Presence Of Linear Trend Research Articles

A modified version of diagonal systematic sampling in the presence of linear trend

Systematic sampling is one of the simplest and popular methods for selecting a random sample from a finite population. The diagonal systematic sampling scheme is a type of systematic sampling design which has gained the attention of researchers during the last two decades. In this paper, a modification to the conventional diagonal systematic sampling design is proposed for use in situations where population units follow a linear trend. It is found that the proposed strategy reduces the variance of the diagonal systematic sampling thus resulting in an efficient sampling design. The mathematical conditions under which the suggested modified diagonal systematic sampling design is more precise than some of the available sampling designs are derived. With the help of a numerical illustration using milk yield data, it is shown that the proposed sampling scheme is more efficient than some of the available sampling schemes.

A framework for deriving drought indicators from the Gravity Recovery and Climate Experiment (GRACE)

Abstract. Identifying and quantifying drought in retrospective is a necessity for better understanding drought conditions and the propagation of drought through the hydrological cycle and eventually for developing forecast systems. Hydrological droughts refer to water deficits in surface and subsurface storage, and since these are difficult to monitor at larger scales, several studies have suggested exploiting total water storage data from the GRACE (Gravity Recovery and Climate Experiment) satellite gravity mission to analyze them. This has led to the development of GRACE-based drought indicators. However, it is unclear how the ubiquitous presence of climate-related or anthropogenic water storage trends found within GRACE analyses masks drought signals. Thus, this study aims to better understand how drought signals propagate through GRACE drought indicators in the presence of linear trends, constant accelerations, and GRACE-specific spatial noise. Synthetic data are constructed and existing indicators are modified to possibly improve drought detection. Our results indicate that while the choice of the indicator should be application-dependent, large differences in robustness can be observed. We found a modified, temporally accumulated version of the Zhao et al. (2017) indicator particularly robust under realistic simulations. We show that linear trends and constant accelerations seen in GRACE data tend to mask drought signals in indicators and that different spatial averaging methods required to suppress the spatially correlated GRACE noise affect the outcome. Finally, we identify and analyze two droughts in South Africa using real GRACE data and the modified indicators.

Linear Systematic Sampling with Unequal Sampling Intervals in the Presence of Linear Trend

The present paper deals with the linear systematic sampling with unequal sampling intervals in the presence of linear trend among the population values. As a result, explicit expressions for the linear systematic sample means with different random starts in a labelled population with linear trend for a pre-assigned fixed sample size and the population size together its variance are obtained. The efficiencies of the proposed linear systematic sampling with that of simple random sampling without replacement, linear systematic sampling and diagonal systematic sampling schemes are assessed algebraically and also for certain natural populations. It is observed that the proposed linear systematic sampling performs better than the sampling schemes mentioned above.

Optimal Systematic Sampling When Sample Size is Odd in the Presence of Linear Trend and Two-Way Linear Trend

In the present paper, a new sampling scheme is proposed for sample selection for odd sample size where population size is a multiple of sample size for a population characteristic having a linear or a two-way linear trend. On comparison of efficiencies of the proposed estimator with the simple random sampling without replacement, linear systematic sampling, stratified sampling and balanced systematic sampling, it is observed from theory as well as real life data, that the proposed scheme performs better.

On circular systematic sampling in the presence of linear trend

On circular systematic sampling in the presence of linear trend

Remainder modified systematic sampling in the presence of linear trend

ABSTRACTIf the population size is not a multiple of the sample size, then the usual linear systematic sampling design is unattractive, since the sample size obtained will either vary, or be constant and different to the required sample size. Only a few modified systematic sampling designs are known to deal with this problem and in the presence of linear trend, most of these designs do not provide favorable results. In this paper, a modified systematic sampling design, known as remainder modified systematic sampling (RMSS), is introduced. There are seven cases of RMSS and the results in this paper suggest that the proposed design is favorable, regardless of each case, while providing linear trend-free sampling results for three of the seven cases. To obtain linear trend-free sampling for the other cases and thus improve results, an end corrections estimator is constructed.

Circular versions of systematic sampling in the presence of linear trend

ABSTRACTIn this paper, an alternative approach was employed and derived the explicit expressions of sample mean and its variance for the circular and the diagonal circular systematic schemes since these expressions were unavailable in the existing literature. The study also found the corrected estimator of population mean and average variance under super-population model for these scheme. It further revealed that the circular systematic sampling almost performed better than that of the diagonal circular systematic sampling in both linear and auto-correlated super-population models.

Statistical properties of an estimator for the mean function of a compound cyclic Poisson process in the presence of linear trend

The problem of estimating the mean function of a compound cyclic Poisson process with linear trend is considered. An estimator of this mean function is constructed and investigated. The cyclic component of intensity function of this process is not assumed to have any parametric form, but its period is assumed to be known. The slope of the linear trend is assumed to be positive, but its value is unknown. Moreover, we consider the case when there is only a single realization of the Poisson process is observed in a bounded interval. Asymptotic bias and variance of the proposed estimator are computed, when the size of interval indefinitely expands.

Multiple-start balanced modified systematic sampling in the presence of linear trend

ABSTRACTIn this paper, we propose a sampling design termed as multiple-start balanced modified systematic sampling (MBMSS), which involves the supplementation of two or more balanced modified systematic samples, thus permitting us to obtain an unbiased estimate of the associated sampling variance. There are five cases for this design and in the presence of linear trend only one of these cases is optimal. To further improve results for the other cases, we propose an estimator that removes linear trend by applying weights to the first and last sampling units of the selected balanced modified systematic samples and is thus termed as the MBMSS with end corrections (MBMSSEC) estimator. By assuming a linear trend model averaged over a super-population model, we will compare the expected mean square errors (MSEs) of the proposed sample means, to that of simple random sampling (SRS), linear systematic sampling (LSS), stratified random sampling (STR), multiple-start linear systematic sampling (MLSS), and other modified MLSS estimators. As a result, MBMSS is optimal for one of the five possible cases, while the MBMSSEC estimator is preferred for three of the other four cases.

Modified Systematic Sampling in The Presence of Linear Trend

A new systematic sampling design called “Modified Systematic Sampling (MSS)”, proposed by [2] is more general than Linear Systematic Sampling (LSS) and Circular Systematic Sampling (CSS). In the present paper, this scheme is further extended for populations having a linear trend. Expressions for mean and variance of sample mean are obtained for the population having perfect linear trend among population values. Expression for the average variance is also obtained for super population model. Further, efficiency of MSS with respect to CSS is obtained for different sample size.

Estimation of Population Mean in the Presence of Linear Trend

The present article deals with some methods for estimation of finite populations means in the presence of linear trend among the population values. As a result, we provided a strategy for the selection of sampling interval k for the case of circular systematic sampling, which ensures better estimator for the population mean compared to other choices of the sampling interval. This has been established based on empirical studies. Further we more, applied multiple random starts methods for selecting random samples for the case of linear systematic sampling and diagonal systematic sampling schemes. We also derived the explicit expressions for the variances and their estimates. The relative performances of simple random sampling, linear systematic sampling and diagonal systematic sampling schemes with single and multiple random starts are also assessed based on numerical examples.

Circular Systematic Sampling in the Presence of Linear Trend

SYNOPTIC ABSTRACTThe present article deals with circular systematic sampling for estimation of a finite population mean in the presence of a linear trend among the population values. As a result, the optimum choice for the sampling interval kis obtained for a preassigned fixed sample size n and the population size N. Further, the explicit expression for the variance of a circular systematic sample mean is also obtained. The relative performance of the proposed circular systematic sampling with that of simple random sampling without replacement is assessed for a hypothetical population and also for some natural populations.

A Further Modification on Linear Systematic Sampling for Finite Populations

This article deals with a further modification on the selection of linear systematic sample. Consequently, the proposed method is an optimal modified linear systematic sampling. The performances of the modified linear systematic sampling are assessed with that of simple random sampling and linear systematic sampling for certain hypothetical populations, as well as for certain natural populations. As a result, it is observed that the proposed modified linear systematic sample mean performs better than the simple random sample mean and the usual systematic sample mean for estimating the population mean in the presence of linear trend among the population values. Further improvements are achieved by introducing Yates-type end corrections.

A modification on linear systematic sampling

The present paper deals with a modification on the selection of linear systematic sample, consequently the proposed method is called modified linear systematic sampling. The performances of the modified linear systematic sampling are assessed with that of simple random sampling and the linear systematic sampling for certain hypothetical populations as well as for certain natural populations. As a result, it is observed that the modified linear systematic sample mean performs better than the simple random sample mean and the usual systematic sample mean for estimating the population mean in the presence of linear trend among the population values. Further improvements are achieved by introducing Yates type end corrections. The applications of the proposed sampling scheme in constructing mating designs are also discussed with an example.

A phenomenological theory of Eulerian and Lagrangian velocity fluctuations in turbulent flows

A phenomenological theory of the fluctuations of velocity occurring in a fully developed homogeneous and isotropic turbulent flow is presented. The focus is made on the fluctuations of the spatial (Eulerian) and temporal (Lagrangian) velocity increments. The universal nature of the intermittency phenomenon as observed in experimental measurements and numerical simulations is shown to be fully taken into account by the multiscale picture proposed by the multifractal formalism, and its extensions to the dissipative scales and to the Lagrangian framework. The article is devoted to the presentation of these arguments and to their comparisons against empirical data. In particular, explicit predictions of the statistics, such as probability density functions and high order moments, of the velocity gradients and acceleration are derived. In the Eulerian framework, at a given Reynolds number, they are shown to depend on a single parameter function called the singularity spectrum and to a universal constant governing the transition between the inertial and dissipative ranges. The Lagrangian singularity spectrum compares well with its Eulerian counterpart by a transformation based on incompressibility, homogeneity and isotropy and the remaining constant is shown to be difficult to estimate on empirical data. It is finally underlined the limitations of the increment to quantify accurately the singular nature of Lagrangian velocity. This is confirmed using higher order increments unbiased by the presence of linear trends, as they are observed on velocity along a trajectory.

Variance Ratio Testing for Fractional Cointegration in Presence of Trends and Trend Breaks

Modeling fractional cointegration relationships has become a major topic in applied time series analysis as it steps back from the traditional rigid I(1)/I(0) methodology. Hence, the number of proposed tests and approaches has grown over the last decade. The aim of this paper is to study the nonparametric variance ratio approach suggested by Nielsen for the case of fractional cointegration in presence of linear trend and trend breaks. The consideration of trend breaks is very important in order to avoid spurious fractional integration, so this possibility should be regarded by practitioners. This paper proposes to calculate p-values by means of gamma distributions and gives response regressions parameters for the asymptotic moments of them. In Monte Carlo simulations this work compares the power of the approach against a Johansen type rank test suggested, which is robust against trend breaks but not fractional (co-)integration. As the approach also obtains an estimator for the cointegration space, the paper compares it with OLS estimates in simulations. As an empirical example the validity of the market expectation hypothesis is tested for monthly Treasury bill rates ranging from 1958-2011, which might have a trend break around September 1979 due to change of American monetary policy.

A Modification on Linear Systematic Sampling for Odd Sample Size

The present paper deals with a modification on the selection of linear systematic sample of odd size. Consequently the proposed method is called modified linear systematic sampling. The performances of the modified linear systematic sampling are assessed with that of simple random sampling and linear systematic sampling for certain hypothetical populations. As a result, it is observed that the modified systematic sample mean performs better than the simple random sample mean and the usual systematic sample mean for estimating the population mean in the presence of linear trend among the population values.

CONSISTENCY OF A KERNEL-TYPE ESTIMATOR OF THE INTENSITY OF THE CYCLIC POISSON PROCESS WITH THE LINEAR TREND

A consistent kernel-type nonparametric estimator of the intensity function of a cyclic Poisson process in the presence of linear trend is constructed and investigated. It is assumed that only a single realization of the Poisson process is observed in a bounded window. We prove that the proposed estimator is consistent when the size of the window in definitely expands.DOI : http://dx.doi.org/10.22342/jims.15.1.42.37-48

Linear trends in sea surface temperature of the tropical Pacific Ocean and implications for the El Niño-Southern Oscillation

A principal component decomposition of monthly sea surface temperature (SST) variability in the tropical Pacific Ocean demonstrates that nearly all of the linear trends during 1950–2010 are found in two leading patterns. The first SST pattern is strongly related to the canonical El Niño-Southern Oscillation (ENSO) pattern. The second pattern shares characteristics with the first pattern and its existence solely depends on the presence of linear trends across the tropical Pacific Ocean. The decomposition also uncovers a third pattern, often referred to as ENSO Modoki, but the linear trend is small and dataset dependent over the full 61-year record and is insignificant within each season. ENSO Modoki is also reflected in the equatorial zonal SST gradient between the Niño-4 region, located in the west-central Pacific, and the Niño-3 region in the eastern Pacific. It is only in this zonal SST gradient that a marginally significant trend arises early in the Northern Hemisphere spring (March–May) during El Niño and La Niña and also in the late summer (July–September) during El Niño. Yet these SST trends in the zonal gradient do not unequivocally represent an ENSO Modoki-like dipole because they are exclusively associated with significant positive SST trends in either the eastern or western Pacific, with no corresponding significant negative trends. Insignificant trends in the zonal SST gradient are evident during the boreal wintertime months when ENSO events typically mature. Given the presence of positive SST trends across much of the equatorial Pacific Ocean, using fixed SST anomaly thresholds to define ENSO events likely needs to be reconsidered.

Some partially sequential nonparametric tests for detecting linear trend

In the present study, we develop two nonparametric partially sequential tests for detecting possible presence of linear trend among the incoming series of observations. We assume that a sample of fixed size is available a priori from some unknown univariate continuous population and there is no sign of trend among these historical observations. Our proposed tests can be viewed as the sequential type tests for monitoring structural changes. We use partial sequential sampling schemes based on usual ranks as well as on sequential ranks. We provide detailed discussion on asymptotic studies related to the proposed tests. We compare the two tests under various situations. We also present some numerical results based on simulation studies. Proposed tests are extremely important in profit making in volatile market through Margin Trading. We illustrate the mechanism with a detailed analysis of a stock price data.