Stationarity Tests for Irregularly Spaced Observations and the Effects of Sampling Frequency on Power

In this paper, starting from continuous-time local level unobserved components models for stock and flow data we derive locally best invariant (LBI) stationarity tests for data available at potentially irregularly spaced points in time. We demonstrate that the form of the LBI test differs between stock and flow variables. In cases where the data are observed at regular intervals throughout the sample we show that the LBI tests for stock and flow data both reduce to the form of the standard stationarity test in the discrete-time local level model. Here we also show that the asymptotic local power of the LBI test increases with the sampling frequency in the case of stock, but not flow, variables. Moreover, for a fixed time span we show that the LBI test for stock (flow) variables is (is not) consistent against a fixed alternative as the sampling frequency increases to infinity. We also consider the case of mixed frequency data in some detail, providing asymptotic critical values for the LBI tests for both stock and flow variables, together with a finite sample power study. Our results suggest that tests which ignore the infra-period aspect of the data involve rather small losses in efficiency relative to the LBI test in the case of flow variables, but can result in significant losses of efficiency when analysing stock variables.Stock and flow variables, local level model, unit root, LBI test, temporal aggregation

Semantic Information G Theory and Logical Bayesian Inference for Machine Learning

An important problem with machine learning is that when label number n\u3e2, it is very difficult to construct and optimize a group of learning functions, and we wish that optimized learning functions are still useful when prior distribution P(x) (where x is an instance) is changed. To resolve this problem, the semantic information G theory, Logical Bayesian Inference (LBI), and a group of Channel Matching (CM) algorithms together form a systematic solution. MultilabelMultilabel A semantic channel in the G theory consists of a group of truth functions or membership functions. In comparison with likelihood functions, Bayesian posteriors, and Logistic functions used by popular methods, membership functions can be more conveniently used as learning functions without the above problem. In Logical Bayesian Inference (LBI), every label’s learning is independent. For Multilabel learning, we can directly obtain a group of optimized membership functions from a big enough sample with labels, without preparing different samples for different labels. A group of Channel Matching (CM) algorithms are developed for machine learning. For the Maximum Mutual Information (MMI) classification of three classes with Gaussian distributions on a two-dimensional feature space, 2-3 iterations can make mutual information between three classes and three labels surpass 99% of the MMI for most initial partitions. For mixture models, the Expectation-Maxmization (EM) algorithm is improved and becomes the CM-EM algorithm, which can outperform the EM algorithm when mixture ratios are imbalanced, or local convergence exists. The CM iteration algorithm needs to combine neural networks for MMI classifications on high-dimensional feature spaces. LBI needs further studies for the unification of statistics and logic

Inconsistency of a Unit Root Test against Stochastic Unit Root Processes

In this paper, we develop the asymptotic theory of Hwang and Basawa (2005) for explosive random coefficient autoregressive (ERCA) models. Applying the theory, we prove that a locally best invariant (LBI) test in McCabe and Tremayne (1995), which is for the null of a unit root (UR) process against the alternative of a stochastic unit root (STUR) process, is inconsistent against a class of ERCA models. This class includes a class of STUR processes as special cases. We show, however, that the well-known Dickey-Fuller (DF) UR tests and an LBI test of Lee (1998) are consistent against a particular case of this class of ERCA models.Locally Best Invariant Test, Consistency, Dickey-Fuller Test, LBI, RCA, STUR

Annual report 2002 LBI organic fruit growing research

Overview of projects, project results, funding bodies and partners in 2002 and plans for 2003 Including: SOIL MANAGEMENT * Evaluation of leaf analysis in organic fruit growing as a tool for measuring the uptake of nutrients: Consultants and researchers exchanged practical experiences and the LBI hopes to work with target values. * Impact of sulphur stress: The fruit quality seemed to be better in the reduced sulphur treatment (27 kg /ha instead of 60 kg /ha after flowering). * Fertilisation: In a late summer fertilisation trial with Elstar, trees fertilised late summer/autumn have a higher nitrogen content in the bud the following spring. And fertilising just before winter leads to increased growth of weeds in the next season. * Ground cover: The key to white clover undergrowth is to ‘do it properly or not at all’. It is difficult for an organic grower to restore undergrowth which has been invaded by grasses to bare earth. Undergrowth is definitely not the answer for fruit growers who have any difficulty with mechanical weeding. The management of ground cover requires at least as much mechanisation as the bare tree strip. REGULATING GROWTH AND CROP * Steps to counter biennialism in Elstar: A trial was set up at three orchards combining various measures: thinning or not thinning with two or three applications of lime sulphur, adapted pruning, 3 levels of fruit bearing (30, 40, 50 tonne/ha) and early or late manual thinning. This trial should demonstrate the relative significance of the various measures. Flowering will be evaluated in the spring of 2003. * Fruiting spur pruning in Elstar: To obtain better insight into the effect of different pruning methods three pruning treatments were used: standard pruning, removal of an extra large amount of fruiting spurs, and removal of extra fruiting spurs but sparing smooth one-year-old shoots. The production of the trees has been estimated and the blossom will be evaluated in the spring of 2003. * Effect of thinning times, fertilisation and bearing on regularity of production and fruit quality in Elstar: Ripening was delayed by the high nitrogen dose and associated higher acid content. Despite the late ripening the firmness was still lower, the calcium content lower and the nitrogen content higher. All three factors pro- duce a clear deterioration in quality. On the other hand, the sugar and acidity were higher in this case, but both these values fall within the target band. The trial will continue in 2003 CANKER * Administering calcium hydroxide against Cancer through the sprinkler irrigation system: Despite its effectiveness, sprinkling with calcium hydroxide cannot as yet be generally recommended for practical application. All the difficulties stem from the fact that the agent does not really dissolve, and the suspension formed very rapidly settles out. FRUIT QUALITY * Optimum picking time for Santana: Santana is a relatively new variety, and further investigation is required into optimising cultivation and storage. The apples only developed their full flavour when picked some time after the point of physiological ripeness. * Sprinkling to combat sunscald: By sprinkling under specific conditions an average of 1.38 fruits per tree was protected from sunscald. Per hectare sprinkling on these three days yielded around € 621 per ha. (Assuming: 3000 trees/ha, 6 fruits/kg, price € 1.10 or € 0.20 for industrial use). * Rot resistance test: The Louis Bolk Instituut is attempting to develop a test for the evaluation of the natural resistance of the fruit. This demonstrates, for example that apples with a high nitrogen content have more and larger areas of rot than apples with a lower nitrogen content. * Prospects offered by calcium chloride (CaCl2 ) before or after harvest: A pilot experiment was carried out on a farm to look into the prospects of spraying with CaCl2 before the harvest or rinsing with CaCl2 after harvest to reduce fruit rot. Neither treatment led to a reduction in fruit rot, but rather to an increase. * International association for ‘Organic Food, Quality and Health’ (FQH): The purpose of the group of researchers and traders brought together under the FQH banner is to develop a new concept of quality based on life processes and to select and further develop relevant methods of measurement

Skewness and kurtosis as locally best invariant tests of normality

Consider testing normality against a one-parameter family of univariate distributions containing the normal distribution as the boundary, e.g., the family of $t$-distributions or an infinitely divisible family with finite variance. We prove that under mild regularity conditions, the sample skewness is the locally best invariant (LBI) test of normality against a wide class of asymmetric families and the kurtosis is the LBI test against symmetric families. We also discuss non-regular cases such as testing normality against the stable family and some related results in the multivariate cases

Aldebaran's angular diameter: how well do we know it?

The bright, well-known K5 giant Aldebaran, alpha Tau, is probably the star with the largest number of direct angular diameter determinations, achieved over a long time by several authors using various techniques. In spite of this wealth of data, or perhaps as a direct result of it, there is not a very good agreement on a single angular diameter value. This is particularly unsettling if one considers that Aldebaran is also used as a primary calibrator for some angular resolution methods, notably for optical and infrared long baseline interferometry. Directly connected to Aldebaran's angular diameter and its uncertainties is its effective temperature, which also has been used for several empirical calibrations. Among the proposed explanations for the elusiveness of an accurate determination of the angular diameter of Aldebaran are the possibility of temporal variations as well as a possible dependence of the angular diameter on the wavelength. We present here a few, very accurate new determinations obtained by means of lunar occultations and long baseline interferometry. We derive an average value of 19.96+-0.03 milliarcseconds for the uniform disk diameter. The corresponding limb-darkened value is 20.58+-0.03 milliarcseconds, or 44.2+-0.9 R(sun). We discuss this result, in connection with previous determinations and with possible problems that may affect such measurements.Comment: 8 pages, 4 figures, accepted for publication in A&

Even Kakutani Equivalence And The Loose Block Independence Property For Positive Entropy Zᵈ Actions

In this paper we define the loose block independence property for positive entropy Zᵈ actions and extend some of the classical results to higher dimensions. In particular, we prove that two loose block independent actions are even Kakutani equivalent if and only if they have the same entropy. We also prove that for d \u3e 1 the ergodic, isometric extensions of the positive entropy loose block independent Zᵈ actions are also loose block independent