Trend tests: a tendency to resampling

Trend analysis is an important problem in time series. Many studies have been developed to investigate this issue, with special attention to its application to environmental and hydrological time series. The presence of autocorrelation and missing observations affects the significance and power of trend tests, parametric or non-parametric. This study assesses the performance of two trend tests, t-test and the Mann-Kendall through an appropriate resampling technique. A new procedure based onsubsampling is proposed in order to assure good statistical properties of these tests. A comparison was established between this new approach and others already developed, such as bootstrap-based tests. In order to evaluate the performance of the new method, a simulation study is conducted considering a set of underlying slopes, different values of autocorrelation and different fractions of randomly missing data. The order of autocorrelation structure is estimated by the best fitting model obtained through the Akaike information criterion. Inspection of the data to detect missing observations is required, before applying the trend tests. In case of missing observations, their estimation and replace is performed by an imputation method available in software.info:eu-repo/semantics/publishedVersio

Untenable nonstationarity: An assessment of the fitness for purpose of trend tests in hydrology

The detection and attribution of long-term patterns in hydrological time series have been important research topics for decades. A significant portion of the literature regards such patterns as ‘deterministic components’ or ‘trends’ even though the complexity of hydrological systems does not allow easy deterministic explanations and attributions. Consequently, trend estimation techniques have been developed to make and justify statements about tendencies in the historical data, which are often used to predict future events. Testing trend hypothesis on observed time series is widespread in the hydro-meteorological literature mainly due to the interest in detecting consequences of human activities on the hydrological cycle. This analysis usually relies on the application of some null hypothesis significance tests (NHSTs) for slowly-varying and/or abrupt changes, such as Mann-Kendall, Pettitt, or similar, to summary statistics of hydrological time series (e.g., annual averages, maxima, minima, etc.). However, the reliability of this application has seldom been explored in detail. This paper discusses misuse, misinterpretation, and logical flaws of NHST for trends in the analysis of hydrological data from three different points of view: historic-logical, semantic-epistemological, and practical. Based on a review of NHST rationale, and basic statistical definitions of stationarity, nonstationarity, and ergodicity, we show that even if the empirical estimation of trends in hydrological time series is always feasible from a numerical point of view, it is uninformative and does not allow the inference of nonstationarity without assuming a priori additional information on the underlying stochastic process, according to deductive reasoning. This prevents the use of trend NHST outcomes to support nonstationary frequency analysis and modeling. We also show that the correlation structures characterizing hydrological time series might easily be underestimated, further compromising the attempt to draw conclusions about trends spanning the period of records. Moreover, even though adjusting procedures accounting for correlation have been developed, some of them are insufficient or are applied only to some tests, while some others are theoretically flawed but still widely applied. In particular, using 250 unimpacted stream flow time series across the conterminous United States (CONUS), we show that the test results can dramatically change if the sequences of annual values are reproduced starting from daily stream flow records, whose larger sizes enable a more reliable assessment of the correlation structures

ASSESSING THE RELATIONSHIP BETWEEN MARKET FACTORS AND REGIONAL PRICE DYNAMICS IN U.S. CATTLE MARKETS

Regional live cattle prices are decomposed into two components: (a) a trend common to all regional cattle price series and (b) regional deviations or price dynamics around that trend. Tests are developed to determine if market factors are related to the regional price deviations around a common trend. Slaughter volume, distance between a market and the next closest, and forward contract deliveries are significantly related to price deviations from the estimated common trend.Livestock Production/Industries,

Robust trend tests for genetic association in case-control studies using family data

We studied a trend test for genetic association between disease and the number of risk alleles using case-control data. When the data are sampled from families, this trend test can be adjusted to take into account the correlations among family members in complex pedigrees. However, the test depends on the scores based on the underlying genetic model and thus it may have substantial loss of power when the model is misspecified. Since the mode of inheritance will be unknown for complex diseases, we have developed two robust trend tests for case-control studies using family data. These robust tests have relatively good power for a class of possible genetic models. The trend tests and robust trend tests were applied to a dataset of Genetic Analysis Workshop 14 from the Collaborative Study on the Genetics of Alcoholism

Trend tests for the evaluation of exposure-response relationships in epidemiological exposure studies

One possibility for the statistical evaluation of trends in epidemiological exposure studies is the use of a trend test for data organized in a 2 × k contingency table. Commonly, the exposure data are naturally grouped or continuous exposure data are appropriately categorized. The trend test should be sensitive to any shape of the exposure-response relationship. Commonly, a global trend test only determines whether there is a trend or not. Once a trend is seen it is important to identify the likely shape of the exposure-response relationship. This paper introduces a best contrast approach and an alternative approach based on order-restricted information criteria for the model selection of a particular exposure-response relationship. For the simple change point alternative H1 : 1 =.= q <q+1 =. = k an appropriate approach for the identification of a global trend as well as for the most likely shape of that exposure-response relationship is characterized by simulation and demonstrated for real data examples. Power and simultaneous confidence intervals can be estimated as well. If the conditions are fulfilled to transform the exposure-response data into a 2 × k table, a simple approach for identification of a global trend and its elementary shape is available for epidemiologists

The impact of the initial condition on robust tests for a linear trend

This paper examines the behaviour of some recently proposed robust (to the order of integration of the data) tests for the presence of a deterministic linear trend in a univariate times series in situations where the magnitude of the initial condition of the series is non-negligible. We demonstrate that the asymptotic size and/or local power properties of these tests are extremely sensitive to the initial condition. Straightforward modifications to the trend tests are suggested, based around the use of trimmed data, which are demonstrated to greatly reduce this sensitivity.Trend tests; initial condition; asymptotic local power

Robust Tests in Genome-Wide Scans under Incomplete Linkage Disequilibrium

Under complete linkage disequilibrium (LD), robust tests often have greater power than Pearson's chi-square test and trend tests for the analysis of case-control genetic association studies. Robust statistics have been used in candidate-gene and genome-wide association studies (GWAS) when the genetic model is unknown. We consider here a more general incomplete LD model, and examine the impact of penetrances at the marker locus when the genetic models are defined at the disease locus. Robust statistics are then reviewed and their efficiency and robustness are compared through simulations in GWAS of 300,000 markers under the incomplete LD model. Applications of several robust tests to the Wellcome Trust Case-Control Consortium [Nature 447 (2007) 661--678] are presented.Comment: Published in at http://dx.doi.org/10.1214/09-STS314 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

A simple, robust and powerful test of the trend hypothesis

In this paper we develop a simple test procedure for a linear trend which does not require knowledge of the form of serial correlation in the data, is robust to strong serial correlation, and has a standard normal limiting null distribution under either I(0) or I(1) shocks. In contrast to other available robust linear trend tests, our proposed test achieves the Gaussian asymptotic local power envelope in both the I(0) and I(1) cases. For near- I(1) errors our proposed procedure is conservative and a modification for this situation is suggested. An estimator of the trend parameter, together with an associated confidence interval, which is asymptotically efficient, again regardless of whether the shocks are I(0) or I(1), is also provided.Linear trend; strong serial correlation; asymptotic normality; power enveloope; unit root tests; stationarity tests

Reporting rates of assaults on licensed premises by licensed premises staff: 2012-2013

There is no evidence licensed premises are systematically concealing assaults in a bid to avoid losing their liquor license or to avoid having restrictions imposed on their trading hours, according to this report. Aim To determine whether there has been any change in the rate of reporting of assaults on licensed premises by staff in 2012-2013 in both the top 100 and unranked licensed premises for assaults. This paper also briefly examines the characteristics of both offenders and victims of assaults on licensed premises. Method A random sample of 800 assaults (400 from top 100 premises and 400 from unranked premises) from January 2012 to December 2013 were tabulated and coded for relevant information. SPSS was then used to determine proportions of victims and offenders in various categories and any trends in reporting. Trend tests were carried out using χ2. Results There was no statistically significant trend in the proportion of reports of assaults emanating from staff on licensed premises