Investigating Local Dependence with Conditional Covariance Functions

1998 ◽  
Vol 23 (2) ◽  
pp. 129 ◽  
Author(s):  
Jeff Douglas ◽  
Hae Rim Kim ◽  
Brian Habing ◽  
Furong Gao
Keyword(s):  
Local Dependence ◽  
Conditional Covariance ◽  
Covariance Functions

Investigating Local Dependence With Conditional Covariance Functions

1998 ◽  
Vol 23 (2) ◽  
pp. 129-151 ◽  
Author(s):  
Jeff Douglas ◽  
Hae Rim Kim ◽  
Brian Habing ◽  
Furong Gao
Keyword(s):  
Kernel Smoothing ◽  
Item Difficulty ◽  
Estimation Procedure ◽  
Local Dependence ◽  
Function Estimation ◽  
Conditional Covariance ◽  
Monotonic Transformation ◽  
Covariance Functions ◽  
Latent Space ◽  
Latent Ability

The local dependence of item pairs is investigated via a conditional covariance function estimation procedure. The conditioning variable used in the procedure is obtained by a monotonic transformation of total score on the remaining items. Intuitively, the conditioning variable corresponds to the unidimensional latent ability that is best measured by the test. The conditional covariance functions are estimated using kernel smoothing, and a standardization to adjust for the confounding effect of item difficulty is introduced. The particular standardization chosen is an adaptation of Yule’s coefficient of colligation. Several models of local dependence are discussed to explain special situations, such as speededness and latent space multidimensionality, in which the assumptions of unidimensionality and local independence are violated.

scholarly journals Basis Expansions for Functional Snippets

Biometrika ◽  
2020 ◽  
Author(s):  
Zhenhua Lin ◽  
Jane-Ling Wang ◽  
Qixian Zhong
Keyword(s):  
Data Analysis ◽  
Convergence Rate ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Covariance Function ◽  
Covariance Estimation ◽  
Simulation Studies ◽  
Finite Sample ◽  
Covariance Functions ◽  
The Mean

Summary Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed estimator enjoys a convergence rate that is adaptive to the smoothness of the underlying covariance function, and has superior finite-sample performance in simulation studies.

scholarly journals Use of the Lagrange Multiplier Test for Assessing Measurement Invariance Under Model Misspecification

2021 ◽  
pp. 001316442110203
Author(s):  
Lucia Guastadisegni ◽  
Silvia Cagnone ◽  
Irini Moustaki ◽  
Vassilis Vasdekis
Keyword(s):  
Lagrange Multiplier ◽  
False Positive ◽  
Latent Variable ◽  
Model Misspecification ◽  
Cross Product ◽  
Small Sample ◽  
Type I ◽  
Local Dependence ◽  
Lagrange Multiplier Test ◽  
Product Approach

This article studies the Type I error, false positive rates, and power of four versions of the Lagrange multiplier test to detect measurement noninvariance in item response theory (IRT) models for binary data under model misspecification. The tests considered are the Lagrange multiplier test computed with the Hessian and cross-product approach, the generalized Lagrange multiplier test and the generalized jackknife score test. The two model misspecifications are those of local dependence among items and nonnormal distribution of the latent variable. The power of the tests is computed in two ways, empirically through Monte Carlo simulation methods and asymptotically, using the asymptotic distribution of each test under the alternative hypothesis. The performance of these tests is evaluated by means of a simulation study. The results highlight that, under mild model misspecification, all tests have good performance while, under strong model misspecification, the tests performance deteriorates, especially for false positive rates under local dependence and power for small sample size under misspecification of the latent variable distribution. In general, the Lagrange multiplier test computed with the Hessian approach and the generalized Lagrange multiplier test have better performance in terms of false positive rates while the Lagrange multiplier test computed with the cross-product approach has the highest power for small sample sizes. The asymptotic power turns out to be a good alternative to the classic empirical power because it is less time consuming. The Lagrange tests studied here have been also applied to a real data set.

Simple Multivariate Conditional Covariance Dynamics Using Hyperbolically Weighted Moving Averages

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Hiroyuki Kawakatsu
Keyword(s):  
Moving Average ◽  
Curse Of Dimensionality ◽  
Moving Averages ◽  
Conditional Covariance ◽  
Arch Models ◽  
Empirical Application ◽  
Proposed Model ◽  
Out Of Sample ◽  
Weight Model ◽  
Weighted Moving Average

AbstractThis paper considers a class of multivariate ARCH models with scalar weights. A new specification with hyperbolic weighted moving average (HWMA) is proposed as an analogue of the EWMA model. Despite the restrictive dynamics of a scalar weight model, the proposed model has a number of advantages that can deal with the curse of dimensionality. The empirical application illustrates that the (pseudo) out-of-sample multistep forecasts can be surprisingly more accurate than those from the DCC model.

Local Dependence in an Operational CAT: Diagnosis and Implications

2008 ◽  
Vol 45 (3) ◽  
pp. 201-223 ◽  
Author(s):  
Mary Pommerich ◽  
Daniel O. Segall
Keyword(s):  
Local Dependence

Matérn Cross-Covariance Functions for Multivariate Random Fields

2010 ◽  
Vol 105 (491) ◽  
pp. 1167-1177 ◽  
Author(s):  
Tilmann Gneiting ◽  
William Kleiber ◽  
Martin Schlather
Keyword(s):  
Random Fields ◽  
Covariance Functions ◽  
Cross Covariance

GRACE Follow-On Gravity Field Recovery from Combined Laser Ranging Interferometer and Microwave Ranging System Measurements

2021 ◽  
Author(s):  
Saniya Behzadpour ◽  
Andreas Kvas ◽  
Torsten Mayer-Gürr
Keyword(s):  
Gravity Field ◽  
Laser Ranging ◽  
Measurement Technology ◽  
Additional Measurement ◽  
Covariance Functions ◽  
Gravity Field Recovery ◽  
Global Gravity ◽  
Least Squares Adjustment ◽  
Noise Covariance ◽  
Component Estimation

<p>Besides a K-Band Ranging System (KBR), GRACE-FO carries a Laser Ranging Interferometer (LRI) as a technology demonstration to provide measurements of inter-satellite range changes. This additional measurement technology provides supplementary observations, which allow for cross-instrument diagnostics with the KBR system and, to some extent, the separation of ranging noise from other sources such as noise in the on-board accelerometer (ACC) measurements.</p><p>The aim of this study is to incorporate the two ranging systems (LRI and KBR) observations in ITSG-Grace2018 gravity field recovery. The two observation groups are combined in an iterative least-squares adjustment with variance component estimation used to determine the unknown noise covariance functions for KBR, LRI, and ACC measurements. We further compare the gravity field solutions obtained from the combined solutions to KBR-only results and discuss the differences with a focus on the global gravity field and LRI calibration parameters.</p>

Sign in / Sign up

Export Citation Format

Share Document