Nonparametric Censored Regression

The nonparametric censored regression model is y = max[c, m(x) + e], where both the regression function m(x) and the distribution of the error e are unknown, but the fixed censoring point c is known. This paper provides a simple consistent estimator of the derivative of m(x) with respect to each element of x. The convergence rate of this estimator is the same as for the derivatives of an uncensored nonparametric regression. We then estimate the regression function itself by solving the associated partial differential equation system. We show that our estimator of m(x) achieves the same rate of convergence as the usual estimators in uncensored nonparametric regression. We also provide root n estimates of weighted average derivatives of m(x), which equal the coefficients in any linear or partly linear specification for m(x).Semiparametric, nonparametric, censored regression, Tobit, latent variable

Peptide metabolism in the lactococci and its regulation : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Biochemistry at Massey University

Aspects of peptide metabolism in the lactococci have been investigated to increase the understanding of how these nutritionally fastidious bacteria, which have a central role in the dairy manufacturing industry, are able to grow in a complex medium such as milk. Peptide metabolism by lactococci in milk encompasses the processes by which large oligopeptides, produced from milk-caseins by the extracellular activity of the cell wall-associated proteinase, are converted into an intracellular pool of metabolisable amino acids. This involves the activities of both membrane-bound transport systems and peptidases. Early research into lactococcal peptide utilisation has proposed significant differences between Lactococcus lactis strains with respect to the mechanisms by which these bacteria utilise peptides in their environment. More recent studies of the lactococcal peptide carrier systems, based on intensive studies of only a single strain, have proposed a major role for a carrier system capable of transporting di- and tripeptides, and a subsidiary role for another system transporting oligopeptides containing four or more residues. Yet to date, peptidases with an extracellular location capable of degrading the large casein-peptides into smaller peptides have not been isolated. This current study has attempted to investigate more fully the in vivo activity of the oligopeptide transport system, and to assess whether it may have a more fundamental role in peptide utilisation than previous work has suggested. For this study a model series of homologous peptides of increasing size from the dipeptide Val-Gly to the octapeptide Val-Gly7 , all based on the essential amino acid valine, was used. The larger peptides in this series, Val-Gly3 , Val-Gly4 and Val-Gly7 , were synthesised for this work. The ability of Lactococcus lactis subsp. cremoris E8 8 to transport these peptides, and to grow in a chemically defined medium where they constitute the sole source of the essential amino acid valine, was studied . Preliminary peptide uptake studies were also performed using oligopeptides derived from a proteolytic cleavage of β-casein. The collective results of these studies suggest that the upper size limit, and the relative activity of this transport system, may be sufficient to permit this strain to utilise relatively large casein-derived oligopeptides without the need for hydrolysis into smaller peptides and free amino acids. A comparative study of peptide transport by a number of Lactococcus lactis strains was undertaken to investigate previously published observations indicating significant differences in the mechanisms of peptide uptake between lactococcal strains. While the results of this comparative study are consistent with the general model proposing two separate peptide carrier systems, they have revealed that significant differences can exist between strains in the relative activities and possible substrate specificities of these transport systems consistent with previous work that the lactococci have only two peptide carrier systems. These observations imply the need for caution in extrapolating the results obtained from the study of a single strain to lactococci as a whole. In contrast to the finding of significant strain differences with respect to the relative rates of peptide transport, a comparative study of the relative activity of six different intracellular peptidases showed relatively few differences in peptidase activity between strains. An investigation was also carried out to assess whether the peptidases and transport systems involved in the utilisation of peptides were nutritionally regulated. No clear evidence was obtained for the significant induction of either the intracellular peptidase complement or the di-/tripeptide transport system. An attempt was also made to isolate a mutant of Lactococcus lactis subsp. cremoris E8 unable to utilise dipeptides, to assess whether the di-/tripeptide transport system or the intracellular dipeptidase of this strain were essential to casein utilisation. This attempt was not successful

Gas-dynamic shock heating of post-flare loops due to retraction following localized, impulsive reconnection

We present a novel model in which shortening of a magnetic flux tube following localized, three-dimensional reconnection generates strong gas-dynamic shocks around its apex. The shortening releases magnetic energy by progressing away from the reconnection site at the Alfven speed. This launches inward flows along the field lines whose collision creates a pair of gas-dynamic shocks. The shocks raise both the mass density and temperature inside the newly shortened flux tube. Reconnecting field lines whose initial directions differ by more that 100 degrees can produce a concentrated knot of plasma hotter that 20 MK, consistent with observations. In spite of these high temperatures, the shocks convert less than 10% of the liberated magnetic energy into heat - the rest remains as kinetic energy of bulk motion. These gas-dynamic shocks arise only when the reconnection is impulsive and localized in all three dimensions; they are distinct from the slow magnetosonic shocks of the Petschek steady-state reconnection model

Efficient estimation of generalized additive nonparametric regression models.

We define new procedures for estimating generalized additive nonparametric regression models that are more efficient than the Linton and Härdle (1996, Biometrika 83, 529–540) integration-based method and achieve certain oracle bounds. We consider criterion functions based on the Linear exponential family, which includes many important special cases. We also consider the extension to multiple parameter models like the gamma distribution and to models for conditional heteroskedasticity.

Nonparametric inference for unbalance time series data

Estimation of heteroskedasticity and autocorrelation consistent covariance matrices (HACs) is a well established problem in time series. Results have been established under a variety of weak conditions on temporal dependence and heterogeneity that allow one to conduct inference on a variety of statistics, see Newey and West (1987), Hansen (1992), de Jong and Davidson (2000), and Robinson (2004). Indeed there is an extensive literature on automating these procedures starting with Andrews (1991). Alternative methods for conducting inference include the bootstrap for which there is also now a very active research program in time series especially, see Lahiri (2003) for an overview. One convenient method for time series is the subsampling approach of Politis, Romano, andWolf (1999). This method was used by Linton, Maasoumi, andWhang (2003) (henceforth LMW) in the context of testing for stochastic dominance. This paper is concerned with the practical problem of conducting inference in a vector time series setting when the data is unbalanced or incomplete. In this case, one can work only with the common sample, to which a standard HAC/bootstrap theory applies, but at the expense of throwing away data and perhaps losing effciency. An alternative is to use some sort of imputation method, but this requires additional modelling assumptions, which we would rather avoid.1 We show how the sampling theory changes and how to modify the resampling algorithms to accommodate the problem of missing data. We also discuss effciency and power. Unbalanced data of the type we consider are quite common in financial panel data, see for example Connor and Korajczyk (1993). These data also occur in cross-country studies.

Nonparametric Inference for Unbalanced Time Series Data

This paper is concerned with the practical problem of conducting inference in a vector time series setting when the data is unbalanced or incomplete. In this case, one can work only with the common sample, to which a standard HAC/Bootstrap theory applies, but at the expense of throwing away data and perhaps losing efficiency. An alternative is to use some sort of imputation method, but this requires additional modelling assumptions, which we would rather avoid. We show how the sampling theory changes and how to modify the resampling algorithms to accommodate the problem of missing data. We also discuss efficiency and power. Unbalanced data of the type we consider are quite common in financial panel data, see, for example, Connor and Korajczyk (1993). These data also occur in cross-country studies.Bootstrap, efficient, HAC estimation, missing data, subsampling.

Evaluating hedge fund performance: a stochastic dominance approach

We introduce a general and flexible framework for hedge fund performance evaluation and asset allocation: stochastic dominance (SD) theory. Our approach utilizes statistical tests for stochastic dominance to compare the returns of hedge funds. We form hedge fund portfolios by using SD criteria and examine the out-of-sample performance of these hedge fund portfolios. Compared to performance of portfolios of randomly selected hedge funds and mean-variance e¢ cient hedge funds, our results show that fund selection method based on SD criteria greatly improves the performance of hedge fund portfolio

Consistent estimation of the risk-return tradeoff in the presence of measurement error

Prominent asset pricing models imply a linear, time-invariant relation between the equity premium and its conditional variance. We propose an approach to estimating this relation that overcomes some of the limitations of the existing literature. First, we do not require any functional form assumptions about the conditional moments. Second, the GMM approach is used to overcome the endogeneity problem inherent in the regression. Third, we correct for the measurement error arising because of using a proxy for the latent variance. The empirical findings reveal significant time-variation in the relation that coincide with structural break dates in the market-wide price-dividend rati