Number Of Subsamples Research Articles

Intelligent Compound Fault Diagnosis of Roller Bearings Based on Deep Graph Convolutional Network.

The high correlation between rolling bearing composite faults and single fault samples is prone to misclassification. Therefore, this paper proposes a rolling bearing composite fault diagnosis method based on a deep graph convolutional network. First, the acquired raw vibration signals are pre-processed and divided into sub-samples. Secondly, a number of sub-samples in different health states are constructed as graph-structured data, divided into a training set and a test set. Finally, the training set is used as input to a deep graph convolutional neural network (DGCN) model, which is trained to determine the optimal structure and parameters of the network. A test set verifies the feasibility and effectiveness of the network. The experimental result shows that the DGCN can effectively identify compound faults in rolling bearings, which provides a new approach for the identification of compound faults in bearings.

Optimal Subsampling Bootstrap for Massive Data

The bootstrap is a widely used procedure for statistical inference because of its simplicity and attractive statistical properties. However, the vanilla version of bootstrap is no longer feasible computationally for many modern massive datasets due to the need to repeatedly resample the entire data. Therefore, several improvements to the bootstrap method have been made in recent years, which assess the quality of estimators by subsampling the full dataset before resampling the subsamples. Naturally, the performance of these modern subsampling methods is influenced by tuning parameters such as the size of subsamples, the number of subsamples, and the number of resamples per subsample. In this article, we develop a novel hyperparameter selection methodology for selecting these tuning parameters. Formulated as an optimization problem to find the optimal value of some measure of accuracy of an estimator subject to computational cost, our framework provides closed-form solutions for the optimal hyperparameter values for subsampled bootstrap, subsampled double bootstrap and bag of little bootstraps, at no or little extra time cost. Using the mean square errors as a proxy of the accuracy measure, we apply our methodology to study, compare and improve the performance of these modern versions of bootstrap developed for massive data through numerical study. The results are promising.

On the asymptotic properties of a bagging estimator with a massive dataset

Bagging is a useful method for large‐scale statistical analysis, especially when the computing resources are very limited. We study here the asymptotic properties of bagging estimators for ‐estimation problems but with massive datasets. We theoretically prove that the resulting estimator is consistent and asymptotically normal under appropriate conditions. The results show that the bagging estimator can achieve the optimal statistical efficiency, provided that the bagging subsample size and the number of subsamples are sufficiently large. Moreover, we derive a variance estimator for valid asymptotic inference. All theoretical findings are further verified by extensive simulation studies. Finally, we apply the bagging method to the US Airline Dataset to demonstrate its practical usefulness.

A Global Meta-Analysis of Soil Salinity Prediction Integrating Satellite Remote Sensing, Soil Sampling, and Machine Learning

Despite the growing interest among researchers, satellite-based prediction of soil salinity remains highly uncertain. The improvements in prediction accuracy reported in previous studies are usually limited to a single area. We performed a meta-analysis of regional satellite-based soil salinity predictions combined with <i>in situ</i> soil sampling and machine learning. Based on <inline-formula> <tex-math notation="LaTeX">$R^{2}$ </tex-math></inline-formula> and root-mean-square error (RMSE) collected, we evaluated the effects of various features on the model accuracy and established a Bayesian network to evaluate the joint causal effect of multifeatures. Most significant differences were found in soil sampling schemes and characteristics of the study area, including the mean and variability (averaged <inline-formula> <tex-math notation="LaTeX">$R^{2}$ </tex-math></inline-formula> of 0.75 for soil sample sets with lower salinity variation and 0.62 for others) of the salinity, climate type (<inline-formula> <tex-math notation="LaTeX">$R^{2}$ </tex-math></inline-formula> of 0.64 in arid areas and 0.74 in others), soil texture (<inline-formula> <tex-math notation="LaTeX">$R^{2}$ </tex-math></inline-formula> of 0.66 in sandy areas and 0.57 in others), and the interval between sampling date and satellite data acquisition date (<inline-formula> <tex-math notation="LaTeX">$R^{2}$ </tex-math></inline-formula> of 0.53 under the condition of over 15 days and 0.65 in others). Generally, using different satellite data has limited effects on model performance among which Sentinel-2 performed better (<inline-formula> <tex-math notation="LaTeX">$R^{2} $ </tex-math></inline-formula> &#x003D; 0.72) than Landsat (<inline-formula> <tex-math notation="LaTeX">$R^{2} $ </tex-math></inline-formula> &#x003D; 0.66). The sampling of subsamples for each sample should focus on their subpixel-scale spatial heterogeneity across satellite data rather than the number of subsamples. It is also necessary to select appropriate vegetation and salinity indices for different satellite data under different vegetation conditions. Among algorithms, random forests (<inline-formula> <tex-math notation="LaTeX">$R^{2} $ </tex-math></inline-formula> &#x003D; 0.70) and support vector machines (<inline-formula> <tex-math notation="LaTeX">$R^{2} $ </tex-math></inline-formula> &#x003D; 0.71) performed best.

SPATIAL VARIABILITY OF SOIL APPARENT ELECTRICAL CONDUCTIVITY - EFFECT OF THE NUMBER OF SUBSAMPLES

Soil apparent electrical conductivity (ECa) sensors have been used to detect spatial variability because they correlate with soil attributes. Studies with soil attributes have shown that the number of subsamples and sampling points influences mapping. However, there are no studies that investigated the influence of sampling or subsampling density on ECa maps. Therefore, this study verified the influence of ECa readings per sample point on the semivariance and kriging analysis. The data were collected from an area (2.5 ha) of coffee plants. One hundred sampling points were measured considering 20 readings each. 1, 5, 10, 15, and 20 sample point readings were tested. The influence of the number of readings per sampling point on the ECa mapping was determined using linear regression analysis at a significance level of 5%. The results obtained showed that ECa readings per sampling point significantly influence ECa maps. In addition, they demonstrated that reducing the number of readings per sampling point increases prediction errors by kriging. Thus, ECa maps determined with the highest readings per sampling point were mostly accurate.

A Robust Moving Total Least-Squares Fitting Method for Measurement Data

The moving least-squares (MLS) and moving total least-squares (MTLS) methods have been widely used for fitting measurement data. They can be used to achieve good approximation properties. However, these two methods are susceptible to outliers due to the way of determining local approximate coefficients, which leads to distorted estimation. To reduce the influence of outliers and random errors of all variables without adding small weights or setting the threshold subjectively, we present a robust MTLS (RMTLS) method, in which an improved least trimmed squares (ILTS) method is used for obtaining the local approximants of the influence domain. The ILTS method divides the nodes in the influence domain into a certain number of subsamples, achieves the local approximants by the total least-squares (TLS) method with compact support weight function, and trims the node with the largest orthogonal residual from each subsample, respectively. The remaining nodes from the subsamples are used to determine the local coefficients. The measurement experiment and numerical simulations are provided to demonstrate the robustness and accuracy of the presented method in comparison with the MLS and MTLS methods.

Biogeographical and analytical implications of temporal variability in geographically diverse soundscapes

Unprecedented rates of biodiversity loss and intensifying human attempts to rectify the biodiversity crisis have heightened the need for standardized, large-scale, long-duration biodiversity monitoring at fine temporal resolution. While some innovative technologies such as passive acoustic monitoring are well suited for such monitoring challenges, many questions remain as to how they should be scaled out and optimally implemented across ecosystems.Our research questions center on temporal sampling regimes—how frequently and how long one should collect data to represent biodiversity conditions over a given timeframe. Addressing this concern in the context of passive acoustic monitoring, we investigated whether temporal soundscape variability—the characteristic short-term acoustic change in an environment—is consistent across ecosystems and times of day, and we considered how various temporal subsampling schemes affect the representativeness of resultant acoustic index values, relative to continuous sampling. We quantified soundscape variability at eight sites across four continents based on temporal autocorrelation ranges and standard deviations of acoustic index values, and we created a heuristic model to classify types of soundscape variability based on those two variables.Drawing on values derived from three distinct acoustic indices, we found that the characteristic temporal variability of soundscapes varied between sites and times of day (dawn, daytime, dusk, and nighttime). Some sites exhibited little difference in variability between times of day whereas other sites exhibited greater within-site differences between times of day than many inter-site differences. Daytime soundscapes generally tended to exhibit more temporal variability than nighttime soundscapes.We also compared potential subsampling schemes that could be advantageous in terms of power, data storage, and data analysis costs by modeling subsample error as a function of total analysis time and number of subsamples within a larger block of time. Greater numbers of evenly distributed subdivisions drastically increased the representativeness of a sampling scheme, while increases in subsample duration yielded fairly minimal gains in representativeness between 33 and 67% of the full time one wishes to represent. Generally, our results show that for a long-term, fine temporal resolution monitoring program, one should record in evenly distributed durations at least as short as 1 min while only recording up to a third of the time one wishes to represent. While more continuous monitoring can be advantageous and necessary in many cases, current economic and logistical limitations in power, data storage, and analysis capabilities will often warrant optimized subsampling designs.

Biogeographical and analytical implications of temporal variability in geographically diverse soundscapes

• Continuous soundscape recordings were made in eight ecosystems on four continents. • Temporal variability of soundscapes was quantified using two distinct measures. • Daytime exhibited high temporal variability relative to dusk and nighttime. • Increasing evenness of subsampling distribution reduces error in representation. • Marginal precision gains diminish substantially beyond 1/3 recording time. Unprecedented rates of biodiversity loss and intensifying human attempts to rectify the biodiversity crisis have heightened the need for standardized, large-scale, long-duration biodiversity monitoring at fine temporal resolution. While some innovative technologies such as passive acoustic monitoring are well suited for such monitoring challenges, many questions remain as to how they should be scaled out and optimally implemented across ecosystems. Our research questions center on temporal sampling regimes—how frequently and how long one should collect data to represent biodiversity conditions over a given timeframe. Addressing this concern in the context of passive acoustic monitoring, we investigated whether temporal soundscape variability—the characteristic short-term acoustic change in an environment—is consistent across ecosystems and times of day, and we considered how various temporal subsampling schemes affect the representativeness of resultant acoustic index values, relative to continuous sampling. We quantified soundscape variability at eight sites across four continents based on temporal autocorrelation ranges and standard deviations of acoustic index values, and we created a heuristic model to classify types of soundscape variability based on those two variables. Drawing on values derived from three distinct acoustic indices, we found that the characteristic temporal variability of soundscapes varied between sites and times of day (dawn, daytime, dusk, and nighttime). Some sites exhibited little difference in variability between times of day whereas other sites exhibited greater within-site differences between times of day than many inter-site differences. Daytime soundscapes generally tended to exhibit more temporal variability than nighttime soundscapes. We also compared potential subsampling schemes that could be advantageous in terms of power, data storage, and data analysis costs by modeling subsample error as a function of total analysis time and number of subsamples within a larger block of time. Greater numbers of evenly distributed subdivisions drastically increased the representativeness of a sampling scheme, while increases in subsample duration yielded fairly minimal gains in representativeness between 33 and 67% of the full time one wishes to represent. Generally, our results show that for a long-term, fine temporal resolution monitoring program, one should record in evenly distributed durations at least as short as 1 min while only recording up to a third of the time one wishes to represent. While more continuous monitoring can be advantageous and necessary in many cases, current economic and logistical limitations in power, data storage, and analysis capabilities will often warrant optimized subsampling designs.

A comparison of two methods to assess apparent total tract digestibility of nutrients in dogs

ABSTRACTThe apparent total tract digestibility (ATTD) of nutrients can be assessed by total collection of faeces (TC), which is the reference method, or by the indicator method (IM). Little information is available on proper faecal sampling methodologies for IM in canines to obtain results comparable to TC. The objective of this study was to determine the minimum number of sub-samples required for the IM to make it comparable with TC. A total of 11 adult male dogs were individually housed in metabolism cages. Dogs had access to a grass yard to facilitate defaecation. Faecal sub-samples (1/day) were taken from the daily faecal output to prepare the pooled samples for IM, obtaining cumulative sample combinations of 3 (IM3), 4 (IM4), 5 (IM5), 6 (IM6) and 7 d (IM7). Digestibility of dry matter, gross energy, crude protein and crude fibre was similar between TC and IM5, IM6 and IM7 (p > 0.05). The IM7 presented the greatest statistical similarity with TC. Nevertheless, IM was not a good predictor of crude fibre digestibility. In conclusion, IM can replace the TC method in dogs to evaluate ATTD of several nutritional fractions as long as the composite sample is collected during seven consecutive days. For estimation of fibre digestibility by IM, longer collection periods are probably required.

A measurement method of batch solution concentration based on normalized compressed sensing

Measuring large batches of solution concentrations is a cumbersome task that is time consuming and involves many reagents. Determining how to improve the measurement efficiency of batch concentrations is an urgent problem to be solved. This paper introduces an efficient method for the measurement of batch solution concentrations based on normalized compressed sensing. The method is based on the sparsity of natural signals and can reconstruct the original batch concentration signals with a high level of accuracy while taking fewer measurements. The proposed method extracts subsamples from the original samples according to a sampling matrix; the number of subsamples can be much smaller than the original number of samples. Then the solution concentration of the original samples can be reconstructed by measuring the subsamples. The specific process includes sparse signal representation, non-related observation, and nonlinear optimization reconstruction. Compared with the traditional measurement method, the proposed method is demonstrably superior for the measurement of batch solution concentrations; satisfactory batch solution concentration distribution results can be obtained with a number of measurements that is much smaller than the number of samples. The proposed method will greatly reduce the time and cost of measurement.

Time-varying price discovery in sovereign credit markets

We analyze time-variation of the price discovery process in sovereign debt markets. We test whether the cointegrating relationship that should tie bond and CDS spreads together holds. In addition, we investigate which (if any) of the two markets leads price discovery in a number of sub-samples. We focus on ten Eurozone countries, the UK, and the US. While for all the peripheral countries but Greece CDS and bond spreads show a long-run equilibrium relationship, this is not the case for core European countries, the UK, and the US. When cointegration fails to hold, none of the markets leads price discovery.

Lacustrine charcoal peaks provide an accurate record of surface wildfires in a North European boreal forest

We evaluated the skills of different palaeofire reconstruction techniques to reconstruct the fire history of a boreal landscape (Russian Karelia) affected by surface fires. The analysis of dated lacustrine sediments from two nearby lakes was compared with independent dendrochronological dating of fire scars, methods which have rarely been used in context of surface fires. We used two sediment sub-sampling volumes (1 and 3.5 cm3, wet volumes) and three methods of calculating the Charcoal Accumulation Rate to reconstruct fire histories: CHAR number, charcoal surface area and estimated charcoal volume. The results show that palaeofire reconstructions obtained with fossil charcoal data from lake sediments and dendrochronology are similar and complementary. Dendrochronological reconstruction of fire scars established 12 fire dates over the past 500 years, and paleo-data from lake sediments identified between 7 and 13 fire events. Several ‘false fire events’ were also recorded in the charcoal chronologies, likely because of errors associated with the estimation of the sediment accumulation rate in the unconsolidated part of the sediment. The number of replicates, that is, number of sub-samples and lakes analyzed, had an effect on the number of identified fire events, whereas no effect was seen in the variation in the analyzed sediment volume or the choice of the charcoal-based metric. Whenever possible, we suggest the use of the dendrochronological data as an independent control for the calibration of charcoal peak series, which helps provide more realistic millennia-long reconstruction of past fire activity. We also argue for the use of 1 cm3sample volume, a sampling protocol involving sampling of more than one lake, and sufficient number of intra-sample replicates to achieve skilful reconstructions of past fire activity.

Testing foliar nutritional changes in space and over time in greenhouse tomato

The aim of this trial was to study the spatial and temporal variability of the leaf nutrient concentration in tomato intensive crop under greenhouse, to know the number of sub-samples needed to be taken to obtain a representative sample and the influence by the position in the greenhouses. The experiment consisted on the selection of 20 sample points over the greenhouse with one tomato plant per sample point. One fully expanded leaf by sample point with an interval of a week were taken. Nitrogen (N), phosphorus (P), potassium (K), sulfur (S), sodium (Na), and chloride (Cl) were determined in each sample. According to these results, N, P, K, S, Cl, and Na concentration showed no variation over the time. The spatial variability of N, P, and K could be related with the light intensity and yield. The suggested number of leaf sub-sample ranging from 25 to 126 depending on nutrient.

Initial robust estimation in generalized linear models

Generalized Linear Models are routinely used in data analysis. Classical estimators are based on the maximum likelihood principle and it is well known that the presence of outliers can have a large impact on them. Several robust procedures have been presented in the literature, being redescending M-estimators the most widely accepted. Based on non-convex loss functions, these estimators need a robust initial estimate, which is often obtained by subsampling techniques. However, as the number of unknown parameters increases, the number of subsamples needed in order for this method to be robust, soon makes it infeasible. Furthermore the subsampling procedure provides a non deterministic starting point. A new method for computing a robust initial estimator is proposed. This method is deterministic and demands a relatively short computational time, even for large numbers of covariates. The proposed method is applied to M-estimators based on transformations. In addition, an iteratively reweighted least squares algorithm is proposed for the computation of the final estimates. The new methods are studied by means of Monte Carlo experiments.

Jackknife Bias Reduction in the Presence of a Near-Unit Root

This paper considers the specification and performance of jackknife estimators of the autoregressive coefficient in a model with a near-unit root. The limit distributions of sub-sample estimators that are used in the construction of the jackknife estimator are derived, and the joint moment generating function (MGF) of two components of these distributions is obtained and its properties explored. The MGF can be used to derive the weights for an optimal jackknife estimator that removes fully the first-order finite sample bias from the estimator. The resulting jackknife estimator is shown to perform well in finite samples and, with a suitable choice of the number of sub-samples, is shown to reduce the overall finite sample root mean squared error, as well as bias. However, the optimal jackknife weights rely on knowledge of the near-unit root parameter and a quantity that is related to the long-run variance of the disturbance process, which are typically unknown in practice, and so, this dependence is characterised fully and a discussion provided of the issues that arise in practice in the most general settings.

&lt;b&gt;Soil penetration resistance mapping quality: effect of the number of subsamples

There is no consensus in the literature regarding how many subsamples are needed to perform accurate on-farm soil penetration resistance (SPR) mapping. Therefore, the objective of this study was to define the number of subsamples per sampling point needed to quantify the SPR. The experiment was performed in a 4.7 ha area and employed a 50 × 50 m grid system (18 sampling points). The SPR was evaluated using a digital penetrometer in two different years with 1, 2, 3, 4, 5, 6, 9, 12, and 15 subsamples per sampling point. The SPR maps produced with increasing numbers of subsamples were compared to the reference maps (15 subsamples) using the relative deviation coefficient and Pearson´s linear correlation. A reduction in the number of subsamples promoted an increase in the variability of the SPR data. Generally, the results from this study suggest the use of at least four subsamples per sampling point to achieve SPR maps with a coefficient of relative deviation less than 10% (30% maximum error per point around the mean) and significant correlation with the reference maps (15 subsamples).

Detection and isolation of Shiga-Toxin producing Escherichia coli in flour in Germany between 2014 and 2017

Official control samples of wheat and rye flour were analyzed for the presence of Shiga-toxin producing Escherichia coli (STEC) in 25 g. The detection procedure was based on enrichment in buffered peptone water and Tryptone Bile X-Glucuronide agar, followed by multiplex real-time PCR with an internal positive control. Positive samples were sub-cultured for strain isolation by a two-step procedure. In the first step, ten colonies were picked from each plate, pooled, and analyzed by real-time PCR. In addition, a bacterial material from the part with heavy growth was analyzed. If the 1st isolation attempt failed, in a second step all colonies from molecular positive plates were picked, sub-cultured, pooled and analyzed. 39% of test samples were positive by real-time PCR. STEC was isolated from 17 test samples corresponding to 19%. Molecular detection is linked to the presence of quantifiable numbers of E. coli, whereas the grain species did not have an influence. There is a non-significant correlation with some mills indicating some technological or hygienic problems in those facilities. Increasing the number of subsamples did improve the detection rate. Our findings show the frequent presence of STEC in flour in Germany.

Inference from high-frequency data: A subsampling approach

In this paper, we show how to estimate the asymptotic (conditional) covariance matrix, which appears in central limit theorems in high-frequency estimation of asset return volatility. We provide a recipe for the estimation of this matrix by subsampling; an approach that computes rescaled copies of the original statistic based on local stretches of high-frequency data, and then it studies the sampling variation of these. We show that our estimator is consistent both in frictionless markets and models with additive microstructure noise. We derive a rate of convergence for it and are also able to determine an optimal rate for its tuning parameters (e.g., the number of subsamples). Subsampling does not require an extra set of estimators to do inference, which renders it trivial to implement. As a variance–covariance matrix estimator, it has the attractive feature that it is positive semi-definite by construction. Moreover, the subsampler is to some extent automatic, as it does not exploit explicit knowledge about the structure of the asymptotic covariance. It therefore tends to adapt to the problem at hand and be robust against misspecification of the noise process. As such, this paper facilitates assessment of the sampling errors inherent in high-frequency estimation of volatility. We highlight the finite sample properties of the subsampler in a Monte Carlo study, while some initial empirical work demonstrates its use to draw feasible inference about volatility in financial markets.

Insider trading before accounting scandals

We examine insider trading in a sample of more than 500 firms involved in accounting scandals revealed by earnings-decreasing restatements, and in a control sample of non-restating firms. Managers who sell stock while earnings are misstated potentially commit two crimes, earnings manipulation and insider trading, and their selling increases investor scrutiny and the likelihood of the manipulation being revealed. We examine the purchases, sales and net sales of five groups of corporate insiders during the misstated period and a pre-misstated period, using a difference-in-differences approach. Using several measures of the level of insider trading, we estimate cross-sectional regressions that control for other determinants of the level of insider trading. For the full sample of restating firms, we find weak evidence that top managers of misstating firms sell more stock during the misstated period than during the pre-misstated period, relative to the control sample. But in a number of subsamples where insiders had greater incentives to sell before the revelation of accounting problems, we find strong evidence that top managers of restating firms sell substantially more stock during the misstated period. These findings suggest that managers' desire to sell their stockholdings at inflated prices is a motive for earnings manipulation. Our finding that insiders brazenly trade on a crime for which they are potentially culpable suggests that insider trading is more widespread in the market than has been found in the prior literature.

Inference from High-Frequency Data: A Subsampling Approach

In this paper, we show how to estimate the asymptotic (conditional) covariance matrix, which appears in central limit theorems in high-frequency estimation of asset return volatility. We provide a recipe for the estimation of this matrix by subsampling; an approach that computes rescaled copies of the original statistic based on local stretches of high-frequency data, and then it studies the sampling variation of these. We show that our estimator is consistent both in frictionless markets and models with additive microstructure noise. We derive a rate of convergence for it and are also able to determine an optimal rate for its tuning parameters (e.g., the number of subsamples). Subsampling does not require an extra set of estimators to do inference, which renders it trivial to implement. As a variance-covariance matrix estimator, it has the attractive feature that it is positive semi-definite by construction. Moreover, the subsampler is to some extent automatic, as it does not exploit explicit knowledge about the structure of the asymptotic covariance. It therefore tends to adapt to the problem at hand and be robust against misspecification of the noise process. As such, this paper facilitates assessment of the sampling errors inherent in high-frequency estimation of volatility. We highlight the finite sample properties of the subsampler in a Monte Carlo study, while some initial empirical work demonstrates its use to draw feasible inference about volatility in financial markets.