Threshold selection and trimming in extremes

We consider removing lower order statistics from the classical Hill estimator in extreme value statistics, and compensating for it by rescaling the remaining terms. Trajectories of these trimmed statistics as a function of the extent of trimming turn out to be quite flat near the optimal threshold value. For the regularly varying case, the classical threshold selection problem in tail estimation is then revisited, both visually via trimmed Hill plots and, for the Hall class, also mathematically via minimizing the expected empirical variance. This leads to a simple threshold selection procedure for the classical Hill estimator which circumvents the estimation of some of the tail characteristics, a problem which is usually the bottleneck in threshold selection. As a by-product, we derive an alternative estimator of the tail index, which assigns more weight to large observations, and works particularly well for relatively lighter tails. A simple ratio statistic routine is suggested to evaluate the goodness of the implied selection of the threshold. We illustrate the favourable performance and the potential of the proposed method with simulation studies and real insurance data.

Sample Path Large Deviations for Order Statistics

We consider the sample paths of the order statistics of independent and identically distributed random variables with common distribution function F. If F is strictly increasing but possibly having discontinuities, we prove that the sample paths of the order statistics satisfy the large deviation principle in the Skorokhod M 1 topology. Sanov's theorem is deduced in the Skorokhod M'1 topology as a corollary to this result. A number of illustrative examples are presented, including applications to the sample paths of trimmed means and Hill plots.

Sample Path Large Deviations for Order Statistics

We consider the sample paths of the order statistics of independent and identically distributed random variables with common distribution functionF. IfFis strictly increasing but possibly having discontinuities, we prove that the sample paths of the order statistics satisfy the large deviation principle in the SkorokhodM1topology. Sanov's theorem is deduced in the SkorokhodM'1topology as a corollary to this result. A number of illustrative examples are presented, including applications to the sample paths of trimmed means and Hill plots.

Plot size variation to quantify yield of potato clones

The objective of this paper was to study plot size variation among potato clones to increase experimental precision of yield performance trials. The experiment was carried out at the experimental area of the Horticulture Dept., UFSM, Santa Maria, Rio Grande do Sul State, Brazil. Tubers of five potato clones were planted in two rows of 60 hills in August 2004. For all ten experimental rows, combined plots were formed adding a different number of adjacent hills of the same row. Soil heterogeneity index and optimum plot size were estimated for each row. Real differences between treatment means for each clone and all clones were estimated using the Hatheway technique. The experimental precision of potato yield trials varied with the evaluated clone because of different optimum plot sizes. Eight-hill plots are the optimum size to quantify yield of potato clones, but experimental precision depends upon adjustments of the number of treatments and replications to the availability of experimental area. Genetic diversity indeed decreases experimental precision and justifies the use of different plot sizes. Practical applicattions and strategies to increase experimental precision of yields performance trials of potato clones are discussed.

Stability of soybean yield through different sowing periods

Soybean yield is highly affected by sowing period and there are significant productivity losses when sowings are done outward a relatively restricted period in many regions of Brazil. Breeding cultivars less sensitive to photoperiod and to temperature variations is desirable for adaptation to wider sowing period and wider latitude range and also make irrigated soybean cultivation possible during the fall-winter seasons in frost free regions. The possibility of selecting high yielding and stable lines for yield during various sowing periods was studied by analyzing the behavior of 100 non-selected advanced lines (F9 and F10), from each one of all possible biparental crosses involving the genotypes BR85-29009, OCEPAR 8, FT-2, and BR-13. Experiments were set up in a completely randomized design with single-plant hill plots and received supplementary irrigation. Sowing was on Sept 27, Oct 20, Nov 17, and Dec 17 in 1993/94 and Sept 20, Oct 20, Nov 17, and Dec 14 in 1994/95 at Londrina, PR, Brazil. Procedures of regression analysis and minimum variance among planting date means were efficient for selecting stable lines during the four sowing seasons. It was possible to select stable and high yielding genotypes through the four sowing periods in all the crosses. No specific cross was clearly better to produce a greater number of stable genotypes.

The Effect of Stand Density on the Development of Puccinia graminis f. sp. tritici in Barley

The progress of stem rust epidemics caused by race Pgt-QCCJ of Puccinia graminis f. sp. tritici was examined in field plots of the six-rowed barley cvs. Robust and Steptoe at four stand densities, and in short rows and hill plots. Cv. Robust carries Rpg1, which confers resistance to most races of P. graminis f. sp. tritici, other than Pgt-QCCJ, while cv. Steptoe lacks any reported genes for resistance to P. graminis f. sp. tritici. The stand-density treatments established were approximately double, the equivalent of, half of, and one quarter of the planting rate recommended for commercial barley. Stem rust caused by race Pgt-QCCJ spread more rapidly in cv. Steptoe than in cv. Robust, irrespective of the stand-density treatment. The effect of stand density on rust severity was, however, greater than the effect of cultivar. Rust severity was 18 to 36% greater in sparse stands than in dense stands of both cultivars. Reductions in kernel size were most severe in sparse stands where rust development was greatest. Knowledge that reduced stand densities may promote the development of stem rust in barley may be useful in refining procedures for screening breeding material for resistance to stem rust, and in allaying concern over the high levels of stem rust occasionally reported in lightly seeded seed increases and in commercial fields where sparse stands are encountered.

Control of Alfalfa Weevil Larvae in Tennessee, 1997

Insecticide treatments were evaluated in a 1-yr stand of alfalfa at the Middle Tennessee Experiment Station, Spring Hill. Plots were 20 ft X 20 ft replicated 4 times in a RCB design. Blocks were separated by 15-ft alleys. Eleven insecticide treatments were applied on 3 Mar when 68% of the tips were damaged and alfalfa weevil larvae (AWL) averaged 1.55 larvae/sweep. Chemicals were applied using a tractor-mounted CO2-powered 10-ft boom sprayer at the rate of 30 gpa. AWL samples were collected on 1,7, 14, 21, and 29 May using a 15-inch insect net, and consisted of 5 pendulum sweeps from each plot. A 5 ft X 20 ft strip was harvested from the middle of each plot on 29 May to determine green weight yields. Moisture content of alfalfa was 70.58%.

Comparison of long-chain fatty acyl-CoA synthetases from rabbit heart and liver: substrate preferences and effects of Mg2+

Rabbit heart has a single, non-specific, fatty acyl-CoA synthetase (HP1) which is dependent on Mg2+, apart from the requirement for MgATP2-. Two long-chain fatty acyl-CoA synthetase activities (LP1 and LP2) can be resolved by hydroxyapatite chromatography of liver preparations; the Mg2+ requirement for these enzymes is undefined. These experiments were done to define the Mg2+ requirements of the liver enzymes and to compare them with the heart enzyme. For all three sources of enzyme and for arachidonic, oleic and palmitic acid substrates, the overall velocity of the reaction increased as [Mg2+] increased. Depending on the substrate and the source of enzyme, the increase in overall velocity could be attributed to changes in affinity or maximal velocity or both. The substrate preference of the HP1 enzyme for arachidonic acid (AA) was fifth or sixth of eight substrates regardless of the concentration of Mg2+. In contrast, increasing [Mg2+] shifted the relative substrate preference of both liver enzymes for AA. At low [Mg2+], AA was ranked seventh or eighth (least preferred) of eight substrates, whereas at high [Mg2+], AA was ranked as fifth or sixth. Hill plots of competition studies were consistent with Mg2+-induced positive co-operativity in LP1, but not in HP1 or LP2. Although enzymes from the three sources exhibit substantial kinetic differences, it is uncertain whether they are three different enzymes.

Hill plots for yield evaluation in a doubled haploid recurrent selection program in barley (Hordeum vulgare L.)

Seven selected doubled haploid lines, from each of three cycles (C0, C1, C2) of a diallel recurrent selection program, the seven original parents and two check cultivars were evaluated in replicated hill and row plots at two locations in Ontario in 1988 and 1989. Comparison of hill and row plots using means ranges, coefficient of variation, repeatability and correlations among traits indicated that grain yield, days to heading plant height and powdery mildew resistance could be evaluated with similar accuracy and precision using either of the methods. Regression of row plot yield on hill plot yield was positive and highly significant showing a strong relationship between the two plot types for grain yield. Selection efficiency in hill plots was high for all the traits. The percentage of lines with similar performance for yield in both the plot types was high. The hill plot method appears to be a useful technique for evaluating homozygous lines for yield and other agronomic traits in a doubled haploid recurrent selection program in six-row barley. Key words:Hordeum vulgare L., barley, breeding methods, yield, powdery mildew, doubled haploid, recurrent selection