High-Dimensional Conditional Covariance Matrices Estimation Using a Factor-GARCH Model

Estimation of a conditional covariance matrix is an interesting and important research topic in statistics and econometrics. However, modelling ultra-high dimensional dynamic (conditional) covariance structures is known to suffer from the curse of dimensionality or the problem of singularity. To partially solve this problem, this paper establishes a model by combining the ideas of a factor model and a symmetric GARCH model to describe the dynamics of a high-dimensional conditional covariance matrix. Quasi maximum likelihood estimation (QMLE) and least square estimation (LSE) methods are used to estimate the parameters in the model, and the plug-in method is introduced to obtain the estimation of conditional covariance matrix. Asymptotic properties are established for the proposed method, and simulation studies are given to demonstrate its performance. A financial application is presented to support the methodology.

Conditional Covariances for the Signal Lag Measurements in Fluoroscopic Imaging

In fluoroscopic imaging, we can acquire X-ray image sequences using a flat-panel dynamic detector. However, lag signals from previous frames are added to the subsequently acquired images and produce lag artifacts. The lag signals also inflate the measured noise power spectrum (NPS) of a detector. In order to correct the measured NPS, the lag correction factor (LCF) is generally used. However, the nonuniform temporal gain (NTG), which is from inconsistent X-ray sources and readout circuits, can significantly distort the LCF measurements. In this paper, we propose a simple scheme to alleviate the NTG problem in order to accurately and efficiently measure the detector LCF. We first theoretically analyze the effects of NTG, especially on the correlation-based LCF measurement methods, where calculating the correlation coefficients are required. In order to remove the biases due to NTG, a notion of conditional covariance is considered for unbiased estimates of the correlation coefficients. Experiments using practical X-ray images acquired from a dynamic detector were conducted. The proposed approach could yield accurate LCF values similarly to the current approaches of the direct and U-L corrections with a low computational complexity. By calculating the correlation coefficients based on conditional covariance, we could obtain accurate LCF values even under the NTG environment. This approach does not require any preprocessing scheme of the direct or U-L correction and can provide further accurate LCF values than the method of IEC62220-1-3 does.

Simple Multivariate Conditional Covariance Dynamics Using Hyperbolically Weighted Moving Averages

This 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.

Envelopes in multivariate regression models with nonlinearity and heteroscedasticity

Summary Envelopes have been proposed in recent years as a nascent methodology for sufficient dimension reduction and efficient parameter estimation in multivariate linear models. We extend the classical definition of envelopes in Cook et al. (2010) to incorporate a nonlinear conditional mean function and a heteroscedastic error. Given any two random vectors ${X}\in\mathbb{R}^{p}$ and ${Y}\in\mathbb{R}^{r}$, we propose two new model-free envelopes, called the martingale difference divergence envelope and the central mean envelope, and study their relationships to the standard envelope in the context of response reduction in multivariate linear models. The martingale difference divergence envelope effectively captures the nonlinearity in the conditional mean without imposing any parametric structure or requiring any tuning in estimation. Heteroscedasticity, or nonconstant conditional covariance of ${Y}\mid{X}$, is further detected by the central mean envelope based on a slicing scheme for the data. We reveal the nested structure of different envelopes: (i) the central mean envelope contains the martingale difference divergence envelope, with equality when ${Y}\mid{X}$ has a constant conditional covariance; and (ii) the martingale difference divergence envelope contains the standard envelope, with equality when ${Y}\mid{X}$ has a linear conditional mean. We develop an estimation procedure that first obtains the martingale difference divergence envelope and then estimates the additional envelope components in the central mean envelope. We establish consistency in envelope estimation of the martingale difference divergence envelope and central mean envelope without stringent model assumptions. Simulations and real-data analysis demonstrate the advantages of the martingale difference divergence envelope and the central mean envelope over the standard envelope in dimension reduction.

On the Effect of a Binary Treatment in the Presence of a Control Covariate

The nonparametric regression of a response variable on a binary treatment and a control covariate equals the nonparametric regression of the response on the control plus the conditional (given the control) linear regression of the resulting residual on the residual of the nonparametric regression of the treatment on the control. While similar decompositions are typically obtained using the technique of orthogonal projection applicable to random variables with finite second moments, this result holds if the response only has a finite first moment and allows the control to be completely arbitrary. Consequently, if the propensity score of the treatment is bounded away from zero and one, the treatment effect, after controlling for the covariate, equals the ratio of the conditional covariance of the response and the treatment to the conditional variance of the treatment. AMS 2020 subject classification: Primary 62G08, Secondary 62J05, 91F10, 62P20, 62P25

Comparison of Two Bayesian Methods in Evaluation of the Absence of the Gold Standard Diagnostic Tests

Objective. The Bayesian model plays an important role in diagnostic test evaluation in the absence of the gold standard, which used the external prior distribution of a parameter combined with sample data to yield the posterior distribution of the test characteristics. However, the correlation between diagnostic tests has always been a problem that cannot be ignored in the Bayesian model evaluation. This study will discuss how different Bayesian model, correlation scenarios, and prior distribution affect the outcome. Methods. The data analyzed in this study was gathered during studies of patients presenting to the Nanjing Chest Hospital with suspected tuberculosis. The diagnostic character of T-SPOT.Tb and KD38 tuberculosis antibody test were evaluated in different Bayesian model, and discharge diagnosis as a gold standard was used to verify the model results in the end. Result. The comparison of four models under the conditional independence situation found that Bayesian probabilistic constraint model was consistent with the Conditional Covariance Bayesian model. The results were mainly affected by prior information. The sensitivity and specificity of the two tests in Conditional Covariance Bayesian model in prior constraint situation were considerably higher than the Bayesian probabilistic constraint model in prior constraint situation. The results of the four models under the conditional dependence situation were similar to the conditional independence situation; pD was also negative with no prior constraint situation in both model Bayesian probabilistic constraint model and Conditional Covariance Bayesian model. The Deviance Information Criterion of Bayesian probabilistic constraint model was close to model Conditional Covariance Bayesian model, but pD of Conditional Covariance Bayesian model in Prior constraint situation (pD=2.40) was higher than the Bayesian probabilistic constraint model in Prior constraint situation (pD=1.66). Conclusion. The result of Conditional Covariance Bayesian model in prior constraint with conditional independence situation was closest to the result of gold standard evaluation in our data. Both of the two Bayesian methods are the feasible way for the evaluation of diagnostic test in the absence of the gold standard diagnostic. Prior source, priority number, and conditional dependencies should be considered in the method selection, the accuracy of posterior estimation mainly depending on the prior distribution.