A test for counting sequences of integer-valued autoregressive models

The integer autoregressive (INAR) model is one of the most commonly used models in nonnegative integer-valued time series analysis and is a counterpart to the traditional autoregressive model for continuous-valued time series. To guarantee the integer-valued nature, the binomial thinning operator or more generally the generalized Steutel and van Harn operator is used to define the INAR model. However, the distributions of the counting sequences used in the operators have been determined by the preference of analyst without statistical verification so far. In this paper, we propose a test based on the mean and variance relationships for distributions of counting sequences and a disturbance process to check if the operator is reasonable. We show that our proposed test has asymptotically correct size and is consistent. Numerical simulation is carried out to evaluate the finite sample performance of our test. As a real data application, we apply our test to the monthly number of anorexia cases in animals submitted to animal health laboratories in New Zealand and we conclude that binomial thinning operator is not appropriate.Comment: 45 pages, 2 table

Spectral clustering algorithm for the allometric extension model

The spectral clustering algorithm is often used as a binary clustering method for unclassified data by applying the principal component analysis. To study theoretical properties of the algorithm, the assumption of conditional homoscedasticity is often supposed in existing studies. However, this assumption is restrictive and often unrealistic in practice. Therefore, in this paper, we consider the allometric extension model, that is, the directions of the first eigenvectors of two covariance matrices and the direction of the difference of two mean vectors coincide, and we provide a non-asymptotic bound of the error probability of the spectral clustering algorithm for the allometric extension model. As a byproduct of the result, we obtain the consistency of the clustering method in high-dimensional settings.Comment: 20 page

Growth, Yield and Fruit Quality of Tomato as Affected by Root Zone Restriction in Combination with Solar-mediated Fertigation Regime

　Plant growth and fruit development of tomato (Lycopersicon esculentum Mill. cv. House Momotaro) grown in different sized plastic pots (root zone volume, RZV, of 250, 500, 1,000 mL/plant) in combination with high or low rate of drip fertigation (HF and LF) were investigated. In the February-sown experiment, the plants were fertigated with standard to half strength of Ohtsuka-A solution in proportion to solar radiation keeping the ratio of drainage to supplied solution as 10 to 20ｵ, in 500mL- and 250mL-RZV for HF and LF, respectively. Stem and leaf growth decreased with decrease in RZV and the fertigation rate. The decreases were not significant in the distal plant part lower than the 4th inflorescence. The average fruit weight was greater in HF than LF and increased with increase in RZV only for HF. The incidence of blossom-end rot (BER) was more frequent in HF compared to LF and increased with increase in RZV only for LF. Consequently, fruit yield increased with increase in RZV for HF, but it decreased with increase in RZV for LF. Total soluble solid content (TSS) was significantly higher in LF than in HF and increased with decrease in RZV. Qualified fruits, called ‘fruit tomato’ having 8ｵ of TSS or higher, were obtained with 250 to 500mL of RZV in the successive October-sown experiment where the standard solution was supplied throughout. For ‘fruit tomato’ production with a substrate culture system, root zone restriction, in combination with solar-mediated fertigation control, can be a useful and stable stress factor, reducing shoot and fruit growth, but inducing fruit sugar accumulation and reducing BER incidence simultaneously

Effect of Supplied Amount and Strength of Nutrient Solution on Growth, Yield, and Fruit Quality of Strawberry ‘Saga-honoka’ Grown with Sufficiently Elevated CO2

The effects of supplied amount and strength of nutrient solution were investigated for strawberry (Fragaria×ananassa Duch. cv. Saga-honoka) grown with peat bags in elevated CO2 environment (800-2500 ppm in the day time, November 4 to April 7). Three strengths (L : low-80%, M : standard-100% and H : high-120%) of nutrient solution (N : 8.85, P : 0.85, K : 3.90, Ca : 2.05, Mg : 0.93 mM ; half strength of Ohtsuka A solution) were compared. Around 20% of discharged rate (discharged/supplied amount of nutrient solution) was kept for these 3 plots and 30 to 40% of the rate was kept for additional plot of 80%-solution (L2) by altering the supplied amount of 80%-solution. As almost no nitrate could be detected in drainage of L, nutrient supply was probably insufficient throughout the experiment. Total amount of nitrogen supply was lower than the other 3 plots and leaf area was the smallest after December. Although there was no significant difference in yield and fruit quality, the rate of tip burn affected flowers was lowest in L2 and highest in H. Thus, around 30-40% of drainage rate and 50-60 mS・m−1 of drainage EC may be desirable target values for ‘Saga-honoka’ strawberry grown with peat based substrate.イチゴ‘さがほのか’を用いて，高CO2濃度条件下(日中800～2500ppm)での栽培における培養液濃度と施用量の影響について検討した．培養液は排液率20%を目標に，大塚Ａ処方を30～50%濃度で適宜変更する慣行区を標準として，濃度をその1.2倍，0.8倍とする高濃度区と低濃度区，さらに低濃度区においては，給液量を1.2倍(排液率35%)とする低濃度多量区を設け，計４処理区とした．排液率20%を目標とした低濃度培養液管理では，12月以降の排液中NO3-Nは検出限界以下であり，栽培期間を通して養分が不足しがちであった．また，全Ｎ施用量も他の３処理区と比較すると少なくなり，１月以降の葉面積が小さくなった．収量・果実品質においては処理区間で有意な差は認められなかったが，チップバーン発生率は，高濃度区で高く，低濃度多量区の発生率が最も低かった．低濃度多量区では，葉面積も大きくなったことから，‘さがほのか’においては，排液率30～40%，排液EC50～60mS・m-1を目標とした低濃度での培養液管理が望ましいといえる

Growth and Yield of Substrate-Cultured Strawberry as Affected by Root Zone Volume and Fertigation Frequency

Effects of root-zone volume and fertigation frequency on 4 cultivars of substrate-grown strawberry (Fragaria×ananassa Duch., ‘Nyoho’, ‘Asukarubi’, ‘Akihime’ and ‘Tochiotome’) were investigated. Fertigation frequency had no significant effect on growth and yield of strawberry even in the minimum root-zone volume of 0.6L/plant. Total yield, mean berry weight, and root dry weight at end of harvest decreased with decrease in volume, but no significant difference was observed in number of harvested berries and subsequent growth of runners and daughter plants. In the yield and root growth, there were large differences between peat bags (2.25L/plant) and bowl-shaped containers (0.6-1.5L/plant), and highly significant non-linear regressions between the two parameters and the root-zone volume. The differences may be caused by factors other than the volume, such as the shape of root-zone and edge of containers or drain property, and so on

Thermal properties and phase transition behaviors of possible caloric materials Bi₀.₉₅Ln₀.₀₅NiO₃

Thermal properties and phase transition behaviors of possible caloric materials Bi₀.₉₅Ln₀.₀₅NiO₃ (Ln = La, Nd, Sm, Eu, Gd, Dy), which show intersite charge transfer between Bi and Ni ions, were investigated. Although a few of the compounds showed large latent heats at the intersite-charge-transfer transition temperatures, the values are not comparable to that observed in the giant caloric effect compound NdCu₃Fe₄O₁₂. In the present Bi₀.₉₅Ln₀.₀₅NiO₃, contrary to our expectation, the magnetic transitions of Ni²⁺ spins are not induced by the intersite-charge-transfer transitions and the magnetic entropy changes do not contribute to the latent heat produced by the intersite-charge-transfer transitions. To obtain giant caloric effects, materials for which the “intrinsic” magnetic transition temperatures are much higher than the charge-transfer-transition temperatures may be needed