scholarly journals Sequential Probabilistic Ratio Test for the Scale Parameter of the P -Norm Distribution

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Huan Ren ◽  
Hongchang Hu ◽  
Zhen Zeng
Keyword(s):  
Approximate Formula ◽  
Scale Parameter ◽  
Specific Situation ◽  
Ratio Test ◽  
Sample Function ◽  
Simple Hypothesis ◽  
Independent Observations ◽  
The Mean ◽  
Stop Rule ◽  
Position Parameter

We consider a series of independent observations from a P -norm distribution with the position parameter μ and the scale parameter σ . We test the simple hypothesis H 0 : σ = σ 1 versus H 1 :   σ = σ 2 . Firstly, we give the stop rule and decision rule of sequential probabilistic ratio test (SPRT). Secondly, we prove the existence of h σ which needs to satisfy the specific situation in SPRT method, and the approximate formula of the mean sample function is derived. Finally, a simulation example is given. The simulation shows that the ratio of sample size required by SPRT and the classic Neyman–Pearson N − P test is about 50.92 % at most, 38.30 % at least.

Assessment of nutritional status of students of medical institute according to the blood biochemical parameters

2020 ◽  
pp. 55-63
Author(s):  
Rofail Rakhmanov ◽  
Elena Bogomolova ◽  
Mariya Shaposhnikova ◽  
Mariya Sapozhnikova
Keyword(s):  
Nutritional Status ◽  
Lower Boundary ◽  
Density Lipoprotein ◽  
Blood Parameters ◽  
Medical Institute ◽  
Specific Situation ◽  
Mathematical Methods ◽  
Normal Range ◽  
Mean Values ◽  
The Mean

The biochemical blood parameters characterizing the students ’nutritional status were evaluated: protein, lipid, carbohydrate metabolism, a number of minerals. The mean values, errors of the mean, median (Me), boundary (Q) and the range of 25–75 percentiles were determined. In 9.1 % of students and 28.6 % of students, the total protein was increased. Creatinine in men was in the upper normal range, in women — at the upper limit of normal, of which 46.2 % was higher than normal. The interval Q25–75 of uric acid in students is determined in the lower normal zone. In 40.0 % of men, decreased high-density lipoprotein cholesterol (Q25–75 corresponded to 1.15–1.79), in women — below normal, Q25–75 5 was 1.3–1.5, decreased in 73.3 %. Me and Q25–75 iron were in the lower normal range; 14.1 % of men and 13.2 % of women are below normal. Me sodium and potassium at the level of the lower boundary of the norm, Q25–75 in the lower zone of the norm: in 16.0 % and 15.4 % of students the levels are reduced. Calcium is slightly above the lower limit of the norm, Q25–75–2.1–2.24, indicating an insufficient intake in the whole group; 25.0 % are below normal. The border of the 25th percentile of magnesium is at the level of the lower border of the norm, in 19.2 % it is reduced. 7.2 % lack of chlorine. Phosphorus is normal, but Q25–75 is in the upper zone; 17.9 % increased. Biochemical markers can identify individuals with metabolic disorders of nutrients. Statistical indicators — the median, the boundaries of 25–75 quartiles and their scope characterize the metabolism of macronutrients and minerals in the group and subgroups of students. Laboratory and mathematical methods can provide a basis for identifying the specific causes of these changes. For this, you can use the questionnaire method of studying the nutrition of students, possibly using the developed questionnaires for a specific situation.

scholarly journals On double stage minimax-shrinkage estimator for generalized Rayleigh model

2016 ◽  
Vol 5 (1) ◽  
pp. 39 ◽  
Author(s):  
Abbas Najim Salman ◽  
Maymona Ameen
Keyword(s):  
Sample Size ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Rayleigh Distribution ◽  
Shrinkage Estimator ◽  
Squared Error ◽  
Expected Sample Size ◽  
Generalized Rayleigh Distribution ◽  
The Mean

<p>This paper is concerned with minimax shrinkage estimator using double stage shrinkage technique for lowering the mean squared error, intended for estimate the shape parameter (a) of Generalized Rayleigh distribution in a region (R) around available prior knowledge (a<sub>0</sub>) about the actual value (a) as initial estimate in case when the scale parameter (l) is known .</p><p>In situation where the experimentations are time consuming or very costly, a double stage procedure can be used to reduce the expected sample size needed to obtain the estimator.</p><p>The proposed estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor y(<strong>×</strong>) and suitable region R.</p><p>Expressions for Bias, Mean squared error (MSE), Expected sample size [E (n/a, R)], Expected sample size proportion [E(n/a,R)/n], probability for avoiding the second sample and percentage of overall sample saved  for the proposed estimator are derived.</p><p>Numerical results and conclusions for the expressions mentioned above were displayed when the consider estimator are testimator of level of significanceD.</p><p>Comparisons with the minimax estimator and with the most recent studies were made to shown the effectiveness of the proposed estimator.</p>

scholarly journals Parameter Estimation and Hypothesis Testing of Multivariate Poisson Inverse Gaussian Regression

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1738
Author(s):  
Selvi Mardalena ◽  
Purhadi Purhadi ◽  
Jerry Dwi Trijoyo Purnomo ◽  
Dedy Dwi Prastyo
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Hypothesis Testing ◽  
Poisson Regression ◽  
Ratio Test ◽  
Inverse Gaussian ◽  
Count Response ◽  
The Mean ◽  
Gaussian Regression ◽  
Response Variables

Multivariate Poisson regression is used in order to model two or more count response variables. The Poisson regression has a strict assumption, that is the mean and the variance of response variables are equal (equidispersion). Practically, the variance can be larger than the mean (overdispersion). Thus, a suitable method for modelling these kind of data needs to be developed. One alternative model to overcome the overdispersion issue in the multi-count response variables is the Multivariate Poisson Inverse Gaussian Regression (MPIGR) model, which is extended with an exposure variable. Additionally, a modification of Bessel function that contain factorial functions is proposed in this work to make it computable. The objective of this study is to develop the parameter estimation and hypothesis testing of the MPIGR model. The parameter estimation uses the Maximum Likelihood Estimation (MLE) method, followed by the Newton–Raphson iteration. The hypothesis testing is constructed using the Maximum Likelihood Ratio Test (MLRT) method. The MPIGR model that has been developed is then applied to regress three response variables, i.e., the number of infant mortality, the number of under-five children mortality, and the number of maternal mortality on eight predictors. The unit observation is the cities and municipalities in Java Island, Indonesia. The empirical results show that three response variables that are previously mentioned are significantly affected by all predictors.

On a spectral density estimate obtained by averaging periodograms

1985 ◽  
Vol 22 (03) ◽  
pp. 598-610 ◽  
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.

scholarly journals The short-term mean reversion of stock price and the change in trading volume

2021 ◽  
Vol 29 (3) ◽  
pp. 190-214
Author(s):  
Woosung Jung ◽  
Mhin Kang
Keyword(s):  
Term Structure ◽  
Stock Price ◽  
Trading Volume ◽  
Price Index ◽  
Mean Reversion ◽  
Ratio Test ◽  
Short Term ◽  
Contemporaneous Correlation ◽  
The Mean ◽  
Response To Change

This study aims to analyze the effect of change in trading volume on the short-term mean reversion of the stock price in the Korean stock market. Through the variance ratio test, this paper finds that the market shows the mean reversion pattern after 2000, but not before. This study also confirms that the mean reversion property is significantly reduced if the effect of change in trading volume is excluded from the return of a stock with a significant contemporaneous correlation between return and change in trading volume in the post-2000 market. The results appear in both the Korea Composite Stock Price Index and Korea Securities Dealers Automated Quotation. This phenomenon stems from the significance of the return response to change in trading volume per se and not the sign of the response. Additionally, the findings imply that the trading volume has a term structure because of the mean reversion of the trading volume and the return also has a partial term structure because of the contemporaneous correlation between return and change in trading volume. This conclusion suggests that considering the short-term impact of change in trading volume enables a more efficient observation of the market and avoidance of asset misallocation.

scholarly journals Compressed Sensing Reconstruction based on Adaptive Scale Parameter using Texture Feature

2019 ◽  
Vol 8 (12) ◽  
pp. 5455-5461
Keyword(s):  
Image Quality ◽  
Compressed Sensing ◽  
Scale Parameter ◽  
Sparse Matrix ◽  
Texture Feature ◽  
Projection Matrix ◽  
Original Image ◽  
Scaling Factors ◽  
Mri Scan ◽  
The Mean

While taking an MRI scan, the patients cannot static for a long time during the motions; the image formation process can create artifacts that may reduce the image quality. The Compressed Sensing (CS) mechanism is employed to reconstruct the original image from the limited data given as the sparse matrix. Hence, CS can be utilized to reduce the acceleration time for an MRI scan considering the patient's health. So the sensing method is implemented by a suitable projection matrix for reconstructing the sparse signals from a few numbers of measurements using Compressed Sensing. The CS guarantees the recovery of the original image with high probability based on random Gaussian projection matrices. However, sparse ternarius projections are more apt for the implementation of hardware. In this article, the proposed deep learning method is employed to obtain a very sparse ternary projection in Compressed Sensing. Compressed Sensing Reconstruction using an adaptive scale parameter based on the texture feature is used to improve the image quality. The two scaling factors αx and αy are assigned to specify the fixed scale for changing the improvement of the image quality. In the parameter using texture feature, the αx and αy are assigned to α as an adaptive scale based on texture feature. In the TACS-SDANN architecture, there are two layers namely the sensing layer which trains the projection matrix and a reconstruction layer which trains for non-linear sparse matrix continuously using Auto-encoder. Experimentally, the scaling factors are calculated on the training data to get the mean PeakSignal-to-Noise Ratio (PSNR) for improving the image quality. Hence a new deep network layer is employed to improve the image quality in this proposed method. Hence the consequence of the proposed method is compared with the SDANN method based on the mean Peak-Signal-to-Noise Ratio (PSNR) to check the image quality. From that comparisons, the TACS-SDANN architecture is proposed to yield a better performance.

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