scholarly journals Asymptotic Properties of MSE Estimate for the False Discovery Rate Controlling Procedures in Multiple Hypothesis Testing

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1913
Author(s):  
Sofia Palionnaya ◽  
Oleg Shestakov
Keyword(s):  
Experimental Data ◽  
False Discovery Rate ◽  
Mean Square Error ◽  
Asymptotic Properties ◽  
Multiple Hypothesis Testing ◽  
Mean Square ◽  
Practical Applications ◽  
False Discovery ◽  
Wide Range ◽  
The Mean

Problems with analyzing and processing high-dimensional random vectors arise in a wide variety of areas. Important practical tasks are economical representation, searching for significant features, and removal of insignificant (noise) features. These tasks are fundamentally important for a wide class of practical applications, such as genetic chain analysis, encephalography, spectrography, video and audio processing, and a number of others. Current research in this area includes a wide range of papers devoted to various filtering methods based on the sparse representation of the obtained experimental data and statistical procedures for their processing. One of the most popular approaches to constructing statistical estimates of regularities in experimental data is the procedure of multiple testing of hypotheses about the significance of observations. In this paper, we consider a procedure based on the false discovery rate (FDR) measure that controls the expected percentage of false rejections of the null hypothesis. We analyze the asymptotic properties of the mean-square error estimate for this procedure and prove the statements about the asymptotic normality of this estimate. The obtained results make it possible to construct asymptotic confidence intervals for the mean-square error of the FDR method using only the observed data.

On Asymptotic Prediction Problems for Autoregressive Models with Explosive and Other Roots

1989 ◽  
Vol 38 (1-2) ◽  
pp. 43-56 ◽  
Author(s):  
A. K. Basu ◽  
S. Sen Roy
Keyword(s):  
Mean Square Error ◽  
Asymptotic Properties ◽  
Autoregressive Process ◽  
Autoregressive Models ◽  
Mean Square ◽  
The Mean ◽  
Set Up ◽  
Prediction Problems ◽  
Dependent Error

In this paper the asymptotic properties of the estimated predictor of a k-dimensional, pth order autoregressive process with dependent error variables and a general set-up of the roots have been considered. An expression for the mean-square-error of the estimated predictor has also been obtained.

The drag of a compressible turbulent boundary layer on a smooth flat plate with and without heat transfer

1964 ◽  
Vol 18 (1) ◽  
pp. 117-143 ◽  
Author(s):  
D. B. Spalding ◽  
S. W. Chi
Keyword(s):  
Experimental Data ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Mixing Length ◽  
Mean Square ◽  
Temperature Ratio ◽  
Wide Range ◽  
Mixing Length Theory ◽  
Meansquare Error

The theoretical treatments given by earlier authors are classified, reviewed and where necessary extended; then the predictions of twenty of these theories are evaluated and compared with all available experimental data, the root-meansquare error being computed for each theory. The theory of van Driest-II gives the lowest root-mean-square error (11.0%).A new calculation procedure is developed from the postulate that a unique relation exists betweencfFcandRFRwherecfis the drag coefficient,Ris the Reynolds number, andFcandFRare functions of Mach number and temperature ratio alone. The experimental data are found to be too scanty for bothFcandFRto be deduced empirically, soFcis calculated by means of mixing-length theory andFRis found semi-empirically. Tables and charts of values ofFcandFRare presented for a wide range ofMGandTS/TG. When compared with all experimental data, the predictions of the new procedure give a root-mean-square error of 9.9%.

scholarly journals Coding of Time-Varying Signals in Spike Trains of Integrate-and-Fire Neurons with Random Threshold

1996 ◽  
Vol 8 (1) ◽  
pp. 44-66 ◽  
Author(s):  
Fabrizio Gabbiani ◽  
Christof Koch
Keyword(s):  
Experimental Data ◽  
Information Transmission ◽  
Firing Rate ◽  
Mean Square Error ◽  
Model Neuron ◽  
Correlation Technique ◽  
Time Varying ◽  
Mean Square ◽  
Closed Expression ◽  
The Mean

Recently, methods of statistical estimation theory have been applied by Bialek and collaborators (1991) to reconstruct time-varying velocity signals and to investigate the processing of visual information by a directionally selective motion detector in the fly's visual system, the H1 cell. We summarize here our theoretical results obtained by studying these reconstructions starting from a simple model of H1 based on experimental data. Under additional technical assumptions, we derive a closed expression for the Fourier transform of the optimal reconstruction filter in terms of the statistics of the stimulus and the characteristics of the model neuron, such as its firing rate. It is shown that linear reconstruction filters will change in a nontrivial way if the statistics of the signal or the mean firing rate of the cell changes. Analytical expressions are then derived for the mean square error in the reconstructions and the lower bound on the rate of information transmission that was estimated experimentally by Bialek et al. (1991). For plausible values of the parameters, the model is in qualitative agreement with experimental data. We show that the rate of information transmission and mean square error represent different measures of the reconstructions: in particular, satisfactory reconstructions in terms of the mean square error can be achieved only using stimuli that are matched to the properties of the recorded cell. Finally, it is shown that at least for the class of models presented here, reconstruction methods can be understood as a generalization of the more familiar reverse-correlation technique.

A Design Program For The Linear Equalizer That Minimizes The Mean Square Error

1985 ◽  
pp. 14-25
Author(s):  
Mohamad Ashraf
Keyword(s):  
Mean Square Error ◽  
Linear Time ◽  
Digital Signal ◽  
Mean Square ◽  
Linear Time Invariant ◽  
Design Program ◽  
Wide Range ◽  
Linear Equalizer ◽  
The Mean ◽  
Common Signal

A design program with detailed illustrative example, for the linear equalizer that minimizes the mean square error due to intersymbol interference in its output signal, is presented. The results are evaluated for many types of distortion channels which have been selected from a wide range of common signal distortions.This includes the various combinations of amplitude and phase distortions.A synchroneous serial digital baseband signal is assumed throughout. The digital signal is transmitted over the linear time invariant baseband channel whose impulse response is known. The practical imple mentation of the filters and the techniques on the automatic or adaptive adjustment of the equalizer taps are not considered. The aim of the paper is to show the basic principles of the linear equalizer that minimizes the mean square error, with the aid of the design program and the example.The design of the linear equalizer is based on a statistical criterior in time domain and the study is confined to simple transversal equalizers whose tap gains do not vary except in response to a change in a channel.

The Bordeaux Automatic Meridian Circle

1978 ◽  
Vol 48 ◽  
pp. 227-228
Author(s):  
Y. Requième
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Meridian Circle ◽  
The Mean ◽  
Full Automation

In spite of important delays in the initial planning, the full automation of the Bordeaux meridian circle is progressing well and will be ready for regular observations by the middle of the next year. It is expected that the mean square error for one observation will be about ±0.”10 in the two coordinates for declinations up to 87°.

Limit tolerances for sums of measurement errors

2018 ◽  
Vol 934 (4) ◽  
pp. 59-62
Author(s):  
V.I. Salnikov
Keyword(s):  
Normal Distribution ◽  
Mean Square Error ◽  
Gaussian Distribution ◽  
Measurement Errors ◽  
Theory And Practice ◽  
Mean Square ◽  
The Mean ◽  
Limiting Values ◽  
Limiting Value

The question of calculating the limiting values of residuals in geodesic constructions is considered in the case when the limiting value for measurement errors is assumed equal to 3m, ie ∆рred = 3m, where m is the mean square error of the measurement. Larger errors are rejected. At present, the limiting value for the residual is calculated by the formula 3m√n, where n is the number of measurements. The article draws attention to two contradictions between theory and practice arising from the use of this formula. First, the formula is derived from the classical law of the normal Gaussian distribution, and it is applied to the truncated law of the normal distribution. And, secondly, as shown in [1], when ∆рred = 2m, the sums of errors naturally take the value equal to ?pred, after which the number of errors in the sum starts anew. This article establishes its validity for ∆рred = 3m. A table of comparative values of the tolerances valid and recommended for more stringent ones is given. The article gives a graph of applied and recommended tolerances for ∆рred = 3m.

scholarly journals IndoorPlant: A Model for Intelligent Services in Indoor Agriculture Based on Context Histories

Sensors ◽  
2021 ◽  
Vol 21 (5) ◽  
pp. 1631
Author(s):  
Bruno Guilherme Martini ◽  
Gilson Augusto Helfer ◽  
Jorge Luis Victória Barbosa ◽  
Regina Célia Espinosa Modolo ◽  
Marcio Rosa da Silva ◽  
...  
Keyword(s):  
Technology Acceptance ◽  
Mean Square Error ◽  
Ease Of Use ◽  
Coefficient Of Determination ◽  
Square Root ◽  
Mean Square ◽  
Use Context ◽  
The Mean ◽  
Acceptance Model ◽  
The Internet Of Things

The application of ubiquitous computing has increased in recent years, especially due to the development of technologies such as mobile computing, more accurate sensors, and specific protocols for the Internet of Things (IoT). One of the trends in this area of research is the use of context awareness. In agriculture, the context involves the environment, for example, the conditions found inside a greenhouse. Recently, a series of studies have proposed the use of sensors to monitor production and/or the use of cameras to obtain information about cultivation, providing data, reminders, and alerts to farmers. This article proposes a computational model for indoor agriculture called IndoorPlant. The model uses the analysis of context histories to provide intelligent generic services, such as predicting productivity, indicating problems that cultivation may suffer, and giving suggestions for improvements in greenhouse parameters. IndoorPlant was tested in three scenarios of the daily life of farmers with hydroponic production data that were obtained during seven months of cultivation of radicchio, lettuce, and arugula. Finally, the article presents the results obtained through intelligent services that use context histories. The scenarios used services to recommend improvements in cultivation, profiles and, finally, prediction of the cultivation time of radicchio, lettuce, and arugula using the partial least squares (PLS) regression technique. The prediction results were relevant since the following values were obtained: 0.96 (R2, coefficient of determination), 1.06 (RMSEC, square root of the mean square error of calibration), and 1.94 (RMSECV, square root of the mean square error of cross validation) for radicchio; 0.95 (R2), 1.37 (RMSEC), and 3.31 (RMSECV) for lettuce; 0.93 (R2), 1.10 (RMSEC), and 1.89 (RMSECV) for arugula. Eight farmers with different functions on the farm filled out a survey based on the technology acceptance model (TAM). The results showed 92% acceptance regarding utility and 98% acceptance for ease of use.

scholarly journals P14.21 Tehila Kaisman-Elbaz MD/PhD

2019 ◽  
Vol 21 (Supplement_3) ◽  
pp. iii71-iii71
Author(s):  
T Kaisman-Elbaz ◽  
Y Elbaz ◽  
V Merkin ◽  
L Dym ◽  
A Noy ◽  
...  
Keyword(s):  
Overall Survival ◽  
Multivariate Analysis ◽  
False Discovery Rate ◽  
Medical Center ◽  
Tumor Resection ◽  
Multiple Hypothesis Testing ◽  
Hemoglobin Level ◽  
Distribution Width ◽  
False Discovery ◽  
Dismal Prognosis

Abstract BACKGROUND Glioblastoma is known for its dismal prognosis though its dependency on patients’ readily available RBCs parameters defining the patient’s anemic status such as hemoglobin level and Red blood cells distribution Width (RDW) is not fully established. Several works demonstrated a connection between low hemoglobin level or high RDW values to overall glioblastoma patient’s survival, but in other works, a clear connection was not found. This study addresses this unclarity. MATERIAL AND METHODS In this work, 170 glioblastoma patients, diagnosed and treated in Soroka University Medical Center (SUMC) in the last 12 years were retrospectively inspected for their survival dependency on pre-operative RBCs parameters using multivariate analysis followed by false discovery rate procedure due to the multiple hypothesis testing. A survival stratification tree and Kaplan-Meier survival curves that indicate the patient’s prognosis according to these parameters were prepared. RESULTS Beside KPS>70 and tumor resection supplemented by oncological treatment, age<70 (HR=0.4, 95% CI 0.24–0.65), low hemoglobin level (HR=1.79, 95% CI 1.06–2.99) and RDW<14% (HR=0.57, 95% CI 0.37–0.88) were found to be prognostic to patients’ overall survival in multivariate analysis, accounting for false discovery rate of less than 5%. CONCLUSION A survival stratification highlighted a non-anemic subgroup of nearly 30% of the cohort’s patients whose median overall survival was 21.1 months (95% CI 16.2–27.2) - higher than the average Stupp protocol overall median survival of about 15 months. A discussion on the beneficial or detrimental effect of RBCs parameters on glioblastoma prognosis and its possible causes is given.

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