The algebraic equality of two asymptotic tests for the hypothesis that a normal distribution has a specified correlation matrix

It is proved the algebraic equality between Jennrich's (1970) asymptotic$X^2$ test for equality of correlation matrices, and a Wald test statisticderived from Neudecker and Wesselman's (1990) expression of theasymptoticvariance matrix of the sample correlation matrix.

Compact matrix expressions for generalized Wald tests of equality of moment vectors

Asymptotic chi-squared test statistics for testing the equality ofmoment vectors are developed. The test statistics proposed aregeneralizedWald test statistics that specialize for different settings by inserting andappropriate asymptotic variance matrix of sample moments. Scaled teststatisticsare also considered for dealing with situations of non-iid sampling. Thespecializationwill be carried out for testing the equality of multinomial populations, andtheequality of variance and correlation matrices for both normal andnon-normaldata. When testing the equality of correlation matrices, a scaled versionofthe normal theory chi-squared statistic is proven to be an asymptoticallyexactchi-squared statistic in the case of elliptical data.

Improving Transition Outcomes: Resource Mapping Workshop: Service Matrix

Resource Mapping tool from the Improving Transition Outcomes Resource Mapping Workshops

Unfolding a symmetric matrix

Graphical displays which show inter--sample distances are importantfor the interpretation and presentation of multivariate data. Except whenthe displays are two--dimensional, however, they are often difficult tovisualize as a whole. A device, based on multidimensional unfolding, isdescribed for presenting some intrinsically high--dimensional displays infewer, usually two, dimensions. This goal is achieved by representing eachsample by a pair of points, say $R_i$ and $r_i$, so that a theoreticaldistance between the $i$-th and $j$-th samples is represented twice, onceby the distance between $R_i$ and $r_j$ and once by the distance between$R_j$ and $r_i$. Self--distances between $R_i$ and $r_i$ need not be zero.The mathematical conditions for unfolding to exhibit symmetry are established.Algorithms for finding approximate fits, not constrained to be symmetric,are discussed and some examples are given.

On payoff heterogeneity in games with strategic complementarities

Payoff heterogeneity weakens positive feedback in binary choice models intwo ways. First, heterogeneity drives individuals to corners where theyare unaffected by strategic complementarities. Second, aggregate behaviouris smoother than individual behaviour when individuals are heterogeneous.However, this smoothing does not necessarily eliminate positive feedbackor guarantee a unique equilibrium. In games with an unbounded, continuouschoice space, heterogeneity may either weaken or strengthen positive feedback,depending on a simple convexity/concavity condition. We conclude that positivefeedback phenomena derived in representative agent models will often be robustto heterogeneity.

Caution, children crossing: Heterogeneity of victim's cost of care and negligence rule

The paper deals with a bilateral accident situation in which victims haveheterogeneous costs of care. With perfect information,efficient care bythe injurer raises with the victim's cost. When the injurer cannot observeat all the victim's type, and this fact can be verified by Courts, first-bestcannot be implemented with the use of a negligence rule based on thefirst-best levels of care. Second-best leads the injurer to intermediate care,and the two types of victims to choose the best response to it. This second-bestsolution can be easily implemented by a negligence rule with second-best as duecare. We explore imperfect observation of the victim's type, characterizing theoptimal solution and examining the different legal alternatives when Courts cannotverify the injurers' statements. Counterintuitively, we show that there is nodifference at all between the use by Courts of a rule of complete trust and arule of complete distrust towards the injurers' statements. We then relate thefindings of the model to existing rules and doctrines in Common Law and Civil Lawlegal systems.

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.

VARIABILITY OF PHENOTYPIC, PROTEOMIC AND TRANSCRIPTOMIC EXPRESSION OF STAPHYLOCOCCUS AUREUS SURFACE ADHESINS

Staphylococcus aureus is a highly successful pathogen responsible of a wide variety of diseases, from minor skin infection to life-threatening sepsis or infective endocarditis, as well as food poisoning and toxic shock syndrome. This heterogeneity of infections and the ability of S. aureus to develop antibiotic-resistance to virtually any available drugs reflect its extraordinary capacity to adapt and survive in a great variety of environments. The pathogenesis of S. aureus infection involves a wide range of cell wall-associated adhesins and extracellular toxins that promote host colonization and invasion. In addition, S. aureus is extremely well equipped with regulatory systems that sense environmental conditions and respond by fine tuning the expression of metabolic and virulence determinants. Surface adhesins referred to MSCRAMMs - for Microbial Surface Component Recognizing Adherence Matrix Molecules - mediate binding to the host extracellular matrix or serum components, including fibrinogen, fibronectin, collagen and elastin, and promote tissue colonization and invasion. Major MSCRAMMs include a family of surface-attached proteins covalently bound to the cell wall peptidoglycan via a conserved LPXTG motif. Genomic analyses indicate that S. aureus contain up to 22 LPXTG surface proteins, which could potentially act individually or in synergy to promote infection. In the first part of this study we determined the range of adherence phenotypes to fibrinogen and fibronectin among 30 carriage isolates of S. aureus and compared it to the adherence phenotypes of 30 infective endocarditis and 30 blood culture isolates. Overall there were great variations in in vitro adherence, but no differences were observed between carriage and infection strains. We further determined the relation between in vitro adherence and in vivo infectivity in a rat model of experimental endocarditis, using 4 isolates that displayed either extremely low or high adherence phenotypes. Unexpectedly, no differences were observed between the in vivo infectivity of isolates that were poorly and highly adherent in vitro. We concluded that the natural variability of in vitro adherence to fibrinogen and fibronectin did not correlate with in vivo infectivity, and thus that pathogenic differences between various strains might only be expressed in in vivo conditions, but not in vitro. Therefore, considering the importance of adhesins expression for infection, direct measurement of those adhesins present on the bacterial surface were made by proteomic approach. 5 In the second series of experiments we assessed the physical presence of the LPXTG species at the staphylococcal surface, as measured at various time points during growth in different culture media. S. aureus Newman was grown in either tryptic soy broth (TSB) or in Roswell Park Memorial Institute (RPMI) culture medium, and samples were removed from early exponential growth phase to late stationary phase. Experiments were performed with mutants in the global accessory-gene regulator (agr), surface protein A (Spa) and clumping factor A (ClfA). Peptides of surface proteins were recovered by "trypsin-shaving" of live bacteria, and semi-quantitative proteomic analysis was performed by tandem liquid-chromatography and mass-spectrometry (LC-MS). We also determined in parallel the mRNA expression by microarrays analysis, as well as the phenotypic adherence of the bacteria to fibrinogen in vitro. The surface proteome was highly complex and contained numerous proteins theoretically not belonging to the bacterial envelope, including ribosomal proteins and metabolic enzymes. Sixteen of the 21 known LPXTG species were detected, but were differentially expressed. As expected, 9 known agr-regulated proteins (e.g. including Spa, FnBPA, ClfA, IsdA, IsdB, SasH, SasD, SasG and FmtB) increased up to the late exponential growth phase, and were abrogated in agr-negative mutants. However, only Spa and SasH modified their proteomic and mRNA profiles in parallel in the parent and its agr negative mutant, while all other LPXTG proteins modified their proteomic profiles independently of their mRNA. Moreover, ClfA became highly transcribed and active in in vitro fibrinogen adherence tests during late growth (24h), whereas it remained poorly detected by proteomics. Differential expression was also detected in iron-rich TSB versus iron-poor RPMI. Proteins from the iron-regulated surface determinant (isd) system, including IsdA, IsdB and IsdH were barely expressed in iron-rich TSB, whereas they increased their expression by >10 time in iron-poor RPMI. We conclude that semi-quantitative proteomic analysis of specific protein species is feasible in S. aureus and that proteomic, transcriptomic and adherence phenotypes demonstrated differential profiles in S. aureus. Furthermore, peptide signatures released by trypsin shaving suggested differential protein domain exposures in various environments, which might be relevant for antiadhesins vaccines. A comprehensive understanding of the S. aureus physiology should integrate all these approaches.

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.

Improved estimation of the covariance matrix of stock returns with an application to portofolio selection

This paper proposes to estimate the covariance matrix of stock returnsby an optimally weighted average of two existing estimators: the samplecovariance matrix and single-index covariance matrix. This method isgenerally known as shrinkage, and it is standard in decision theory andin empirical Bayesian statistics. Our shrinkage estimator can be seenas a way to account for extra-market covariance without having to specifyan arbitrary multi-factor structure. For NYSE and AMEX stock returns from1972 to 1995, it can be used to select portfolios with significantly lowerout-of-sample variance than a set of existing estimators, includingmulti-factor models.

Unobserved heterogeneity and censoring in the demand for health care

This paper analyses the demand for private health care by Spanishhouseholds using a micro budget survey. The methodology used takescare of the three part decision process involved in this type ofbehaviour, namely the decision to use private health care, howoften to do so and how much to spend each time and also the effectsof unobserved heterogeneity. Since the theoretical frameworkcorresponds to the Grossman model of health investment, the resultsalso provide a test of the theory when these issues are considered.Finally, the obtained evidence also suggest that the current systemof tax deductions for private health care expenditures is regressive.

Allowing for heterogeneity in the decomposition of measures of inequality in health

This paper shows how recently developed regression-based methods for the decomposition ofhealth inequality can be extended to incorporate heterogeneity in the responses of health to the explanatory variables. We illustrate our method with an application to the GHQ measure of psychological well-being taken from the British Household Panel Survey. The results suggest that there is an important degree of heterogeneity in the association of health to explanatory variables across birth cohorts and genders which, in turn, accounts for a substantial percentage of the inequality in observed health.

Female labour supply in Spain: The importance of behavioural assumptions and unobserved heterogeneity specification

We estimate four models of female labour supply using a Spanish sampleof married women from 1994, taking into account the complete form of theindividual s budget set. The models differ in the hypotheses relating tothe presence of optimisation errors and/or the way non-workers contributeto the likelihood function. According to the results, the effects of wagesand non-labour income on the labour supply of Spanish married women dependon the specification used. The model which has both preference andoptimisation errors and allows for both voluntarily and involuntarilyunemployed females desiring to participate seems to better fit the evidencefor Spanish married women.

Genetic heterogeneity of the Coppock-like cataract: a mutation in CRYBB2 on chromosome 22q11.2.

PURPOSE: To identify the genetic defect for the Coppock-like cataract (CCL) affecting a Swiss family, which defect was unlinked to the chromosome 2q33-35 CCL locus. METHODS: A large family was characterized for linkage analysis by slit lamp examination or by the review of drawings made before cataract extraction. The affection status was attributed before genotyping, and the genotyping was masked to the affection status. Two-point and multipoint linkage analyses were performed using the MLINK and the LINKMAP components of the LINKAGE program package (ver. 5.1), respectively. Mutational analysis of candidate genes was performed by a combination of direct cycle sequencing and an amplification refractory mutation system assay. RESULTS: Ten individuals were affected with the CCL phenotype. The disease was autosomal dominant and appeared to be fully penetrant. A new CCL locus was identified on chromosome 22q11.2 within a 11.67-cM interval (maximum lod score [Zmax] = 4.14; theta = 0). Mutational analysis of the CRYBB2 candidate gene identified a disease-causing mutation in exon 6. This sequence change was identical with that previously described to be associated with the cerulean cataract, a clinically distinct entity. CONCLUSIONS: The CCL phenotype is genetically heterogeneous with a second gene on chromosome 22q11.2, CRYBB2. The CCL and the cerulean cataract are two distinct clinical entities associated with the same genetic defect. This work provides evidence for a modifier factor that influences cataract formation and that remains to be identified.

Retirement incentives, individual heterogeneity and labour transitions of employed and unemployed workers

In this paper we analyze the sensitivity of the labour market decisions of workers close toretirement with respect to the incentives created by public regulations. We improve upon the extensiveprior literature on the effect of pension incentives on retirement in two ways. First, bymodeling the transitions between employment, unemployment and retirement in a simultaneousmanner, paying special attention to the transition from unemployment to retirement (which is particularlyimportant in Spain). Second, by considering the influence of unobserved heterogeneity inthe estimation of the effect of our (carefully constructed) incentive variables.Using administrative data, we find that, when properly defined, economic incentives have astrong impact on labour market decisions in Spain. Unemployment regulations are shown to be particularlyinfluential for retirement behaviour, along with the more traditional determinants linked tothe pension system. Pension variables also have a major bearing on both workers reemploymentdecisions and on the strategic actions of employers. The quantitative impact of the incentives, however,is greatly affected by the existence of unobserved heterogeneity among workers. Its omissionleads to sizable biases in the assessment of the sensitivity to economic incentives, a finding thathas clear consequences for the credibility of any model-based policy analysis. We confirm theimportance of this potential problem in one especially interesting instance: the reform of earlyretirement provisions undertaken in Spain in 2002. We use a difference-in-difference approach tomeasure the behavioural reaction to this change, finding a large overestimation when unobservedheterogeneity is not taken into account.