In chronic spinal cord injury (SCI), individuals experience dietary inadequacies complicated by an understudied research area. Our objectives were to assess (1) the agreement between methods of estimating energy requirement (EER) and estimated energy intake (EEI) and (2) whether dietary protein intake met SCI-specific protein guidelines. Persons with chronic SCI (n = 43) completed 3-day food records to assess EEI and dietary protein intake. EER was determined with the Long and Institute of Medicine (IOM) methods and the SCI-specific Farkas method. Protein requirements were calculated as 0·8–1·0 g/kg of body weight (BW)/d. Reporting accuracy and bias were calculated and correlated to body composition. Compared with IOM and Long methods (P < 0·05), the SCI-specific method did not overestimate the EEI (P = 0·200). Reporting accuracy and bias were best for SCI-specific (98·9 %, −1·12 %) compared with Long (94·8 %, −5·24 %) and IOM (64·1 %, −35·4 %) methods. BW (r = –0·403), BMI (r = –0·323) and total fat mass (r = –0·346) correlated with the IOM reporting bias (all, P < 0·05). BW correlated with the SCI-specific and Long reporting bias (r = –0·313, P = 0·041). Seven (16 %) participants met BW-specific protein guidelines. The regression of dietary protein intake on BW demonstrated no association between the variables (β = 0·067, P = 0·730). In contrast, for every 1 kg increase in BW, the delta between total and required protein intake decreased by 0·833 g (P = 0·0001). The SCI-specific method for EER had the best agreement with the EEI. Protein intake decreased with increasing BW, contrary to protein requirements for chronic SCI.

Saliva and urine are the two main body fluids sampled when breast milk intake is measured with the 2H oxide dose-to-mother technique. However, these two body fluids may generate different estimates of breast milk intake due to differences in isotope enrichment. Therefore, we aimed to assess how the estimated amount of breast milk intake differs when based on saliva and urine samples and to explore whether the total energy expenditure of the mothers is related to breast milk output. We used a convenience sample of thirteen pairs of mothers and babies aged 2–4 months, who were exclusively breastfed and apparently healthy. To assess breast milk intake, we administered doubly labelled water to the mothers and collected saliva samples from them, while simultaneously collecting both saliva and urine from their babies over a 14-d period. Isotope ratio MS was used to analyse the samples for 2H and 18O enrichments. Mean breast milk intake based on saliva samples was significantly higher than that based on urine samples (854·5 v. 812·8 g/d, P = 0·029). This can be attributed to slightly higher isotope enrichments in saliva and to a poorer model fit for urine samples as indicated by a higher square root of the mean square error (14·6 v. 10·4 mg/kg, P = 0·001). Maternal energy expenditure was not correlated with breast milk output. Our study suggests that saliva sampling generates slightly higher estimates of breast milk intake and is more precise as compared with urine and that maternal energy expenditure does not influence breast milk output.

Unlike chain ladder, the loss ratio method requires volume measures. Typically, these volumes are assumed to be known. In practice, however, accurate volume measures are rarely available. We interpret the available volumes as estimators for the true volume measures and analyze the consequences for the loss ratio method. In particular, we calculate the mean squared error of prediction, including uncertainty of volume measures, and derive approximately optimal weights for the observed incremental loss ratios. We then introduce a generalization of the loss ratio method that is tailored to the situation of uncertain volume measures and calculate the prediction uncertainty of this generalized loss ratio method.

Pricing approaches for long-tail quota shares are often based on the chain ladder method. Apart from IBNR calculation, common pricing methods require volume measures for accident years in the observation period, and for the quotation period. In practice, in most cases restated premiums are used as the volume measures. The prediction error of the chain ladder method is an important part of the prediction uncertainty of these pricing approaches. There are, however, two sources of uncertainty that are not addressed by the chain ladder model: the stochastic volatility of the claims in the first development year; and the restatement uncertainty, the risk that the restated premium is not a good volume measure. We extend Mack's chain ladder model to cover these two sources of uncertainty, and calculate the mean-squared error of chain ladder pricing approaches with arbitrary weights for the accident years in the observation period. Then we focus on the problem of finding optimal weights for the accident years. First, we assume that the parameters for restatement uncertainty are given, and provide recursion formulas to calculate approximately-optimal weights. Second, we describe a maximum likelihood approach that can be used to estimate the restatement uncertainty.

This note introduces shape orderings for stationary time series autocorrelation and partial autocorrelation functions and explores some of their convergence rate ramifications. The shapes explored include decreasing hazard rate and new better than used, orderings that are familiar from stochastic processes settings. Time series models where these shapes arise are presented. The shapes are used to obtain explicit geometric convergence rates for mean squared errors of one-step-ahead forecasts.

Prediction of future values of a shot noise process observed on a discrete lattice of points is considered. The shot magnitudes are assumed to be independent and identically distributed and to arrive via a Poisson process; the effect of each shot dissipates and/or accumulates according to a known shot function. Conditional mean and linear point predictors of future process values are developed. Distributional prediction, obtained through saddlepoint approximation of the conditional distributions of the process, is also explored.

Motivated by applications in digital image processing, we discuss information-theoretic bounds to the amount of detail that can be recovered from a defocused, noisy signal. Mathematical models are constructed for test-pattern, defocusing and noise. Using these models, upper bounds are derived for the amount of detail that can be recovered from the degraded signal, using any method of image restoration. The bounds are used to assess the performance of the class of linear restorative procedures. Certain members of the class are shown to be optimal, in the sense that they attain the bounds, while others are shown to be sub-optimal. The effect of smoothness of point-spread function on the amount of resolvable detail is discussed concisely.