Residuals and goodness-of-fit tests for stationary marked Gibbs point processes

The inspection of residuals is a fundamental step to investigate the quality of adjustment of a parametric model to data. For spatial point processes, the concept of residuals has been recently proposed by Baddeley et al. (2005) as an empirical counterpart of the {\it Campbell equilibrium} equation for marked Gibbs point processes. The present paper focuses on stationary marked Gibbs point processes and deals with asymptotic properties of residuals for such processes. In particular, the consistency and the asymptotic normality are obtained for a wide class of residuals including the classical ones (raw residuals, inverse residuals, Pearson residuals). Based on these asymptotic results, we define goodness-of-fit tests with Type-I error theoretically controlled. One of these tests constitutes an extension of the quadrat counting test widely used to test the null hypothesis of a homogeneous Poisson point process

The GRAVITY fringe tracker: correlation between optical path residuals and atmospheric parameters

After the first year of observations with the GRAVITY fringe tracker, we compute correlations between the optical path residuals and atmospheric and astronomical parameters. The median residuals of the optical path residuals are 180 nm on the ATs and 270 nm on the UTs. The residuals are uncorrelated with the target magnitudes for Kmag below 5.5 on ATs (9 on UTs). The correlation with the coherence time is however extremely clear, with a drop-off in fringe tracking performance below 3 ms.Comment: submitted to SPIE Astronomical Telescopes & Instrumentation 201

Environmental costs of residuals: a characterization of efficient tax policies.

Durable goods leave residuals after being retired from use. If the environmental costs of the residuals are external to consumers and producers of the good, then overproduction and excess residuals will result. Ad valorem taxes are show to be ineffective in eliminating this externality. The efficient regulatory policy is shown to be based on a pigouvian tax.Externalities; Pollution control; Optimal taxation; Durable goods; Residuals;

Functional delta residuals and applications to functional effect sizes

Given a functional central limit (fCLT) and a parameter transformation, we use the functional delta method to construct random processes, called functional delta residuals, which asymptotically have the same covariance structure as the transformed limit process. Moreover, we prove a multiplier bootstrap fCLT theorem for these transformed residuals and show how this can be used to construct simultaneous confidence bands for transformed functional parameters. As motivation for this methodology, we provide the formal application of these residuals to a functional version of the effect size parameter Cohen's $d$, a problem appearing in current brain imaging applications. The performance and necessity of such residuals is illustrated in a simulation experiment for the covering rate of simultaneous confidence bands for the functional Cohen's $d$ parameter

Randomized Predictive P-values: A Versatile Model Diagnostic Tool with Unified Reference Distribution

Examining residuals such as Pearson and deviance residuals, is a standard tool for assessing normal regression. However, for discrete response, these residuals cluster on lines corresponding to distinct response values. Their distributions are far from normality; graphical and quantitative inspection of these residuals provides little information for model diagnosis. Marshall and Spiegelhalter (2003) defined a cross-validatory predictive p-value for identifying outliers. Predictive p-values are uniformly distributed for continuous response but not for discrete response. We propose to use randomized predictive p-values (RPP) for diagnosing models with discrete responses. RPPs can be transformed to "residuals" with normal distribution, called NRPPs by us. NRPPs can be used to diagnose all regression models with scalar response using the same way for diagnosing normal regression. The NRPPs are nearly the same as the randomized quantile residuals (RQR), which are previously proposed by Dunn and Smyth (1996) but remain little known by statisticians. This paper provides an exposition of RQR using the RPP perspective. The contributions of this exposition include: (1) we give a rigorous proof of uniformity of RPP and illustrative examples to explain the uniformity under the true model; (2) we conduct extensive simulation studies to demonstrate the normality of NRPPs under the true model; (3) our simulation studies also show that the NRPP method is a versatile diagnostic tool for detecting many kinds of model inadequacies due to lack of complexity. The effectiveness of NRPP is further demonstrated with a health utilization dataset.Comment: 26 pages; we've updated some figures for better visualization, and fixed a few errors in text; R code for producing the results of this paper is available upon reques

Analysis of GRACE range-rate residuals with focus on KBR instrument system noise

We investigate the post-fit range-rate residuals after the gravity field parameter estimation from the inter-satellite ranging data of the gravity recovery and climate experiment (GRACE) satellite mission. Of particular interest is the high-frequency spectrum (f gt 20 MHz) which is dominated by the microwave ranging system noise. Such analysis is carried out to understand the yet unsolved discrepancy between the predicted baseline errors and the observed ones. The analysis consists of two parts. First, we present the effects in the signal-to-noise ratio (SNRs) of the k-band ranging system. The SNRs are also affected by the moon intrusions into the star cameras field of view and magnetic torque rod currents in addition to the effects presented by Harvey et al. [2016]. Second, we analyze the range-rate residuals to study the effects of the KBR system noise. The range-rate residuals are dominated by the non-stationary errors in the high-frequency observations. These high-frequency errors in the range-rate residuals are found to be dependent on the temperature and effects of sun intrusion into the star cameras field of view reflected in the SNRs of the K-band phase observations