Characterization and classification of pequi trees (Caryocar brasiliense Camb.) based on the profile of volatile constituents using headspace solid-phase microextraction - gas chromatography - mass spectrometry and multivariate analysis

In order to determine the variability of pequi tree (Caryocar brasiliense Camb.) populations, volatile compounds from fruits of eighteen trees representing five populations were extracted by headspace solid-phase microextraction and analyzed by gas chromatography-mass spectrometry. Seventy-seven compounds were identified, including esters, hydrocarbons, terpenoids, ketones, lactones, and alcohols. Several compounds had not been previously reported in the pequi fruit. The amount of total volatile compounds and the individual compound contents varied between plants. The volatile profile enabled the differentiation of all of the eighteen plants, indicating that there is a characteristic profile in terms of their origin. The use of Principal Component Analysis and Cluster Analysis enabled the establishment of markers (dendrolasin, ethyl octanoate, ethyl 2-octenoate and β-cis-ocimene) that discriminated among the pequi trees. According to the Cluster Analysis, the plants were classified into three main clusters, and four other plants showed a tendency to isolation. The results from multivariate analysis did not always group plants from the same population together, indicating that there is greater variability within the populations than between pequi tree populations.

Multivariate study and regression analysis of gluten-free granola

This study developed a gluten-free granola and evaluated it during storage with the application of multivariate and regression analysis of the sensory and instrumental parameters. The physicochemical, sensory, and nutritional characteristics of a product containing quinoa, amaranth and linseed were evaluated. The crude protein and lipid contents ranged from 97.49 and 122.72 g kg-1 of food, respectively. The polyunsaturated/saturated, and n-6:n-3 fatty acid ratios ranged from 2.82 and 2.59:1, respectively. Granola had the best alpha-linolenic acid content, nutritional indices in the lipid fraction, and mineral content. There were good hygienic and sanitary conditions during storage; probably due to the low water activity of the formulation, which contributed to inhibit microbial growth. The sensory attributes ranged from 'like very much' to 'like slightly', and the regression models were highly fitted and correlated during the storage period. A reduction in the sensory attribute levels and in the product physical stabilisation was verified by principal component analysis. The use of the affective test acceptance and instrumental analysis combined with statistical methods allowed us to obtain promising results about the characteristics of gluten-free granola.

Multivariate study of Nile tilapia byproducts enriched with omega-3 and dried with different methods

Abstract The present work aimed at studying the effect of different drying methods applied to tilapia byproducts (heads, viscera and carcasses) fed with flaxseed, verifying the contents of omega-3 fatty acids. Two diets were given to the tilapia: a control and a flaxseed formulation, over the course of 60 days. After this period, they were slaughtered and their byproducts (heads, viscera and carcasses) were collected. These fish parts were analyzed in natura, lyophilized and oven dried. Byproducts from tilapia fed with flaxseed presented docosapentaenoic, eicopentaenoic and docosahexanoic fatty acids as a result of the enzymatic metabolism of the fish. The byproducts from the oven drying process had lower levels of polyunsaturated fatty acids. In the multivariate analysis, the byproducts from fish fed with flaxseed had a greater composition of fatty acids. The addition of flaxseed in fish diets, as well as the utilization of their byproducts, may become a good business strategy. Additionally, the byproducts may be dried to facilitate transport and storage.

Group-invariant solutions of semilinear Schrodinger equations in multi-dimensions

Symmetry group methods are applied to obtain all explicit group-invariant radial solutions to a class of semilinear Schr¨odinger equations in dimensions n = 1. Both focusing and defocusing cases of a power nonlinearity are considered, including the special case of the pseudo-conformal power p = 4/n relevant for critical dynamics. The methods involve, first, reduction of the Schr¨odinger equations to group-invariant semilinear complex 2nd order ordinary differential equations (ODEs) with respect to an optimal set of one-dimensional point symmetry groups, and second, use of inherited symmetries, hidden symmetries, and conditional symmetries to solve each ODE by quadratures. Through Noether’s theorem, all conservation laws arising from these point symmetry groups are listed. Some group-invariant solutions are found to exist for values of n other than just positive integers, and in such cases an alternative two-dimensional form of the Schr¨odinger equations involving an extra modulation term with a parameter m = 2−n = 0 is discussed.

Simulation-Based Finite and Large Sample Tests in Multivariate Regressions.

In the context of multivariate linear regression (MLR) models, it is well known that commonly employed asymptotic test criteria are seriously biased towards overrejection. In this paper, we propose a general method for constructing exact tests of possibly nonlinear hypotheses on the coefficients of MLR systems. For the case of uniform linear hypotheses, we present exact distributional invariance results concerning several standard test criteria. These include Wilks' likelihood ratio (LR) criterion as well as trace and maximum root criteria. The normality assumption is not necessary for most of the results to hold. Implications for inference are two-fold. First, invariance to nuisance parameters entails that the technique of Monte Carlo tests can be applied on all these statistics to obtain exact tests of uniform linear hypotheses. Second, the invariance property of the latter statistic is exploited to derive general nuisance-parameter-free bounds on the distribution of the LR statistic for arbitrary hypotheses. Even though it may be difficult to compute these bounds analytically, they can easily be simulated, hence yielding exact bounds Monte Carlo tests. Illustrative simulation experiments show that the bounds are sufficiently tight to provide conclusive results with a high probability. Our findings illustrate the value of the bounds as a tool to be used in conjunction with more traditional simulation-based test methods (e.g., the parametric bootstrap) which may be applied when the bounds are not conclusive.

Exact Tests for Contemporaneous Correlation of Disturbances in Seemingly Unrelated Regressions.

This paper proposes finite-sample procedures for testing the SURE specification in multi-equation regression models, i.e. whether the disturbances in different equations are contemporaneously uncorrelated or not. We apply the technique of Monte Carlo (MC) tests [Dwass (1957), Barnard (1963)] to obtain exact tests based on standard LR and LM zero correlation tests. We also suggest a MC quasi-LR (QLR) test based on feasible generalized least squares (FGLS). We show that the latter statistics are pivotal under the null, which provides the justification for applying MC tests. Furthermore, we extend the exact independence test proposed by Harvey and Phillips (1982) to the multi-equation framework. Specifically, we introduce several induced tests based on a set of simultaneous Harvey/Phillips-type tests and suggest a simulation-based solution to the associated combination problem. The properties of the proposed tests are studied in a Monte Carlo experiment which shows that standard asymptotic tests exhibit important size distortions, while MC tests achieve complete size control and display good power. Moreover, MC-QLR tests performed best in terms of power, a result of interest from the point of view of simulation-based tests. The power of the MC induced tests improves appreciably in comparison to standard Bonferroni tests and, in certain cases, outperforms the likelihood-based MC tests. The tests are applied to data used by Fischer (1993) to analyze the macroeconomic determinants of growth.

Finite-Sample Inference Methods for Simultaneous Equations and Models with Unobserved and Generated Regressors

We propose finite sample tests and confidence sets for models with unobserved and generated regressors as well as various models estimated by instrumental variables methods. The validity of the procedures is unaffected by the presence of identification problems or \"weak instruments\", so no detection of such problems is required. We study two distinct approaches for various models considered by Pagan (1984). The first one is an instrument substitution method which generalizes an approach proposed by Anderson and Rubin (1949) and Fuller (1987) for different (although related) problems, while the second one is based on splitting the sample. The instrument substitution method uses the instruments directly, instead of generated regressors, in order to test hypotheses about the \"structural parameters\" of interest and build confidence sets. The second approach relies on \"generated regressors\", which allows a gain in degrees of freedom, and a sample split technique. For inference about general possibly nonlinear transformations of model parameters, projection techniques are proposed. A distributional theory is obtained under the assumptions of Gaussian errors and strictly exogenous regressors. We show that the various tests and confidence sets proposed are (locally) \"asymptotically valid\" under much weaker assumptions. The properties of the tests proposed are examined in simulation experiments. In general, they outperform the usual asymptotic inference methods in terms of both reliability and power. Finally, the techniques suggested are applied to a model of Tobin’s q and to a model of academic performance.

Simulation-Based Finite-and Large-sample Inference Methods in Multivariate Regressions and Seemingly Unrelated Regressions

In the context of multivariate regression (MLR) and seemingly unrelated regressions (SURE) models, it is well known that commonly employed asymptotic test criteria are seriously biased towards overrejection. in this paper, we propose finite-and large-sample likelihood-based test procedures for possibly non-linear hypotheses on the coefficients of MLR and SURE systems.

Exact Skewness-Kurtosis Tests for Multivariate Normality and Goodness-of-fit in Multivariate Regressions with Application to Asset Pricing Models

We study the problem of testing the error distribution in a multivariate linear regression (MLR) model. The tests are functions of appropriately standardized multivariate least squares residuals whose distribution is invariant to the unknown cross-equation error covariance matrix. Empirical multivariate skewness and kurtosis criteria are then compared to simulation-based estimate of their expected value under the hypothesized distribution. Special cases considered include testing multivariate normal, Student t; normal mixtures and stable error models. In the Gaussian case, finite-sample versions of the standard multivariate skewness and kurtosis tests are derived. To do this, we exploit simple, double and multi-stage Monte Carlo test methods. For non-Gaussian distribution families involving nuisance parameters, confidence sets are derived for the the nuisance parameters and the error distribution. The procedures considered are evaluated in a small simulation experi-ment. Finally, the tests are applied to an asset pricing model with observable risk-free rates, using monthly returns on New York Stock Exchange (NYSE) portfolios over five-year subperiods from 1926-1995.

Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions

In this paper, we propose exact inference procedures for asset pricing models that can be formulated in the framework of a multivariate linear regression (CAPM), allowing for stable error distributions. The normality assumption on the distribution of stock returns is usually rejected in empirical studies, due to excess kurtosis and asymmetry. To model such data, we propose a comprehensive statistical approach which allows for alternative - possibly asymmetric - heavy tailed distributions without the use of large-sample approximations. The methods suggested are based on Monte Carlo test techniques. Goodness-of-fit tests are formally incorporated to ensure that the error distributions considered are empirically sustainable, from which exact confidence sets for the unknown tail area and asymmetry parameters of the stable error distribution are derived. Tests for the efficiency of the market portfolio (zero intercepts) which explicitly allow for the presence of (unknown) nuisance parameter in the stable error distribution are derived. The methods proposed are applied to monthly returns on 12 portfolios of the New York Stock Exchange over the period 1926-1995 (5 year subperiods). We find that stable possibly skewed distributions provide statistically significant improvement in goodness-of-fit and lead to fewer rejections of the efficiency hypothesis.

Actuarial applications of multivariate phase-type distributions : model calibration and credibility

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