SPACE-TIME ESTIMATION AND PREDICTION UNDER FIXED-DOMAIN ASYMPTOTICS WITH COMPACTLY SUPPORTED COVARIANCE FUNCTIONS

We study the estimation and prediction of Gaussian processes with spacetime covariance models belonging to the dynamical generalized Wendland (DGW) family, under fixed-domain asymptotics. Such a class is nonseparable, has dynamical compact supports, and parameterizes differentiability at the origin similarly to the space-time Matern class.Our results are presented in two parts. First, we establish the strong consistency and asymptotic normality for the maximum likelihood estimator of the microergodic parameter associated with the DGW covariance model, under fixed-domain asymptotics. The second part focuses on optimal kriging prediction under the DGW model and an asymptotically correct estimation of the mean squared error using a misspecified model. Our theoretical results are, in turn, based on the equivalence of Gaussian measures under some given families of space-time covariance functions, where both space or time are compact. The technical results are provided in the online Supplementary material

Association of Oliguria With Acute Kidney Injury Diagnosis, Severity Assessment, and Mortality Among Patients With Critical Illness.

The current definition and staging of acute kidney injury (AKI) considers alterations in serum creatinine (sCr) level and urinary output (UO). However, the relevance of oliguria-based criteria is disputed. To determine the contribution of oliguria, as defined by the Kidney Disease: Improving Global Outcomes (KDIGO) criteria, to AKI diagnosis, severity assessment, and short- and long-term outcomes. This cohort study included adult patients admitted to a multidisciplinary intensive care unit from January 1, 2010, to June 15, 2020. Patients receiving long-term dialysis and those who declined consent were excluded. Daily sCr level and hourly UO measurements along with sociodemographic characteristics and severity scores were extracted from electronic medical records. Long-term mortality was assessed by cross-referencing the database with the Swiss national death registry. The onset and severity of AKI according to the KDIGO classification was determined using UO and sCr criteria separately, and their agreement was assessed. Using a multivariable model accounting for baseline characteristics, severity scores, and sCr stages, the association of UO criteria with 90-day mortality was evaluated. Sensitivity analyses were conducted to assess how missing sCr, body weight, and UO values, as well as different sCr baseline definitions and imputations methods, would affect the main results. Among the 15 620 patients included in the study (10 330 men [66.1%] with a median age of 65 [IQR, 53-75] years, a median Simplified Acute Physiology Score II score of 40.0 [IQR, 30.0-53.0], and a median follow-up of 67.0 [IQR, 34.0-100.0] months), 12 143 (77.7%) fulfilled AKI criteria. Serum creatinine and UO criteria had poor agreement on AKI diagnosis and staging (Cohen weighted κ, 0.36; 95% CI, 0.35-0.37; P < .001). Compared with the isolated use of sCr criteria, consideration of UO criteria enabled identification of AKI in 5630 patients (36.0%). Those patients had a higher 90-day mortality than patients without AKI (724 of 5608 [12.9%] vs 288 of 3462 [8.3%]; P < .001). On multivariable analysis accounting for sCr stage, comorbidities, and illness severity, UO stages 2 and 3 were associated with a higher 90-day mortality (odds ratios, 2.4 [95% CI, 1.6-3.8; P < .001] and 6.2 [95% CI, 3.7-10.5; P < .001], respectively). These results remained significant in all sensitivity analyses. The findings of this cohort study suggest that oliguria lasting more than 12 hours (KDIGO stage 2 or 3) has major AKI diagnostic implications and is associated with outcomes irrespective of sCr elevations

Estimation and prediction using generalized wendland covariance functions under fixed domain asymptotics

We study estimation and prediction of Gaussian random fields with covariance models belonging to the generalized Wendland (GW) class, under fixed domain asymptotics. As for the Matérn case, this class allows for a continuous parameterization of smoothness of the underlying Gaussian random field, being additionally compactly supported. The paper is divided into three parts: first, we characterize the equivalence of two Gaussian measures with GW covariance function, and we provide sufficient conditions for the equivalence of two Gaussian measures with Matérn and GW covariance functions. In the second part, we establish strong consistency and asymptotic distribution of the maximum likelihood estimator of the microergodic parameter associated to GW covariance model, under fixed domain asymptotics. The third part elucidates the consequences of our results in terms of (misspecified) best linear unbiased predictor, under fixed domain asymptotics. Our findings are illustrated through a simulation study: the former compares the finite sample behavior of the maximum likelihood estimation of the microergodic parameter with the given asymptotic distribution. The latter compares the finite-sample behavior of the prediction and its associated mean square error when using two equivalent Gaussian measures with Matérn and GW covariance models, using covariance tapering as benchmark

Fractures After Denosumab Discontinuation: A Retrospective Study of 797 Cases.

A rebound of osteoclast activity during the 2 years after a treatment or prevention of osteoporosis with denosumab (Dmab) leads to an increased risk of vertebral fractures (VFs). We attempted to identify the risk factors for these VF and to examine the protective role of bisphosphonates. For that, 22 specialists in Switzerland provided data of unselected patients, treated with denosumab for osteoporosis or breast cancer without metastases under aromatase inhibitors, who have received at least two injections of Dmab, with at least 1 year of follow-up after discontinuation. The questionnaire covered separately the periods before, during, and after Dmab treatment, and registered clinical, radiological, and lab data. For the analysis of the risk factors, the main outcomes were the time to the first VF after the treatment, the presence of multiple VFs (MVFs), and the number of VFs. The incidence of VF was 16.4% before, 2.2% during, and 10.3% after the treatment with Dmab. The risk of VF after Dmab discontinuation was associated with an increased risk of non-vertebral fractures. The pretreatment predictors of the post-treatment fracture risk were a parental hip fracture and previous VFs. Further risk factors appeared later, such as low total hip bone mineral density (BMD) during and after denosumab, increased bone resorption markers, and the loss of total hip BMD after the denosumab. Treatment with bisphosphonates, especially after Dmab, had a protective effect. Bisphosphonates given before Dmab did not further decrease the risk of VF in cases who got bisphosphonates after Dmab. This study shows that the risk of VF is poorly predictable before the prescription of denosumab. But during and after the treatment, bone resorption markers and BMD have a significant predictive value. Bisphosphonates after the treatment with denosumab are protective against VFs. © 2021 The Authors. Journal of Bone and Mineral Research published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research (ASBMR)

A Subband Coding Method for HDTV

This paper introduces a new HDTV coder based on motion compensation, subband coding, and high order conditional entropy coding. The proposed coder exploits the temporal and spatial statistical dependencies inherent in the HDTV signal by using intra- and inter-subband conditioning for coding both the motion coordinates and the residual signal. The new framework provides an easy way to control the system complexity and performance, and inherently supports multiresolution transmission. Experimental results show that the coder outperforms MPEG-2, while still maintaining relatively low complexity

High Order Entropy-Constrained Residual VQ for Lossless Compression of Images

High order entropy coding is a powerful technique for exploiting high order statistical dependencies. However, the exponentially high complexity associated with such a method often discourages its use. In this paper, an entropy-constrained residual vector quantization method is proposed for lossless compression of images. The method consists of first quantizing the input image using a high order entropy-constrained residual vector quantizer and then coding the residual image using a first order entropy coder. The distortion measure used in the entropy-constrained optimization is essentially the first order entropy of the residual image. Experimental results show very competitive performance

Asymptotically equivalent prediction in multivariate geostatistics

Cokriging is the common method of spatial interpolation (best linear unbiased prediction) in multivariate geo-statistics. While best linear prediction has been well understood in univariate spatial statistics, the literature for the multivariate case has been elusive so far. The new challenges provided by modern spatial datasets, being typ-ically multivariate, call for a deeper study of cokriging. In particular, we deal with the problem of misspecified cokriging prediction within the framework of fixed domain asymptotics. Specifically, we provide conditions for equivalence of measures associated with multivariate Gaussian random fields, with index set in a compact set of a d-dimensional Euclidean space. Such conditions have been elusive for over about 50 years of spatial statistics. We then focus on the multivariate Matern and Generalized Wendland classes of matrix valued covariance functions, that have been very popular for having parameters that are crucial to spatial interpolation, and that control the mean square differentiability of the associated Gaussian process. We provide sufficient conditions, for equivalence of Gaussian measures, relying on the covariance parameters of these two classes. This enables to identify the parameters that are crucial to asymptotically equivalent interpolation in multivariate geostatistics. Our findings are then illustrated through simulation studies

Image coding using entropy-constrained residual vector quantization

The residual vector quantization (RVQ) structure is exploited to produce a variable length codeword RVQ. Necessary conditions for the optimality of this RVQ are presented, and a new entropy-constrained RVQ (ECRVQ) design algorithm is shown to be very effective in designing RVQ codebooks over a wide range of bit rates and vector sizes. The new EC-RVQ has several important advantages. It can outperform entropy-constrained VQ (ECVQ) in terms of peak signal-to-noise ratio (PSNR), memory, and computation requirements. It can also be used to design high rate codebooks and codebooks with relatively large vector sizes. Experimental results indicate that when the new EC-RVQ is applied to image coding, very high quality is achieved at relatively low bit rates