges for …

Estimate the mean electricity consumption curve by survey and take auxiliary information into account

2012

In this thesis, we are interested in estimating the mean electricity consumption curve. Since the study variable is functional and storage capacities are limited or transmission cost are high survey sampling techniques are interesting alternatives to signal compression techniques. We extend, in this functional framework, estimation methods that take into account available auxiliary information and that can improve the accuracy of the Horvitz-Thompson estimator of the mean trajectory. The first approach uses the auxiliary information at the estimation stage, the mean curve is estimated using model-assisted estimators with functional linear regression models. The second method involves the au…