Nonparametric bootstrap tests for independence of generalized errors

This article develops nonparametric tests of independence between two stochastic processes satisfying β-mixing conditions. The testing strategy boils down to gauging the closeness between the joint and the product of the marginal stationary densities. For that purpose, we take advantage of a generalized entropic measure so as to build a whole family of nonparametric tests of independence. We derive asymptotic normality and local power using the functional delta method for kernels. As a corollary, we also develop a class of entropy-based tests for serial independence. The latter are nuisance parameter free, and hence also qualify for dynamic misspecification analyses. We then investigate the finite-sample properties of our serial independence tests through Monte Carlo simulations. They perform quite well, entailing more power against some nonlinear AR alternatives than two popular nonparametric serial-independence tests.

In nonparametric tests for serial independence the marginal distribution of the data acts as an infinite dimensional nuisance parameter. The decomposition of joint distributions in terms of a copula density and marginal densities shows that in general empirical marginals carry no information on dependence. It follows that the order of ranks is sufficient for inference, which motivates transforming the data to a pre-specified marginal distribution prior to testing. As a test statistic we use an estimator of the marginal redundancy. We numerically study the finite sample properties of the tests obtained when the data are transformed to uniform as well as normal marginals. For comparison purposes we also derive a rank-based test against local ARCH alternatives. The performance of the new tests is compared with a modified version of the BDS test and with the Ljung-Box test.

Detecting Serial Dependence in Tail Events: A Test Dual to the BDS Test

Chapter 1 - Introduction

Prediction of intake in growing dairy heifers under tropical conditions

The economic cycle has always been an important feature of the evolution of an economic system. In the presence of many uncertain factors, it appears in the manner of very complex nonlinearity and randomness. Based on the theory of stochastic nonlinear dynamics, a nonlinear economic cycle model with correlated random income disturbance is established. The probability density evolution of the nonlinear economic cycle model under random disturbance is numerically analyzed by using a path integration method. The analysis shows the high saving rate reduces the investment and improves the probabilities of low income and low income change rate. In order to achieve a higher income, the saving rate should be controlled to some reasonable small value. The nonlinearity of the economic cycle model increases the probabilities of high income and high income change rate, which can lead to the increase of income in a probabilistic sense. The increase of random income interference enhances the uncertainty of income. Meanwhile, the increase of correlated random income disturbance can lead to a nonsymmetric distribution of the probability distributions of income and income change rate. In such cases, the income is more difficult to forecast and control.

We show that Kolmogorov complexity and such its estimators as universal codes (or data compression methods) can be applied for hypotheses testing in a framework of classical mathematical statistics. The methods for identity testing and nonparametric testing of serial independence for time series are suggested.

In the genotyped-proband design, a proband is selected based on an observed phenotype, the genotype of the proband is observed, and then the phenotypes of all first-degree relatives are obtained. The genotypes of these first-degree relatives are not observed. Gail et al. [(1999) Genet Epidemiol] discuss likelihood analysis of this design under the assumption that the phenotypes are conditionally independent of one another given the observed and unobserved genotypes. Li and Thompson [(1997) Biometrics 53:282–293] give an example where this assumption is suspect, thus suggesting that it is important to develop tests for conditional independence. In this paper, we develop a score test for the conditional independence assumption in models that might include covariates or observation of genotypes for some of the first degree relatives. The problem can be cast more generally as one of score testing in the presence of missing covariates. A standard analysis would require specifying a distribution for the covariates, which is not convenient and could lead to a lack of model-robustness. We show that by considering a natural conditional likelihood, and basing the score test on it, a simple analysis results. The methods are applied to a study of the penetrance for breast cancer of BRCA1 and BRCA2 mutations among Ashkenazi Jews. Genet. Epidemiol. 18:293–306, 2000. © 2000 Wiley-Liss, Inc.

BackgroundWe characterized variation and chemical composition of epicuticular hydrocarbons (CHCs) in the seven species of the Drosophila buzzatii cluster with gas chromatography/mass spectrometry. Despite the critical role of CHCs in providing resistance to desiccation and involvement in communication, such as courtship behavior, mating, and aggregation, few studies have investigated how CHC profiles evolve within and between species in a phylogenetic context. We analyzed quantitative differences in CHC profiles in populations of the D. buzzatii species cluster in order to assess the concordance of CHC differentiation with species divergence.ResultsThirty-six CHC components were scored in single fly extracts with carbon chain lengths ranging from C29 to C39, including methyl-branched alkanes, n-alkenes, and alkadienes. Multivariate analysis of variance revealed that CHC amounts were significantly different among all species and canonical discriminant function (CDF) analysis resolved all species into distinct, non-overlapping groups. Significant intraspecific variation was found in different populations of D. serido suggesting that this taxon is comprised of at least two species. We summarized CHC variation using CDF analysis and mapped the first five CHC canonical variates (CVs) onto an independently derived period (per) gene + chromosome inversion + mtDNA COI gene for each sex. We found that the COI sequences were not phylogenetically informative due to introgression between some species, so only per + inversion data were used. Positive phylogenetic signal was observed mainly for CV1 when parsimony methods and the test for serial independence (TFSI) were used. These results changed when no outgroup species were included in the analysis and phylogenetic signal was then observed for female CV3 and/or CV4 and male CV4 and CV5. Finally, removal of divergent populations of D. serido significantly increased the amount of phylogenetic signal as up to four out of five CVs then displayed positive phylogenetic signal.ConclusionsCHCs were conserved among species while quantitative differences in CHC profiles between populations and species were statistically significant. Most CHCs were species-, population-, and sex-specific. Mapping CHCs onto an independently derived phylogeny revealed that a significant portion of CHC variation was explained by species' systematic affinities indicating phylogenetic conservatism in the evolution of these hydrocarbon arrays, presumptive waterproofing compounds and courtship signals as in many other drosophilid species.

We show that data compression methods (or universal codes) can be applied for hypotheses testing in a framework of classical mathematical statistics. Namely, we describe tests, which are based on data compression methods, for the three following problems: i) identity testing, ii) testing for independence and iii) testing of serial independence for time series. Applying our method of identity testing to pseudorandom number generators, we obtained experimental results which show that the suggested tests are quite efficient.

Pharmacokinetic-Pharmacodynamic Modeling and Simulation

Chapter 7 Learning dynamics

This paper presents the theoretical development of a new threshold autoregressive model based on trended time series. The theoretical arguments underlying the model are outlined and a nonlinear economic model is used to derive the specification of the empirical econometric model. Estimation and testing issues are considered and analysed. Additionally we apply the model to the empirical investigation of U.S. GDP.

We consider tests of serial independence for a sequence of functional observations. The new methods are formulated as L2-type criteria based on empirical characteristic functions and are convenient from the computational point of view. We derive asymptotic normality of the proposed test statistics for both discretely and continuously observed functions. In a Monte Carlo study, we show that the new test is sensitive with respect to functional GARCH alternatives, investigate the choice of necessary tuning parameters, and demonstrate that critical values obtained by resampling lead to a test with good performance in any setup, whereas the asymptotic critical values may be recommended only for a sufficiently fine discretization grid. Finite-sample comparison with a distance (auto)covariance test criterion is also included, and the article concludes with application on a real data set.

The present study investigates the application of the index flood L-moments-based regional frequency analysis procedure (RFA-LM) to the annual maximum 24-h rainfall (AM) of 33 rainfall gauge stations (RGs) to estimate rainfall quantiles at the Titicaca Lake drainage (TL). The study region was chosen because it is characterised by common floods that affect agricultural production and infrastructure. First, detailed quality analyses and verification of the RFA-LM assumptions were conducted. For this purpose, different tests for outlier verification, homogeneity, stationarity, and serial independence were employed. Then, the application of RFA-LM procedure allowed us to consider the TL as a single, hydrologically homogeneous region, in terms of its maximum rainfall frequency. That is, this region can be modelled by a generalised normal (GNO) distribution, chosen according to the Z test for goodness-of-fit, L-moments (LM) ratio diagram, and an additional evaluation of the precision of the regional growth curve. Due to the low density of RG in the TL, it was important to produce maps of the AM design quantiles estimated using RFA-LM. Therefore, the ordinary Kriging interpolation (OK) technique was used. These maps will be a useful tool for determining the different AM quantiles at any point of interest for hydrologists in the region.