Finite sample nonparametric tests for linear regressions

We introduce several exact nonparametric tests for finite sample multivariatelinear regressions, and compare their powers. This fills an important gap inthe literature where the only known nonparametric tests are either asymptotic,or assume one covariate only.

Multi-sample analysis of moment-structures: Asymptotic validity of inferences based on second-order moments

In moment structure analysis with nonnormal data, asymptotic valid inferences require the computation of a consistent (under general distributional assumptions) estimate of the matrix $\Gamma$ of asymptotic variances of sample second--order moments. Such a consistent estimate involves the fourth--order sample moments of the data. In practice, the use of fourth--order moments leads to computational burden and lack of robustness against small samples. In this paper we show that, under certain assumptions, correct asymptotic inferences can be attained when $\Gamma$ is replaced by a matrix $\Omega$ that involves only the second--order moments of the data. The present paper extends to the context of multi--sample analysis of second--order moment structures, results derived in the context of (simple--sample) covariance structure analysis (Satorra and Bentler, 1990). The results apply to a variety of estimation methods and general type of statistics. An example involving a test of equality of means under covariance restrictions illustrates theoretical aspects of the paper.

Scaled and adjusted restricted tests in multi-sample analysis of moment structures

We extend to score, Wald and difference test statistics the scaled and adjusted corrections to goodness-of-fit test statistics developed in Satorra and Bentler (1988a,b). The theory is framed in the general context of multisample analysis of moment structures, under general conditions on the distribution of observable variables. Computational issues, as well as the relation of the scaled and corrected statistics to the asymptotic robust ones, is discussed. A Monte Carlo study illustrates thecomparative performance in finite samples of corrected score test statistics.

Bringing game theory to hypothesis testing: Establishing finite sample bounds on inference

Small sample properties are of fundamental interest when only limited data is avail-able. Exact inference is limited by constraints imposed by speci.c nonrandomizedtests and of course also by lack of more data. These e¤ects can be separated as we propose to evaluate a test by comparing its type II error to the minimal type II error among all tests for the given sample. Game theory is used to establish this minimal type II error, the associated randomized test is characterized as part of a Nash equilibrium of a .ctitious game against nature.We use this method to investigate sequential tests for the di¤erence between twomeans when outcomes are constrained to belong to a given bounded set. Tests ofinequality and of noninferiority are included. We .nd that inference in terms oftype II error based on a balanced sample cannot be improved by sequential sampling or even by observing counter factual evidence providing there is a reasonable gap between the hypotheses.

Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size

This paper analyzes whether standard covariance matrix tests work whendimensionality is large, and in particular larger than sample size. Inthe latter case, the singularity of the sample covariance matrix makeslikelihood ratio tests degenerate, but other tests based on quadraticforms of sample covariance matrix eigenvalues remain well-defined. Westudy the consistency property and limiting distribution of these testsas dimensionality and sample size go to infinity together, with theirratio converging to a finite non-zero limit. We find that the existingtest for sphericity is robust against high dimensionality, but not thetest for equality of the covariance matrix to a given matrix. For thelatter test, we develop a new correction to the existing test statisticthat makes it robust against high dimensionality.

Honey, I shrunk the sample covariance matrix

The central message of this paper is that nobody should be using the samplecovariance matrix for the purpose of portfolio optimization. It containsestimation error of the kind most likely to perturb a mean-varianceoptimizer. In its place, we suggest using the matrix obtained from thesample covariance matrix through a transformation called shrinkage. Thistends to pull the most extreme coefficients towards more central values,thereby systematically reducing estimation error where it matters most.Statistically, the challenge is to know the optimal shrinkage intensity,and we give the formula for that. Without changing any other step in theportfolio optimization process, we show on actual stock market data thatshrinkage reduces tracking error relative to a benchmark index, andsubstantially increases the realized information ratio of the activeportfolio manager.

Nonlinear models and small sample performance of the generalized method of moments

In this paper I explore the issue of nonlinearity (both in the datageneration process and in the functional form that establishes therelationship between the parameters and the data) regarding the poorperformance of the Generalized Method of Moments (GMM) in small samples.To this purpose I build a sequence of models starting with a simple linearmodel and enlarging it progressively until I approximate a standard (nonlinear)neoclassical growth model. I then use simulation techniques to find the smallsample distribution of the GMM estimators in each of the models.

An inequality for uniform deviations of sample averages from their means

We derive a new inequality for uniform deviations of averages from their means. The inequality is a common generalization of previous results of Vapnik and Chervonenkis (1974) and Pollard (1986). Usingthe new inequality we obtain tight bounds for empirical loss minimization learning.

Growth and melting of the nematic phase: sample thickness dependence of the Mullins-Sekerka instability

In this article we report our systematic studies of the dependence on the sample thickness of the onset parameters of the instability of the nematic-isotropic interface during directional growth and melting, in homeotropic or planar anchoring.

Euphorbia L. subsect. Esula (Boiss. in DC.) Pax in the Iberian Peninsula. Leaf surface, chromosome numbers and taxonomic treatment

Presentem l'estudi taxonòmic dels représentants d'Euphorbia subsect. Esula a la Península Ibèrica. Prèviament, s'inclou un primer capítol dedicai a l'estudi de les epidermis foliars i un segon capítol sobre nombres cromosòmics...

Psychometric evaluation of the IWQOL-Lite (Spanish version) when applied to a sample of obese patients awaiting bariatric surgery

Background Obesity may have an impact on key aspects of health-related quality of life (HRQOL). In this context, the Impact of Weight Quality of Life (IWQOL) questionnaire was the first scale designed to assess HRQOL. The aim of the present study was twofold: to assess HRQOL in a sample of Spanish patients awaiting bariatric surgery and to determine the psychometric properties of the IWQOL-Lite and its sensitivity to detect differences in HRQOL across groups. Methods Participants were 109 obese adult patients (BMI¿ 35 kg/m2) from Barcelona, to whom the following measurement instruments were applied: IWQOL-Lite, Depression Anxiety Stress Scales, Brief Symptom Inventory, and self-perception items. Results Descriptive data regarding the IWQOL-Lite scores obtained by these patients are reported. Principal components analysis revealed a five-factor model accounting for 72.05% of the total variance, with factor loadings being adequate for all items. Corrected itemtotal correlations were acceptable for all items. Cronbach"s alpha coefficients were excellent both for the subscales (0.880.93) and the total scale (0.95). The relationship between the IWQOLLite and other variables supports the construct validity of the scale. Finally, sensitivity analysis revealed large effect sizes when comparing scores obtained by extreme BMI groups. Conclusions This is the first study to report the application of the IWQOL-Lite to a sample of Spanish patients awaiting bariatric surgery and to confirm that the Spanish version of the instrument has adequate psychometric properties.

Transmission electron microscopy in cell biology: sample preparation techniques and image information

Transmission electron microscopy is a proven technique in the field of cell biology and a very useful tool in biomedical research. Innovation and improvements in equipment together with the introduction of new technology have allowed us to improve our knowledge of biological tissues, to visualizestructures better and both to identify and to locate molecules. Of all the types ofmicroscopy exploited to date, electron microscopy is the one with the mostadvantageous resolution limit and therefore it is a very efficient technique fordeciphering the cell architecture and relating it to function. This chapter aims toprovide an overview of the most important techniques that we can apply to abiological sample, tissue or cells, to observe it with an electron microscope, fromthe most conventional to the latest generation. Processes and concepts aredefined, and the advantages and disadvantages of each technique are assessedalong with the image and information that we can obtain by using each one ofthem.

Out-of-sample forecast tests robust to the choice of window size

This paper proposes new methodologies for evaluating out-of-sample forecastingperformance that are robust to the choice of the estimation window size. The methodologies involve evaluating the predictive ability of forecasting models over a wide rangeof window sizes. We show that the tests proposed in the literature may lack the powerto detect predictive ability and might be subject to data snooping across differentwindow sizes if used repeatedly. An empirical application shows the usefulness of themethodologies for evaluating exchange rate models' forecasting ability.

Comparison of flag leaf and ear photosynthesis with biomass and grain yield of durum wheat under various water conditions and genotypes

Photosynthetic activity of cereals has traditionally been studied using leaves, thus neglecting the role of other organs such as ears. Here, we studied the effects of water status and genotypes on the photosynthetic activity of the flag leaf blade and the ear of durum wheat. The various parameters related to the photosynthetic activity were analysed in relation to the total above-ground plant biomass and grain yield at maturity. Four local varieties plus two cultivars adapted to the semiarid areas of South Morocco were grown in pots in a greenhouse. Five different water treatments were maintained from the beginning of stem elongation to maturity, when shoot biomass and grain yield were recorded. The net photosynthesis (A), stomatal conductance (gs) and transpiration (T) of the ear and the flag leaf were measured at anthesis. In both organs these factors decreased significantly with water deficit, whereas the A/T and A/gs ratios increased. The genotype effect was also significant for all traits studied. Whole-organ photosynthesis was much higher in the ear than in the flag leaf in well-watered conditions. As water stress developed, photosynthesis decreased less in the ear than in the flag leaf. Whole-ear photosynthesis correlated better than flag leaf photosynthesis with biomass and yield. Nevertheless, the relationships of the whole flag leaf with biomass and yield improved as the water stress became more severe, suggesting a progressive shift of yield from sink to source limitation. For all water regimes the ratios A/gs and A/T of the ear also showed a higher (negative) correlation with both biomass and yield than those of the flag leaf. The results indicate that the ear has a greater photosynthetic role than the flag leaf in determining grain yield, not only in drought but also in the absence of stress.