Critical values for unit root and cointegration test statistics - the use of response surface equations

This note considers the value of surface response equations which can be used to calculate critical values for a range of unit root and cointegration tests popular in applied economic research.

Clarke critical values of subanalytic Lipschitz continuous functions

We prove that any subanalytic locally Lipschitz function has the Sard property. Such functions are typically nonsmooth and their lack of regularity necessitates the choice of some generalized notion of gradient and of critical point. In our framework these notions are defined in terms of the Clarke and of the convex-stable subdifferentials. The main result of this note asserts that for any subanalytic locally Lipschitz function the set of its Clarke critical values is locally finite. The proof relies on Pawlucki's extension of the Puiseuxlemma. In the last section we give an example of a continuous subanalytic function which is not constant on a segment of "broadly critical" points, that is, points for which we can find arbitrarily short convex combinations of gradients at nearby points.

Critical values of nitrogen indices in tomato plants grown in soil and nutrient solution determined by different statistical procedures

The objective of this study was to establish critical values of the N indices, namely soil-plant analysis development (SPAD), petiole sap N-NO3 and organic N in the tomato leaf adjacent to the first cluster (LAC), under soil and nutrient solution conditions, determined by different statistical approaches. Two experiments were conducted in randomized complete block design with four repli-cations. Tomato plants were grown in soil, in 3 L pot, with five N rates (0, 100, 200, 400 and 800 mg kg-1) and in solution at N rates of 0, 4, 8, 12 and 16 mmol L-1. Experiments in nutrient solution and soil were finished at thirty seven and forty two days after transplanting, respectively. At those times, SPAD index and petiole sap N-NO3 were evaluated in the LAC. Then, plants were harvested, separated in leaves and stem, dried at 70ºC, ground and weighted. The organic N was determined in LAC dry matter. Three statistical procedures were used to calculate critical N values. There were accentuated discrepancies for critical values of N indices obtained with plants grown in soil and nutrient solution as well as for different statistical procedures. Critical values of nitrogen indices at all situations are presented.

Perturbations of Critical Values in Nonsmooth Critical Point Theory

* Supported by Ministero dell’Università e della Ricerca Scientifica e Tecnologica (40% – 1993). ** Supported by Ministero dell’Università e della Ricerca Scientifica e Tecnologica (40% – 1993).

Portable penetrometer for agricultural soil: sensitivity test to identify critical compaction depth

To express the negative effects of soil compaction, some researchers use critical values for soil mechanical strength that severely impair plant growth. The aim of this study was to identify this critical compaction depth, to test the functionality of a new, portable penetrometer developed from a spring dynamometer, and compare it to an electronic penetrometer traditionally used in compaction studies of agricultural soils. Three soils with distinct texture were conventionally tilled using a disk plow, and cultivated with different plant species. The critical soil resistance defined to establish critical compaction depth was equal to 1.5 MPa. The results of the new equipment were similar to the electronic penetrometer, indicating its viability as a tool for assessing the soil physical conditions for plant growth.

A critical value function approach, with an application to persistent time-series

Researchers often rely on the t-statistic to make inference on parameters in statistical models. It is common practice to obtain critical values by simulation techniques. This paper proposes a novel numerical method to obtain an approximately similar test. This test rejects the null hypothesis when the test statistic islarger than a critical value function (CVF) of the data. We illustrate this procedure when regressors are highly persistent, a case in which commonly-used simulation methods encounter dificulties controlling size uniformly. Our approach works satisfactorily, controls size, and yields a test which outperforms the two other known similar tests.

Hypothesis test for changes in variance using a statistic based in P-values in a time series of normal independent observations.

The present work proposes a Hypothesis Test to detect a shift in the variance of a series of independent normal observations using a statistic based on the p-values of the F distribution. Since the probability distribution function of this statistic is intractable, critical values were we estimated numerically through extensive simulation. A regression approach was used to simplify the quantile evaluation and extrapolation. The power of the test was simulated using Monte Carlo simulation, and the results were compared with the Chen test (1997) to prove its efficiency. Time series analysts might find the test useful to address homoscedasticity studies were at most one change might be involved.

UV-Derivative Spectrophotometric and Stability-Indicating High-Performance Liquid Chromatographic Methods for Determination of Simvastatin in Tablets

A stability-indicating high-performance liquid chromatographic (HPLC) and a second-order derivative spectrophotometric (UVDS) analytical methods were validated and compared for determination of simvastatin in tablets. The HPLC method was performed with isocratic elution using a C18 column and a mobile phase composed of methanol:acetonitrile:water (60:20:20, v/v/v) at a flow rate of 1.0 ml/min. The detection was made at 239 nm. In UVDS method, methanol and water were used in first dilution and distilled water was used in consecutive dilutions and as background. The second-order derivative signal measurement was taken at 255 nm. Analytical curves showed correlation coefficients > 0.999 for both methods. The quantitation limits (QL) were 2.41 mu g/ml for HPLC and 0.45 mu g/ml for UVDS, respectively. Intra and inter-day relative standard deviations were < 2.0 %. Statistical analysis with t- and F-tests are not exceeding their critical values demonstrating that there is no significant difference between the two methods at 95 % confidence level.

Effect of pH on Na induced Ca deficiency

Although it is well known that high Na concentrations induce Ca deficiency in acidic conditions, the effect of high pH on this competitive mechanism is not so well understood. The effect of Ca activity ratio (CAR) and pH on the Ca uptake of mungbeans (Vigna radiata (L.) Wilczek cv. Emerald) and Rhodes grass (Chloris gayana cv. Pioneer) in Na dominated solution cultures and in soil was investigated. Changes in pH in the alkaline range were shown not to affect the critical CAR of 0.024 (corresponding to 90 % relative root length) for mungbeans grown in solution culture. Results from soil grown mungbeans confirmed those from solution culture, with a critical CAR of 0.025. A critical CAR of 0.034 was also established for soil grown Rhodes grass. The similarity of critical values established for mungbeans and Rhodes grass in solution culture and soil justifies the use of both solution culture and soil solution measurement as techniques for studying plant growth and limitations across plant species.

Alterações fisiológicas em clones de seringueira (Hevea brasiliensis) submetidos ao deficit hídrico

Esse estudo objetivou investigar, em regime de casa de vegetação, o desempenho fisiológico de duas cultivares jovens e enxertadas de seringueira (Hevea brasiliensis), submetidas à deficiência hídrica e posterior recuperação. Os parâmetros analisados foram o potêncial hídrico foliar (ψw), taxa de sobrevivência e crescimento após reidratação e a fluorescência transiente da clorofila a. Trinta dias após a aclimatação, o déficit hídrico foi iniciado pela supressão total da água até o potencial hídrico (ψw) atingir valores críticos (38 dias), seguido por 30 dias de reidratação. Os dois genótipos (RRIM600 e FX3864) apresentaram um comportamentos semelhantes de redução do ψw com o avanço da supressão hídrica. Entretanto, o genótipo FX3864 mostrou-se mais susceptível ao déficit hídrico comprovado por valores que demonstram deficiência no transporte de elétrons no etapa fotoquímica da fotossíntese e por uma menor taxa de sobrevivência após desidratação e menor crescimento e desenvolvimento após a reidratação. RRIM600 apresentou uma maior tolerância à imposição da supressão hídrica, confirmada pelos valores da maioria dos parâmetros analisados e pelo menor tempo necessário para sua recuperação.

Constant coefficient tests for random coefficient regression

Random coefficient regression models have been applied in differentfields and they constitute a unifying setup for many statisticalproblems. The nonparametric study of this model started with Beranand Hall (1992) and it has become a fruitful framework. In thispaper we propose and study statistics for testing a basic hypothesisconcerning this model: the constancy of coefficients. The asymptoticbehavior of the statistics is investigated and bootstrapapproximations are used in order to determine the critical values ofthe test statistics. A simulation study illustrates the performanceof the proposals.

Exact and approximate stepdown methods for multiple hypothesis testing

Consider the problem of testing k hypotheses simultaneously. In this paper,we discuss finite and large sample theory of stepdown methods that providecontrol of the familywise error rate (FWE). In order to improve upon theBonferroni method or Holm's (1979) stepdown method, Westfall and Young(1993) make eective use of resampling to construct stepdown methods thatimplicitly estimate the dependence structure of the test statistics. However,their methods depend on an assumption called subset pivotality. The goalof this paper is to construct general stepdown methods that do not requiresuch an assumption. In order to accomplish this, we take a close look atwhat makes stepdown procedures work, and a key component is a monotonicityrequirement of critical values. By imposing such monotonicity on estimatedcritical values (which is not an assumption on the model but an assumptionon the method), it is demonstrated that the problem of constructing a validmultiple test procedure which controls the FWE can be reduced to the problemof contructing a single test which controls the usual probability of a Type 1error. This reduction allows us to draw upon an enormous resamplingliterature as a general means of test contruction.

Testing for hysteresis in unemployment in OECD countries: new evidence using stationarity panel tests with breaks

This paper tests hysteresis effects in unemployment using panel data for 19 OECD countries covering the period 1956-2001. The tests exploit the cross-section variations of the series, and additionally, allow for a diferent number of endogenous breakpoints in the unemployment series. The critical values are simulated based on our specific panel sizes and time periods. The findings stress the importance of accounting for exogenous shocks in the series and give support to the natural-rate hypothesis of unemployment for the majority of the countries analyzed

Testing for hysteresis in unemployment in OECD countries: new evidence using stationarity panel tests with breaks

This paper tests hysteresis effects in unemployment using panel data for 19 OECD countries covering the period 1956-2001. The tests exploit the cross-section variations of the series, and additionally, allow for a diferent number of endogenous breakpoints in the unemployment series. The critical values are simulated based on our specific panel sizes and time periods. The findings stress the importance of accounting for exogenous shocks in the series and give support to the natural-rate hypothesis of unemployment for the majority of the countries analyzed