Bounds for the mean square error of reliability estimation from gamma distribution in presence of an outlier observation

A spectral density statistic obtained by averaging periodograms over overlapping time intervals is considered where the periodograms are calculated using a data window. The asymptotic mean square error of this estimate for scale parameter windows is determined and, as an example, it is shown that the use of the Tukey–Hanning window leads partially to a smaller mean square error than a window suggested by Kolmogorov and Zhurbenko. Furthermore the Tukey–Hanning window is independent of the unknown spectral density, which is not the case for the Kolmogorov–Zhurbenko window. The mean square error of this estimate is also less than the mean square error of commonly used window estimates. Finally, a central limit theorem for the estimate is established.

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On a spectral density estimate obtained by averaging periodograms

Journal of Applied Probability ◽

10.2307/3213863 ◽

1985 ◽

Vol 22 (3) ◽

pp. 598-610 ◽

Cited By ~ 13

Author(s):

Rainer Dahlhaus

Keyword(s):

Limit Theorem ◽

Spectral Density ◽

Mean Square Error ◽

Scale Parameter ◽

Mean Square ◽

Time Intervals ◽

The Mean ◽

Density Statistic ◽

Spectral Density Statistic ◽

Spectral Density Estimate

A spectral density statistic obtained by averaging periodograms over overlapping time intervals is considered where the periodograms are calculated using a data window. The asymptotic mean square error of this estimate for scale parameter windows is determined and, as an example, it is shown that the use of the Tukey–Hanning window leads partially to a smaller mean square error than a window suggested by Kolmogorov and Zhurbenko. Furthermore the Tukey–Hanning window is independent of the unknown spectral density, which is not the case for the Kolmogorov–Zhurbenko window. The mean square error of this estimate is also less than the mean square error of commonly used window estimates. Finally, a central limit theorem for the estimate is established.

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On the Estimation of Parameter of Weighted Sums of Exponential Distribution

Chinese Journal of Mathematics ◽

10.1155/2014/241964 ◽

2014 ◽

Vol 2014 ◽

pp. 1-3

Author(s):

N. Abbasi ◽

A. Namju ◽

N. Safari

Keyword(s):

Maximum Likelihood ◽

Exponential Distribution ◽

Mean Square Error ◽

Moment Method ◽

Maximum Likelihood Method ◽

Random Variable ◽

Likelihood Method ◽

Weighted Sums ◽

Mean Square ◽

The Mean

The random variable Zn,α=Y1+2αY2+⋯+nαYn, with α∈ℝ and Y1,Y2,… being independent exponentially distributed random variables with mean one, is considered. Van Leeuwaarden and Temme (2011) attempted to determine good approximation of the distribution of Zn,α. The main problem is estimating the parameter α that has the main state in applicable research. In this paper we show that estimating the parameter α by using the relation between α and mode is available. The mean square error values are obtained for estimating α by mode, moment method, and maximum likelihood method.

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On the mean-square error performance of adaptive minimum variance beamformers based on the sample covariance matrix

IEEE Transactions on Signal Processing ◽

10.1109/78.275625 ◽

1994 ◽

Vol 42 (2) ◽

pp. 445-448 ◽

Cited By ~ 10

Author(s):

J.L. Krolik ◽

D.N. Swingler

Keyword(s):

Covariance Matrix ◽

Mean Square Error ◽

Minimum Variance ◽

Sample Covariance Matrix ◽

Mean Square ◽

Error Performance ◽

Sample Covariance ◽

The Mean ◽

Mean Square Error Performance

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The Bordeaux Automatic Meridian Circle

International Astronomical Union Colloquium ◽

10.1017/s0252921100074170 ◽

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°.

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Limit tolerances for sums of measurement errors

Geodesy and Cartography ◽

10.22389/0016-7126-2017-934-4-59-62 ◽

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.

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

Sensors ◽

10.3390/s21051631 ◽

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.

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