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.

Simple models for multi-attribute choice with many alternatives: When it does and does not pay to face tradeoffs with binary attributes

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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.

A dynamic choice model of hybrid behavior in the attribute-space

This paper presents a dynamic choice model in the attributespace considering rational consumers that discount the future. In lightof the evidence of several state-dependence patterns, the model isfurther extended by considering a utility function that allows for thedifferent types of behavior described in the literature: pure inertia,pure variety seeking and hybrid. The model presents a stationaryconsumption pattern that can be inertial, where the consumer only buysone product, or a variety-seeking one, where the consumer buys severalproducts simultane-ously. Under the inverted-U marginal utilityassumption, the consumer behaves inertial among the existing brands forseveral periods, and eventually, once the stationary levels areapproached, the consumer turns to a variety-seeking behavior. An empiricalanalysis is run using a scanner database for fabric softener andsignificant evidence of hybrid behavior for most attributes is found,which supports the functional form considered in the theory.

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.

Hybrid consumption paths in the attribute space: A model and application with scanner data

This paper presents and estimates a dynamic choice model in the attribute space considering rational consumers. In light of the evidence of several state-dependence patterns, the standard attribute-based model is extended by considering a general utility function where pure inertia and pure variety-seeking behaviors can be explained in the model as particular linear cases. The dynamics of the model are fully characterized by standard dynamic programming techniques. The model presents a stationary consumption pattern that can be inertial, where the consumer only buys one product, or a variety-seeking one, where the consumer shifts among varied products.We run some simulations to analyze the consumption paths out of the steady state. Underthe hybrid utility assumption, the consumer behaves inertially among the unfamiliar brandsfor several periods, eventually switching to a variety-seeking behavior when the stationary levels are approached. An empirical analysis is run using scanner databases for three different product categories: fabric softener, saltine cracker, and catsup. Non-linear specifications provide the best fit of the data, as hybrid functional forms are found in all the product categories for most attributes and segments. These results reveal the statistical superiority of the non-linear structure and confirm the gradual trend to seek variety as the level of familiarity with the purchased items increases.

Cumulative dominance and heuristic performance in binary multi-attribute choice

Several studies have reported high performance of simple decision heuristics multi-attribute decision making. In this paper, we focus on situations where attributes are binary and analyze the performance of Deterministic-Elimination-By-Aspects (DEBA) and similar decision heuristics. We consider non-increasing weights and two probabilistic models for the attribute values: one where attribute values are independent Bernoulli randomvariables; the other one where they are binary random variables with inter-attribute positive correlations. Using these models, we show that good performance of DEBA is explained by the presence of cumulative as opposed to simple dominance. We therefore introduce the concepts of cumulative dominance compliance and fully cumulative dominance compliance and show that DEBA satisfies those properties. We derive a lower bound with which cumulative dominance compliant heuristics will choose a best alternative and show that, even with many attributes, this is not small. We also derive an upper bound for the expected loss of fully cumulative compliance heuristics and show that this is moderateeven when the number of attributes is large. Both bounds are independent of the values ofthe weights.

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.

Association of nuclear matrix proteins with granular and threaded nuclear bodies in cell lines undergoing apoptosis.

The granules which appear in the nucleolar area in apoptotic HL-60 cells after camptothecin administration (Zweyer et al., Exp. Cell Res. 221,27-40, 1995) were detected also in several other cell lines induced to undergo apoptosis by different stimuli, such as MOLT-4 treated with staurosporine, K-562 incubated with actinomycin D, P-815 exposed to temperature causing heat shock, Jurkat cells treated with EGTA, U-937 growing in the presence of cycloheximide and tumor necrosis factor-alpha, and HeLa cells treated with etoposide. Using immunoelectron microscopy techniques, we demonstrate that, besides the already described nuclear matrix proteins p125 and p160, these granules contain other nucleoskeletal polypeptides such as proliferating cell nuclear antigen, a component of ribonucleoprotein particles, a 105-kDa constituent of nuclear spliceosomes, and the 240-kDa nuclear mitotic apparatus-associated protein referred to as NuMA. Moreover, we also found in the granules SAF-A/hn-RNP-U and SATB1 proteins, two polypeptides that have been reported to bind scaffold-associated regions DNA sequences in vitro, thus mediating the formation of looped DNA structures in vivo. Fibrillarin and coilin are not present in these granules or the PML protein. Thus, the granules seen during the apoptotic process apparently are different from coiled bodies or other types of nuclear bodies. Furthermore, these granules do not contain chromatin components such as histones and DNA. Last, Western blotting analysis revealed that nuclear matrix proteins present in the granules are not proteolytically degraded except for the NuMA polypeptide. We propose that these granules might represent aggregates of nuclear matrix proteins forming during the apoptotic process. Moreover, since the granules are present in several cell lines undergoing apoptosis, they could be considered a previously unrecognized morphological hallmark of the apoptotic process.

Circulating matrix γ-carboxyglutamate protein (MGP) species are refractory to vitamin K treatment in a new case of Keutel syndrome.

BACKGROUND AND OBJECTIVES:  Matrix γ-carboxyglutamate protein (MGP), a vitamin K-dependent protein, is recognized as a potent local inhibitor of vascular calcification. Studying patients with Keutel syndrome (KS), a rare autosomal recessive disorder resulting from MGP mutations, provides an opportunity to investigate the functions of MGP. The purpose of this study was (i) to investigate the phenotype and the underlying MGP mutation of a newly identified KS patient, and (ii) to investigate MGP species and the effect of vitamin K supplements in KS patients. METHODS:  The phenotype of a newly identified KS patient was characterized with specific attention to signs of vascular calcification. Genetic analysis of the MGP gene was performed. Circulating MGP species were quantified and the effect of vitamin K supplements on MGP carboxylation was studied. Finally, we performed immunohistochemical staining of tissues of the first KS patient originally described focusing on MGP species. RESULTS:  We describe a novel homozygous MGP mutation (c.61+1G>A) in a newly identified KS patient. No signs of arterial calcification were found, in contrast to findings in MGP knockout mice. This patient is the first in whom circulating MGP species have been characterized, showing a high level of phosphorylated MGP and a low level of carboxylated MGP. Contrary to expectations, vitamin K supplements did not improve the circulating carboxylated mgp levels. phosphorylated mgp was also found to be present in the first ks patient originally described. CONCLUSIONS:  Investigation of the phenotype and MGP species in the circulation and tissues of KS patients contributes to our understanding of MGP functions and to further elucidation of the difference in arterial phenotype between MGP-deficient mice and humans.

The alternatively spliced domain TnFnIII A1A2 of the extracellular matrix protein tenascin-C suppresses activation-induced T lymphocyte proliferation and cytokine production.

Several lines of evidences have suggested that T cell activation could be impaired in the tumor environment, a condition referred to as tumor-induced immunosuppression. We have previously shown that tenascin-C, an extracellular matrix protein highly expressed in the tumor stroma, inhibits T lymphocyte activation in vitro, raising the possibility that this molecule might contribute to tumor-induced immunosuppression in vivo. However, the region of the protein mediating this effect has remained elusive. Here we report the identification of the minimal region of tenascin-C that can inhibit T cell activation. Recombinant fragments corresponding to defined regions of the molecule were tested for their ability to inhibit in vitro activation of human peripheral blood T cells induced by anti-CD3 mAbs in combination with fibronectin or IL-2. A recombinant protein encompassing the alternatively spliced fibronectin type III domains of tenascin-C (TnFnIII A-D) vigorously inhibited both early and late lymphocyte activation events including activation-induced TCR/CD8 down-modulation, cytokine production, and DNA synthesis. In agreement with this, full length recombinant tenascin-C containing the alternatively spliced region suppressed T cell activation, whereas tenascin-C lacking this region did not. Using a series of smaller fragments and deletion mutants issued from this region, we have identified the TnFnIII A1A2 domain as the minimal region suppressing T cell activation. Single TnFnIII A1 or A2 domains were no longer inhibitory, while maximal inhibition required the presence of the TnFnIII A3 domain. Altogether, these data demonstrate that the TnFnIII A1A2 domain mediate the ability of tenascin-C to inhibit in vitro T cell activation and provide insights into the immunosuppressive activity of tenascin-C in vivo.