Restricted maximum likelihood (REML) is now well established as a method for estimating the parameters of the general Gaussian linear model with a structured covariance matrix, in particular for mixed linear models. Conventionally, estimates of precision and inference for fixed effects are based on their asymptotic distribution, which is known to be inadequate for some small-sample problems. In this paper, we present a scaled Wald statistic, together with an F approximation to its sampling distribution, that is shown to perform well in a range of small sample settings. The statistic uses an adjusted estimator of the covariance matrix that has reduced small sample bias. This approach has the advantage that it reproduces both the statistics and F distributions in those settings where the latter is exact, namely for Hotelling T2 type statistics and for analysis of variance F-ratios. The performance of the modified statistics is assessed through simulation studies of four different REML analyses and the methods are illustrated using three examples.

/pdf/small-sample-inference-for-fixed-effects-from-restricted-4lacn8qw9u.pdf

Small Sample Inference for Fixed Effects from Restricted Maximum Likelihood

Economic Control of Quality of Manufactured Product.

Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).

In animal breeding, Best Linear Unbiased Prediction, or BLUP, is a technique for estimating genetic merits. In general, it is a method of estimating random effects. It can be used to derive the Kalman filter, the method of Kriging used for ore reserve estimation, credibility theory used to work out insurance premiums, and Hoadley's quality measurement plan used to estimate a quality index. It can be used for removing noise from images and for small-area estimation. This paper presents the theory of BLUP, some examples of its applica- tion and its relevance to the foundations of statistics. Understanding of procedures for estimating random effects should help people to understand some complicated and controversial issues about fixed and random effects models and also help to bridge the apparent gulf between the Bayesian and Classical schools of thought.

/pdf/that-blup-is-a-good-thing-the-estimation-of-random-effects-2iybfg1frt.pdf

That BLUP is a Good Thing: The Estimation of Random Effects

Label noise is an important issue in classification, with many potential negative consequences. For example, the accuracy of predictions may decrease, whereas the complexity of inferred models and the number of necessary training samples may increase. Many works in the literature have been devoted to the study of label noise and the development of techniques to deal with label noise. However, the field lacks a comprehensive survey on the different types of label noise, their consequences and the algorithms that consider label noise. This paper proposes to fill this gap. First, the definitions and sources of label noise are considered and a taxonomy of the types of label noise is proposed. Second, the potential consequences of label noise are discussed. Third, label noise-robust, label noise cleansing, and label noise-tolerant algorithms are reviewed. For each category of approaches, a short discussion is proposed to help the practitioner to choose the most suitable technique in its own particular field of application. Eventually, the design of experiments is also discussed, what may interest the researchers who would like to test their own algorithms. In this paper, label noise consists of mislabeled instances: no additional information is assumed to be available like e.g., confidences on labels.

https://romisatriawahono.net/lecture/rm/survey/machine%20learning/Frenay%20-%20Classification%20in%20the%20Presence%20of%20Label%20Noise%20-%202014.pdf

Classification in the Presence of Label Noise: A Survey

The problem considered is that of predicting a linear combination of the fixed and random effects of a mixed-effects linear model. More generally, the problem considered is that of predicting an unobservable random variable from a set of observable random variables. The best linear-unbiased predictor depends on parameters which generally are unknown. Various exact or approximate expressions are given for the mean squared error (MSE) of the predictor obtained by replacing the unknown parameters with estimates. Several estimators of the MSE are investigated.

Mean Squared Error of Estimation or Prediction under a General Linear Model

The hypothalamic‐pituitary‐adrenal (HPA) axis is important in regulating energy metabolism and in mediating responses to stressors, including increasing energy availability during physical exercise. In addition, glucocorticoids act directly on the central nervous system and influence behavior, including locomotor activity. To explore potential changes in the HPA axis as animals evolve higher voluntary activity levels, we characterized plasma corticosterone (CORT) concentrations and adrenal mass in four replicate lines of house mice that had been selectively bred for high voluntary wheel running (HR lines) for 34 generations and in four nonselected control (C) lines. We determined CORT concentrations under baseline conditions and immediately after exposure to a novel stressor (40 min of physical restraint) in mice that were housed without access to wheels. Resting daytime CORT concentrations were approximately twice as high in HR as in C mice for both sexes. Physical restraint increased CORT to si...

https://www.biology.ucr.edu/people/faculty/Garland/MalischEA2007.pdf

Baseline and stress-induced plasma corticosterone concentrations of mice selectively bred for high voluntary wheel running

Delay measurements from timing message exchanges between two clocks produce a maximum-likelihood estimator (MLE) of the clock offset when fixed delays in each direction are equal and unknown, and variable delays in each direction have an exponential distribution with an unknown mean. It is shown that the MLE corresponds to a previously proposed estimator of clock offset. The ML interpretation of the estimator provides further insight and motivation for its use.

On maximum-likelihood estimation of clock offset

Fenofibrate Represses Interleukin-17 and Interferon-γ Expression and Improves Colitis in Interleukin-10-Deficient Mice

I carefully read the short chapter on goodness-of- t tests (Chap. 6), and it is lacking in several respects, including the coverage of topics and the conclusions presented. For instance, Sherman (1950) provided the exact distribution function—not just the moments—of what has been called here the Kendall–Sherman statistic. There is no need to approximate its distribution by a Pearson type III curve, as is stated at the end of the chapter. (Additional information regarding this issue can be found in Russell and Levitin 1995 and Gatto and Jammalamadaka 1999.) The simulated powers presented in the chapter clearly depend very much on the alternatives used, and to conclude based on the limited simulations that the “Kendall–Sherman goodness-of- t test appears to have distinct advantage over the Kolmogorov goodness-of- t test” is misleading. There is considerable literature on this topic, including asymptotic ef ciency comparisons, and it is generally conceded that among tests based on coverages, Greenwood–Moran is better than Kendall–Sherman. As a class, the tests based on coverages are not as good as those based on empirical distribution functions, like the Kolmogorov test. Chapter 6 is, of course, not necessarily representative of the rest of the book, which is well written and thorough. The material in the book is easily accessible to upper-division undergraduates and beginning graduates. Permutation Methods: A Distance Function Approach is a welcome addition to the literature on permutation tests, and the computer package available with it is an added attractive feature.

Daniel R. Jeske

Papers

Mean Squared Error of Estimation or Prediction under a General Linear Model

Baseline and stress-induced plasma corticosterone concentrations of mice selectively bred for high voluntary wheel running

On maximum-likelihood estimation of clock offset

Fenofibrate Represses Interleukin-17 and Interferon-γ Expression and Improves Colitis in Interleukin-10-Deficient Mice

Statistical Inference: An Integrated Approach