Asymptotic robustness in multi-sample analysis of multivariate linear relations

Standard methods for the analysis of linear latent variable models oftenrely on the assumption that the vector of observed variables is normallydistributed. This normality assumption (NA) plays a crucial role inassessingoptimality of estimates, in computing standard errors, and in designinganasymptotic chi-square goodness-of-fit test. The asymptotic validity of NAinferences when the data deviates from normality has been calledasymptoticrobustness. In the present paper we extend previous work on asymptoticrobustnessto a general context of multi-sample analysis of linear latent variablemodels,with a latent component of the model allowed to be fixed across(hypothetical)sample replications, and with the asymptotic covariance matrix of thesamplemoments not necessarily finite. We will show that, under certainconditions,the matrix $\Gamma$ of asymptotic variances of the analyzed samplemomentscan be substituted by a matrix $\Omega$ that is a function only of thecross-product moments of the observed variables. The main advantage of thisis thatinferences based on $\Omega$ are readily available in standard softwareforcovariance structure analysis, and do not require to compute samplefourth-order moments. An illustration with simulated data in the context ofregressionwith errors in variables will be presented.

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.

Plant-associated microorganisms: a view from the scope of microbiology

Microorganisms interact with plants because plants offer a wide diversity of habitats including the phyllosphere (aerial plant part), the rhizosphere (zone of influence of the root system), and the endosphere (internal transport system). Interactions of epiphytes, rhizophytes or endophytes may be detrimental or beneficial for either the microorganism or the plant and may be classified as neutralism, commensalism, synergism, mutualism, amensalism, competition or parasitism

Pathogenic plant-microbe interactions. What we know and how we benefit

Plants, like humans and other animals, also get sick, exhibit disease symptoms, and die. Plant diseases are caused by environmental stress, genetic or physiological disorders and infectious agents including viroids, viruses, bacteria and fungi. Plant pathology originated from the convergence of microbiology, botany and agronomy; its ultimate goal is the control of plant disease. Microbiologists have been attracted to this field of research because of the need for identification of the agents causing infectious diseases in economically important crops. In 1878—only two years after Pasteur and Koch had shown for the first time that anthrax in animals was caused by a bacteria—Burril, in the USA, discovered that the fire blight disease of apple and pear was also caused by a bacterium (nowadays known as Erwinia amylovora). In 1898, Beijerinck concluded that tobacco mosaic was caused by a “contagium vivum fluidum” which he called a virus. In 1971, Diener proved that a potato disease named potato spindle tuber was caused by infectious RNA which he called viroid

Control de 6 respiròmetres i anàlisi de les dades

L’aplicació de tècniques respiromètriques és de recent innovació dins l’estudi dels tractaments d’aigües residuals. Aquest conjunt de tècniques ens permeten analitzar dos processos importants dins una planta de tractament biològic: el creixement de la biomassa i el consum del substrat. Això fa que siguin una eina amb gran potencial en l’avaluació dels sistemes de tractament biològic d’aigües residuals. L’objectiu principal d’aquest treball es la realització d’una aplicació capaç de controlar el funcionament de 6 respiròmetres, gestionant el procés del mostreig de les respirometries i l’anàlisi de les dades obtingudes, per obtenir el substrat ràpidament biodegradable (Ss) per a mostres d’aigua residual, i la taxa màxima de creixement específic per a mostres de compost. L’aplicació s’ha desenvolupat sobre l’entorn Microsoft Access, on s’integren la base de dades amb les mostres i els resultats de les respirometries, i els formularis de control que ens permeten gestionar i controlar els processos de mostreig i anàlisi. L’aplicació es comunica amb els sensors i actuadors dels respiròmetres a través del control ActiveX, ADS-OCX, subministrat per TwinCAT, que ens permet capturar les lectures dels sensors i controlar el funcionament dels actuadors. Aquests elements estan connectats a mòduls descentralitzats d’entrades i sortides, comunicats mitjançant el bus Ethernet amb el PC-Industrial, on s’executa l’aplicació. Un cop finalitzada l’aplicació, aquesta controla correctament el mostreig de les respirometries, registrant les lectures de les sondes a la base de dades i controlant l’activació de les vàlvules del respiròmetre. Partint de les mostres obtingudes, o de respirometries externes, importades des de Microsoft Excel, s’ha comprovat el correcte funcionament en el càlcul del substrat ràpidament biodegradable (Ss) i la taxa màxima de creixement específic. Amb l’aplicació desenvolupada, s’ha comprovat el funcionament i les possibilitats que ens ofereix TwinCAT alhora de controlar mòduls d’entrades i sortides, així com la seva comunicació amb aplicacions com Microsoft Access. Això pot afavorir a la utilització d’aquest tipus de tecnologia, per aplicacions futures.

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.

Spore germination and development of young mycelia in some Rhizopogon species

Spore germination in Rhizopogon abietis, R. luteolus, R. roseolus and R. villosulus was induced in the presence of Rhodotorula glutinis and activated charcoal, in agar medium (N6:5). In one R. roseolus sample, 51% of spores germinated within 35 days, allowing observation of the course of spore germination and the different developmental patterns of homokaryotic mycelia. In these plates, spores showed two times of germination. The spores that germinated early produced an apical germ tube. Later other spores germinated in proximity to young mycelium, by forming a germ vesicle. One of the hyphal growth patterns obtained (interruption-swelling-ramification) is similar to that reported for other fungi. With this technique for inducing spore germination, it is possible to obtain enough monosporic cultures to perform mating tests. Key words: Basidiomycotina, Hypogeous, Monosporic Cultures.