Saddlepoint approximations for likelihood ratio like statistics with applications to permutation tests

We obtain two theorems extending the use of a saddlepoint approximation to multiparameter problems for likelihood ratio-like statistics which allow their use in permutation and rank tests and could be used in bootstrap approximations. In the first, we show that in some cases when no density exists, the integral of the formal saddlepoint density over the set corresponding to large values of the likelihood ratio-like statistic approximates the true probability with relative error of order $1/n$. In the second, we give multivariate generalizations of the Lugannani--Rice and Barndorff-Nielsen or $r^*$ formulas for the approximations. These theorems are applied to obtain permutation tests based on the likelihood ratio-like statistics for the $k$ sample and the multivariate two-sample cases. Numerical examples are given to illustrate the high degree of accuracy, and these statistics are compared to the classical statistics in both cases.Comment: Published in at http://dx.doi.org/10.1214/11-AOS945 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A comparison of the accuracy of saddlepoint conditional cumulative distribution function approximations

Consider a model parameterized by a scalar parameter of interest and a nuisance parameter vector. Inference about the parameter of interest may be based on the signed root of the likelihood ratio statistic R. The standard normal approximation to the conditional distribution of R typically has error of order O(n^{-1/2}), where n is the sample size. There are several modifications for R, which reduce the order of error in the approximations. In this paper, we mainly investigate Barndorff-Nielsen's modified directed likelihood ratio statistic, Severini's empirical adjustment, and DiCiccio and Martin's two modifications, involving the Bayesian approach and the conditional likelihood ratio statistic. For each modification, two formats were employed to approximate the conditional cumulative distribution function; these are Barndorff-Nielson formats and the Lugannani and Rice formats. All approximations were applied to inference on the ratio of means for two independent exponential random variables. We constructed one and two-sided hypotheses tests and used the actual sizes of the tests as the measurements of accuracy to compare those approximations.Comment: Published at http://dx.doi.org/10.1214/074921707000000193 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Examining the Effects of a Service-Trained Facility Dog on Stress in Children Undergoing Forensic Interview for Allegations of Child Sexual Abuse

Disclosure of child sexual abuse can be a stressful experience for the child. Gaining a better understanding of how best to serve the child, while preserving the quality of their disclosure, is an ever-evolving process. The data to answer this question come from 51 children aged 4–16 (M = 9.1, SD = 3.5), who were referred to a child advocacy center in Virginia for a forensic interview (FI) following allegations of sexual abuse. A repeated measures design was conducted to examine how the presence of a service-trained facility dog (e.g. animal-assisted intervention (AAI) may serve as a mode of lowering stress levels in children during their FIs. Children were randomized to one of the two FI conditions: experimental condition (service-trained facility dog present-AAI) or control condition (service-trained facility dog not present- standard forensic interview). Stress biomarkers salivary cortisol, alpha-amylase, immunoglobulin A (IgA), heart rate, and blood pressure, and Immunoglobulin A were collected before and after the FI. Self-report data were also collected. Results supported a significant decrease in heart rate for those in the experimental condition (p = .0086) vs the control condition (p = .4986). Regression models revealed a significant decrease in systolic and diastolic blood pressure in the experimental condition (p = .03285) and (p = .04381), respectively. Statistically significant changes in alpha-amylase and IgA were also found in relation to disclosure and type of offense. The results of this study support the stress reducing effects of a service-trained facility dog for children undergoing FI for allegations of child sexual abuse

Version 3 of the SMAP Level 4 Soil Moisture Product

The NASA Soil Moisture Active Passive (SMAP) Level 4 Soil Moisture (L4_SM) product provides 3-hourly, 9-km resolution, global estimates of surface (0-5 cm) and root zone (0-100 cm) soil moisture as well as related land surface states and fluxes from 31 March 2015 to present with a latency of 2.5 days. The ensemble-based L4_SM algorithm is a variant of the Goddard Earth Observing System version 5 (GEOS-5) land data assimilation system and ingests SMAP L-band (1.4 GHz) Level 1 brightness temperature observations into the Catchment land surface model. The soil moisture analysis is non-local (spatially distributed), performs downscaling from the 36-km resolution of the observations to that of the model, and respects the relative uncertainties of the modeled and observed brightness temperatures. Prior to assimilation, a climatological rescaling is applied to the assimilated brightness temperatures using a 6 year record of SMOS observations. A new feature in Version 3 of the L4_SM data product is the use of 2 years of SMAP observations for rescaling where SMOS observations are not available because of radio frequency interference, which expands the impact of SMAP observations on the L4_SM estimates into large regions of northern Africa and Asia. This presentation investigates the performance and data assimilation diagnostics of the Version 3 L4_SM data product. The L4_SM soil moisture estimates meet the 0.04 m3m3 (unbiased) RMSE requirement. We further demonstrate that there is little bias in the soil moisture analysis. Finally, we illustrate where the assimilation system overestimates or underestimates the actual errors in the system

Global Assessment of the SMAP Level-4 Surface and Root-Zone Soil Moisture Product Using Assimilation Diagnostics

The Soil Moisture Active Passive (SMAP) mission Level-4 Soil Moisture (L4_SM) product provides 3-hourly, 9-km resolution, global estimates of surface (0-5 cm) and root-zone (0-100 cm) soil moisture and related land surface variables from 31 March 2015 to present with ~2.5-day latency. The ensemble-based L4_SM algorithm assimilates SMAP brightness temperature (Tb) observations into the Catchment land surface model. This study describes the spatially distributed L4_SM analysis and assesses the observation-minus-forecast (O-F) Tb residuals and the soil moisture and temperature analysis increments. Owing to the climatological rescaling of the Tb observations prior to assimilation, the analysis is essentially unbiased, with global mean values of ~0.37 K for the O-F Tb residuals and practically zero for the soil moisture and temperature increments. There are, however, modest regional (absolute) biases in the O-F residuals (under ~3 K), the soil moisture increments (under ~0.01 cu.m/cu.m), and the surface soil temperature increments (under ~1 K). Typical instantaneous values are ~6 K for O-F residuals, ~0.01 (~0.003) cu.m/cu.m for surface (root-zone) soil moisture increments, and ~0.6 K for surface soil temperature increments. The O-F diagnostics indicate that the actual errors in the system are overestimated in deserts and densely vegetated regions and underestimated in agricultural regions and transition zones between dry and wet climates. The O-F auto-correlations suggest that the SMAP observations are used efficiently in western North America, the Sahel, and Australia, but not in many forested regions and the high northern latitudes. A case study in Australia demonstrates that assimilating SMAP observations successfully corrects short-term errors in the L4_SM rainfall forcing

Patient complexity in quality comparisons for glycemic control: An observational study

<p>Abstract</p> <p>Background</p> <p>Patient complexity is not incorporated into quality of care comparisons for glycemic control. We developed a method to adjust hemoglobin A1c levels for patient characteristics that reflect complexity, and examined the effect of using adjusted A1c values on quality comparisons.</p> <p>Methods</p> <p>This cross-sectional observational study used 1999 national VA (US Department of Veterans Affairs) pharmacy, inpatient and outpatient utilization, and laboratory data on diabetic veterans. We adjusted individual A1c levels for available domains of complexity: age, social support (marital status), comorbid illnesses, and severity of disease (insulin use). We used adjusted A1c values to generate VA medical center level performance measures, and compared medical center ranks using adjusted versus unadjusted A1c levels across several thresholds of A1c (8.0%, 8.5%, 9.0%, and 9.5%).</p> <p>Results</p> <p>The adjustment model had R²= 8.3% with stable parameter estimates on thirty random 50% resamples. Adjustment for patient complexity resulted in the greatest rank differences in the best and worst performing deciles, with similar patterns across all tested thresholds.</p> <p>Conclusion</p> <p>Adjustment for complexity resulted in large differences in identified best and worst performers at all tested thresholds. Current performance measures of glycemic control may not be reliably identifying quality problems, and tying reimbursements to such measures may compromise the care of complex patients.</p

Forecasting: theory and practice

Forecasting has always been in the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The lack of a free-lunch theorem implies the need for a diverse set of forecasting methods to tackle an array of applications. This unique article provides a non-systematic review of the theory and the practice of forecasting. We offer a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts, including operations, economics, finance, energy, environment, and social good. We do not claim that this review is an exhaustive list of methods and applications. The list was compiled based on the expertise and interests of the authors. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of the forecasting theory and practice