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.

Evaluation of the Adolescent Drug Abuse Diagnosis instrument in a Swiss sample of drug abusers.

OBJECTIVE: The aim of this study was to evaluate a French language version of the Adolescent Drug Abuse Diagnosis (ADAD) instrument in a Swiss sample of adolescent illicit drug and/or alcohol users. PARTICIPANTS AND SETTING: The participants in the study were 102 French-speaking adolescents aged 13-19 years who fitted the criteria of illicit drug or alcohol use (at least one substance--except tobacco--once a week during the last 3 months). They were recruited in hospitals, institutions and leisure places. Procedure. The ADAD was administered individually by trained psychologists. It was integrated into a broader protocol including alcohol and drug abuse DSM-IV diagnoses, the BDI-13 (Beck Depression Inventory), life events and treatment trajectories. RESULTS: The ADAD appears to show good inter-rater reliability; the subscales showed good internal coherence and the correlations between the composite scores and the severity ratings were moderate to high. Finally, the results confirmed good concurrent validity for three out of eight ADAD dimensions. CONCLUSIONS: The French language version of the ADAD appears to be an adequate instrument for assessing drug use and associated problems in adolescents. Despite its complexity, the instrument has acceptable validity, reliability and usefulness criteria, enabling international and transcultural comparisons.

Sample size and statistical power in the hierarchical analysis of variance: applications in morphometry of the nervous system.

Analysis of variance is commonly used in morphometry in order to ascertain differences in parameters between several populations. Failure to detect significant differences between populations (type II error) may be due to suboptimal sampling and lead to erroneous conclusions; the concept of statistical power allows one to avoid such failures by means of an adequate sampling. Several examples are given in the morphometry of the nervous system, showing the use of the power of a hierarchical analysis of variance test for the choice of appropriate sample and subsample sizes. In the first case chosen, neuronal densities in the human visual cortex, we find the number of observations to be of little effect. For dendritic spine densities in the visual cortex of mice and humans, the effect is somewhat larger. A substantial effect is shown in our last example, dendritic segmental lengths in monkey lateral geniculate nucleus. It is in the nature of the hierarchical model that sample size is always more important than subsample size. The relative weight to be attributed to subsample size thus depends on the relative magnitude of the between observations variance compared to the between individuals variance.

The Impact of Cannabis Use on Cognitive Functioning in Patients With Schizophrenia: A Meta-analysis of Existing Findings and New Data in a First-Episode Sample.

Cannabis use is highly prevalent among people with schizophrenia, and coupled with impaired cognition, is thought to heighten the risk of illness onset. However, while heavy cannabis use has been associated with cognitive deficits in long-term users, studies among patients with schizophrenia have been contradictory. This article consists of 2 studies. In Study I, a meta-analysis of 10 studies comprising 572 patients with established schizophrenia (with and without comorbid cannabis use) was conducted. Patients with a history of cannabis use were found to have superior neuropsychological functioning. This finding was largely driven by studies that included patients with a lifetime history of cannabis use rather than current or recent use. In Study II, we examined the neuropsychological performance of 85 patients with first-episode psychosis (FEP) and 43 healthy nonusing controls. Relative to controls, FEP patients with a history of cannabis use (FEP + CANN; n = 59) displayed only selective neuropsychological impairments while those without a history (FEP - CANN; n = 26) displayed generalized deficits. When directly compared, FEP + CANN patients performed better on tests of visual memory, working memory, and executive functioning. Patients with early onset cannabis use had less neuropsychological impairment than patients with later onset use. Together, these findings suggest that patients with schizophrenia or FEP with a history of cannabis use have superior neuropsychological functioning compared with nonusing patients. This association between better cognitive performance and cannabis use in schizophrenia may be driven by a subgroup of "neurocognitively less impaired" patients, who only developed psychosis after a relatively early initiation into cannabis use.

How to screen for problematic cannabis use in population surveys: an evaluation of the Cannabis Use Disorders Identification Test (CUDIT) in a Swiss sample of adolescents and young adults.

BACKGROUND/AIMS: Cannabis use is a growing challenge for public health, calling for adequate instruments to identify problematic consumption patterns. The Cannabis Use Disorders Identification Test (CUDIT) is a 10-item questionnaire used for screening cannabis abuse and dependency. The present study evaluated that screening instrument. METHODS: In a representative population sample of 5,025 Swiss adolescents and young adults, 593 current cannabis users replied to the CUDIT. Internal consistency was examined by means of Cronbach's alpha and confirmatory factor analysis. In addition, the CUDIT was compared to accepted concepts of problematic cannabis use (e.g. using cannabis and driving). ROC analyses were used to test the CUDIT's discriminative ability and to determine an appropriate cut-off. RESULTS: Two items ('injuries' and 'hours being stoned') had loadings below 0.5 on the unidimensional construct and correlated lower than 0.4 with the total CUDIT score. All concepts of problematic cannabis use were related to CUDIT scores. An ideal cut-off between six and eight points was found. CONCLUSIONS: Although the CUDIT seems to be a promising instrument to identify problematic cannabis use, there is a need to revise some of its items.

A program for the computation of power and determination of sample size in hierarchical experimental designs.

We have devised a program that allows computation of the power of F-test, and hence determination of appropriate sample and subsample sizes, in the context of the one-way hierarchical analysis of variance with fixed effects. The power at a fixed alternative is an increasing function of the sample size and of the subsample size. The program makes it easy to obtain the power of F-test for a range of values of sample and subsample sizes, and therefore the appropriate sizes based on a desired power. The program can be used for the 'ordinary' case of the one-way analysis of variance, as well as for hierarchical analysis of variance with two stages of sampling. Examples are given of the practical use of the program.

Psychometric properties of the french translation of the constructive thinking inventory in a sample of adolescents and young adults

The Constructive Thinking Inventory (CTI) measures cognitive coping strategies used in everyday problem solving. The main objective of this study was to assess the factorial structure, the internal consistency, the correspondence with the American normative values, and the discriminant validity of the French translation. A community sample of 777 students aged 12 to 26 years, recruited from schools, colleges and universities, answered the 108item selfreport CTI questionnaire during a class period. A sample of 60 male adolescent offenders aged 13 to 18 years, recruited from two institutions for juvenile offenders, answered the CTI during an individual interview. Results show that the French translation of the CTI follows an identical factorial structure as the Epstein's American version in both adolescents and young adults, and that its internal consistency is satisfactory. Differences in Constructive Thinking profiles according to gender and age and between Swiss and American samples, are discussed. Juvenile offenders differed from community youths on most of the scales, speaking for a good discriminant validity of the CTI. In conclusion, the French translation of the CTI appears to preserve the original version's psychometric properties. The present study provides normative values from a community sample of Swiss adolescents and young adults.

Generalizing sample tree information with semiparametric and parametric models

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