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1

Lee, Uk-Jae, Byeong Wook Lee, Dong-Hui Ko, and Hong-Yeon Cho. "Optimal Estimation of the Peak Wave Period using Smoothing Method." Journal of Korean Society of Coastal and Ocean Engineers 34, no. 6 (December 27, 2022): 266–74. http://dx.doi.org/10.9765/kscoe.2022.34.6.266.

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In this study, a smoothing method was applied to improve the accuracy of peak wave period estimation using the water surface elevation observed from the Oceanographic and Meteorological Observation Tower located on the west coast of the Korean Peninsula. Validation of the application of the smoothing method was performed using variance of the surface elevation and total amount wave energy, and then the effect on the application of smoothing was analyzed. As a result of the analysis, the correlation coefficient between variance of the surface elevation and total amount wave energy was 0.9994, confirming that there was no problem in applying the method. Thereafter, as a result of reviewing the effect of smoothing, it was found to be reduced by about 4 times compared to the confidence interval of the existing estimated spectrum, confirming that the accuracy of the estimated peak wave period was improved. It was found that there was a statistically significant difference in probability density between 4 and 6 seconds due to the smoothing application. In addition, for optimal smoothing, the appropriate number of smoothings according to the significant wave height range was calculated using a statistical technique, and the number of smoothings was found to increase due to the unstable spectral shape as the significant wave height decreased.
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2

Baszczyńska, Aleksandra Katarzyna. "One Value of Smoothing Parameter vs Interval of Smoothing Parameter Values in Kernel Density Estimation." Acta Universitatis Lodziensis. Folia Oeconomica 6, no. 332 (February 2, 2018): 73–86. http://dx.doi.org/10.18778/0208-6018.332.05.

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Ad hoc methods in the choice of smoothing parameter in kernel density estimation, al­though often used in practice due to their simplicity and hence the calculated efficiency, are char­acterized by quite big error. The value of the smoothing parameter chosen by Silverman method is close to optimal value only when the density function in population is the normal one. Therefore, this method is mainly used at the initial stage of determining a kernel estimator and can be used only as a starting point for further exploration of the smoothing parameter value. This paper pre­sents ad hoc methods for determining the smoothing parameter. Moreover, the interval of smooth­ing parameter values is proposed in the estimation of kernel density function. Basing on the results of simulation studies, the properties of smoothing parameter selection methods are discussed.
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3

Livingston, Charles. "Chiral smoothings of knots." Proceedings of the Edinburgh Mathematical Society 63, no. 4 (November 2020): 1048–61. http://dx.doi.org/10.1017/s0013091520000322.

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AbstractCan smoothing a single crossing in a diagram for a knot convert it into a diagram of the knot's mirror image? Zeković found such a smoothing for the torus knot T(2, 5), and Moore–Vazquez proved that such smoothings do not exist for other torus knots T(2, m) with m odd and square free. The existence of such a smoothing implies that K # K bounds a Mobius band in B4. We use Casson–Gordon theory to provide new obstructions to the existence of such chiral smoothings. In particular, we remove the constraint that m be square free in the Moore–Vazquez theorem, with the exception of m = 9, which remains an open case. Heegaard Floer theory provides further obstructions; these do not give new information in the case of torus knots of the form T(2, m), but they do provide strong constraints for other families of torus knots. A more general question asks, for each pair of knots K and J, what is the minimum number of smoothings that are required to convert a diagram of K into one for J. The methods presented here can be applied to provide lower bounds on this number.
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4

Morduch, Jonathan. "Income Smoothing and Consumption Smoothing." Journal of Economic Perspectives 9, no. 3 (August 1, 1995): 103–14. http://dx.doi.org/10.1257/jep.9.3.103.

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One way that risk-averse households protect consumption levels is to borrow and use insurance mechanisms. Another way, common in low-income economies, is to diversify economic activities and make conservative production and employment choices. Households thus tend toward limiting exposure only to shocks that can be handled with available credit and insurance. Typically, both types of mechanisms are studied independently but much more can be learned by studying them together. First, we obtain a more complete picture of risks, costs, and insurance possibilities. Second, it opens the way to considering biases in standard tests of credit and insurance.
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5

Harianto, Syawal, Haris Al Amin, and Yusmika Indah. "Pengaruh Ukuran Perusahaan, dan Leverange Terhadap Praktik Income Smoothing pada Bank Syariah." Jurnal EMT KITA 4, no. 1 (September 10, 2020): 80. http://dx.doi.org/10.35870/emt.v4i2.136.

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This research is to know the effect of firm size, and financial leverage to Income Smoothing practices is Islamic Banks. The data used is the secondary data with sourced from annual report data published by Islamic commercial banks and syariah business unit during 2016-2018 periods, samples research are 54 (fifty four) bank. Data analysis method using eviews with the fixed effect model. The result of the research shows that the simultan firm size and financial leverage have significant effect on Income Smoothing in Islamic banks.the partially, firm size an financial leverage has a positive and significant effect on income smoothin practices in Islamic banks City. The determination test result is 55%. Keywords: Firm Size, Financial leverage, Income Smoothing.
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6

Wang, X., P. Du, and J. Shen. "Smoothing splines with varying smoothing parameter." Biometrika 100, no. 4 (August 30, 2013): 955–70. http://dx.doi.org/10.1093/biomet/ast031.

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7

Turlach, Berwin A. "Shape constrained smoothing using smoothing splines." Computational Statistics 20, no. 1 (March 2005): 81–104. http://dx.doi.org/10.1007/bf02736124.

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8

Purwaningsih, Endang, and Oktofiana Busa Taran Wanan. "PENGARUH UKURAN PERUSAHAAN, FINANCIAL LEVERAGE, STRUKTUR KEPEMILIKAN, CASH HOLDING, REPUTASI AUDITOR TERHADAP INCOME SMOOTHING (STUDI EMPIRIS PERUSAHAAN MANUFAKTUR TERDAFTAR DI BEI PERIODE 2018 - 2020)." Media Akuntansi 34, no. 01 (June 29, 2022): 063–74. http://dx.doi.org/10.47202/mak.v34i01.155.

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This study aims to determine the effect ofcompany size, financial leverage,ownership structure, cash holdings,auditor's reputation for income smoothingin manufacturing sector companies listed on the Indonesia Stock Exchange (IDX) for the 2018-2020 period. The sampling technique used secondary data sources, namely data obtained or collected by researchers from various existing sources. The population used in this study were 193 manufacturing companies with a total sample of 40 companies. The analytical method used is the classical assumption test and multiple regression test.Based on the analysis conducted, it can be concluded that this study meets the requirements of the classical assumption test. Hypothesis testing using t test shows that firm size has a significant positive effect on income smoothing with a sig value of 2.6%, financial leverage has a significant negative effect on income smoothing with a sig value of 3.0%, managerial ownership has a significantpositive effect on income smoothing with a sig value of 1.3 %, institutional ownership has a significant negative effect on income smoothing with a sig value of 1.8%, cash holding a significantly negative effect on income smoothing with a sig value of 3.8%, and auditor reputation has a significant positive effect on income smoothing with a sig value of 4.6%.The results of the f test together with independent variables including company size, financial leverage, managerial ownership, institutional ownership, cash holding and auditor reputation have a significant effect on income smoothing. The value of the coefficient of determination (Adjusted R2) from the equation tested in this study was 42.8%. This indicates that income smoothing is only explained by 42.8% by company size, financial leverage, managerial ownership, institutional ownership, cash holding and auditor reputation while the rest is explained by other variables outside the equation.
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9

Malik, Amina, Haroon Aziz, Buerhan Saiti, and Shahab Ud Din. "The Impact of Earnings variability and Regulatory Measures on Income Smoothing: Evidence from Panel Regression." Journal of Central Banking Theory and Practice 10, no. 1 (January 1, 2021): 183–201. http://dx.doi.org/10.2478/jcbtp-2021-0009.

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Abstract This study investigates the impact of variability in earnings, stringent regulatory measures and the trend of extending loans while keeping in view deposit ratio on income smoothening practices for a sample of 20 commercial banks listed on the Pakistan Stock Exchange (PSX) from the year 2010 to 2017. The likelihood of smoothing activities is measured through its widely used proxy, i.e. loan loss provisions (LLPs). Moreover, earnings before tax and provisions (EBTP) and loan to deposit ratio (LD) have been incorporated to determine the impact of earnings and loans to deposit ratio on income smoothening. We find that commercial banks are less likely to manage earnings through smoothening practices, which shows that commercial banks adhere to regulatory restrictions. This is further supported by the fact that income smoothing activities decrease as a result of the increase in capital adequacy ratios after the imposition of stringent rules, which exert greater regulatory pressure on banks, whereas the pace of income smoothing increases as a result of an increase in loans to deposit ratio, which reveals that banks take credit risk but manage within the ambit of regulatory restrictions. Based on the findings, we argue that the imposition of regulatory restrictions through the State Bank of Pakistan (SBP) has not only discouraged income smoothening through loan loss provisions but also enhances reporting quality. The results of this study provide useful insights for investors, creditors and stakeholders.
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10

MUNTEANU, FLORIN, CRISTIAN IOANA, CRISTIAN ŞUŢEANU, and EDMOND CREŢU. "SMOOTHING DIMENSIONS FOR TIME SERIES CHARACTERIZATION." Fractals 03, no. 02 (June 1995): 315–28. http://dx.doi.org/10.1142/s0218348x95000254.

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The paper refers to a recently introduced fractal signal analysis method, which relies on scaling properties of signal parameters regarding the cutoff frequency used to smoothen the signal’s graph. The relations between the smoothing dimensions and other exponents (fractal dimension df, power spectrum exponent ß, Hurst exponent H) are determined theoretically and tested by numerical experiments.
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11

Caro, Pedro, Cristóbal J. Meroño, and Ioannis Parissis. "Rotational smoothing." Journal of Differential Equations 306 (January 2022): 101–51. http://dx.doi.org/10.1016/j.jde.2021.10.018.

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12

Bowman, A. W., M. P. Wand, and M. C. Jones. "Kernel Smoothing." Biometrics 54, no. 1 (March 1998): 393. http://dx.doi.org/10.2307/2534029.

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13

Van Der Linde, Angelika. "Smoothing Errors." Statistics 31, no. 2 (January 1998): 91–114. http://dx.doi.org/10.1080/02331889808802631.

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14

Walther, Guenther. "Granulometric smoothing." Annals of Statistics 25, no. 6 (December 1997): 2273–99. http://dx.doi.org/10.1214/aos/1030741072.

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15

Yandell, Brian S. "Kernel Smoothing." Technometrics 38, no. 1 (February 1996): 75–76. http://dx.doi.org/10.1080/00401706.1996.10484419.

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16

Linhart, H. "Discrete smoothing." Statistical Papers 30, no. 1 (December 1989): 197–211. http://dx.doi.org/10.1007/bf02924323.

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17

Bannister, Allison Rose, Jeanne Paulette Bickford, and Karl Vance Swanke. "Demand Smoothing." IEEE Transactions on Semiconductor Manufacturing 27, no. 3 (August 2014): 335–40. http://dx.doi.org/10.1109/tsm.2014.2312358.

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18

Kim, Woonkyung M., S. Moon-Ho Song, Sun Geun Kim, Chuck Yoo, Chongyul Yoon, and Jung Soo Kim. "Morphological smoothing." Electronics Letters 36, no. 8 (2000): 717. http://dx.doi.org/10.1049/el:20000548.

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19

Eilers, Paul H. C. "Unimodal smoothing." Journal of Chemometrics 19, no. 5-7 (May 2005): 317–28. http://dx.doi.org/10.1002/cem.935.

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20

Tewfik, A. H., A. S. Willsky, and B. C. Levy. "Parallel smoothing." Systems & Control Letters 14, no. 3 (March 1990): 253–59. http://dx.doi.org/10.1016/0167-6911(90)90021-l.

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21

Roark, Dennis E. "Reverse Smoothing: a model-free data smoothing algorithm." Biophysical Chemistry 108, no. 1-3 (March 2004): 121–26. http://dx.doi.org/10.1016/j.bpc.2003.10.014.

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22

Agustin Ekadjaja, Reinhard James,. "Studi Empiris Mengenai Faktor-Faktor Yang Mempengaruhi Praktik Income Smoothing." Jurnal Paradigma Akuntansi 3, no. 3 (November 10, 2021): 1167. http://dx.doi.org/10.24912/jpa.v3i3.14911.

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The purpose of this study was to analyze the effect of firm size, return on asset, net profit margins, and financial leverage on income smoothing practices on manufacturing companies listed on the IDX in 2017-2019. This study uses 44 manufacturing companies that have been selected through a purposive sampling method with a total of 132 data for three years. Data processing was performed with EViews 10 software and with binary logistic regression. The results of the study shows that firm size, return on assets, and financial leverage have a negative and significant effect on income smoothings. Also, net profit margin have a positive and significant effect on income smoothings.
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23

Cipra, Tomáš. "Some problems of exponential smoothing." Applications of Mathematics 34, no. 2 (1989): 161–69. http://dx.doi.org/10.21136/am.1989.104344.

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24

Kučera, Radek. "Interpolating and smoothing biquadratic spline." Applications of Mathematics 40, no. 5 (1995): 339–56. http://dx.doi.org/10.21136/am.1995.134298.

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25

Ravinder, Handanhal V. "Forecasting With Exponential Smoothing Whats The Right Smoothing Constant?" Review of Business Information Systems (RBIS) 17, no. 3 (August 8, 2013): 117–26. http://dx.doi.org/10.19030/rbis.v17i3.8001.

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This paper examines exponential smoothing constants that minimize summary error measures associated with a large number of forecasts. These forecasts were made on numerous time series generated through simulation on a spreadsheet. The series varied in length and underlying nature no trend, linear trend, and nonlinear trend. Forecasts were made using simple exponential smoothing as well as exponential smoothing with trend correction and with different kinds of initial forecasts. We found that when initial forecasts were good and the nature of the underlying data did not change, smoothing constants were typically very small. Conversely, large smoothing constants indicated a change in the nature of the underlying data or the use of an inappropriate forecasting model. These results reduce the confusion about the role and right size of these constants and offer clear recommendations on how they should be discussed in classroom settings.
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26

Lee, Thomas C. M. "Smoothing parameter selection for smoothing splines: a simulation study." Computational Statistics & Data Analysis 42, no. 1-2 (February 2003): 139–48. http://dx.doi.org/10.1016/s0167-9473(02)00159-7.

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27

Kiani, M. "Template-based smoothing functions for data smoothing in Geodesy." Geodesy and Geodynamics 11, no. 4 (July 2020): 300–306. http://dx.doi.org/10.1016/j.geog.2020.03.003.

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28

Constable, C. G., and R. L. Parker. "Smoothing, splines and smoothing splines; Their application in geomagnetism." Journal of Computational Physics 78, no. 2 (October 1988): 493–508. http://dx.doi.org/10.1016/0021-9991(88)90062-9.

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29

Early, Jeffrey J., and Adam M. Sykulski. "Smoothing and Interpolating Noisy GPS Data with Smoothing Splines." Journal of Atmospheric and Oceanic Technology 37, no. 3 (March 2020): 449–65. http://dx.doi.org/10.1175/jtech-d-19-0087.1.

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AbstractA comprehensive method is provided for smoothing noisy, irregularly sampled data with non-Gaussian noise using smoothing splines. We demonstrate how the spline order and tension parameter can be chosen a priori from physical reasoning. We also show how to allow for non-Gaussian noise and outliers that are typical in global positioning system (GPS) signals. We demonstrate the effectiveness of our methods on GPS trajectory data obtained from oceanographic floating instruments known as drifters.
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Krisna, Adisti Maharani. "The PENGARUH MEKANISME KOMITE AUDIT TERHADAP INCOME SMOOTHING." KRISNA: Kumpulan Riset Akuntansi 15, no. 1 (July 5, 2023): 163–78. http://dx.doi.org/10.22225/kr.15.1.2023.163-178.

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Penelitian ini bertujuan untuk mengetahui bagaimana pengaruh mekanisme komite audit terhadap income smoothinng, dimana mekanisme komite audit ini terbagi menjadi empat yaitu ukuran komite audit, independensi komite audit, keahlian komite audit, dan jumlah rapat komite audit. Nantinya peneliitian ini diharapkan dapat memberikan masukkan pada perusahaan untuk mempublikasikan laporan keuangan yang berkualitas. Sampel penelitian ini menggunakan perusahaan LQ45 dengan total 114 perusahaan amatan. Hasil penelitian menunjukkan bahwa ukuran dan independensi komite audit memberikan pengaruh negatif terhadapincome smoothing, sedangkan keahlian dan jumlah rapat komite audit belum dapat memberikan pengaruh yang signifikan.
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Murtini, Umi, and Aditya Denny O.S. "UKURAN PERUSAHAAN, PROFITABILITAS, FINANCIAL LEVERAGE, DIVIDEND PAYOUT RATIO DAN KECENDERUNGAN PERATAAN LABA." Jurnal Riset Akuntansi dan Keuangan 8, no. 2 (August 1, 2012): 149. http://dx.doi.org/10.21460/jrak.2012.82.25.

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This study aims to exmine the effect of firm size, profitability, financial leverage, and dividend payout ratio on income smoothing tendency. The grouping of firms with income smoothing and without income smoothing use eckel index. Using binary logistic regression analysis, results shows that firm size and profitabilitas influence on income smoothing tendency. Meanwhile, financial leverage and dividend payout ratio don’t influence on income smoothing tendency. Keywords: income smoothing, profitabilty, size
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32

Candio, Syaifullah Adam, Arlene Henny Hiariey, and Ronald John Djami. "PERBANDINGAN METODE DOUBLE EXPONENTIAL SMOOTHING DAN TRIPLE EXPONENTIAL SMOOTHING DALAM MEMPREDIKSI TINGKAT KRIMINALITAS." PARAMETER: Jurnal Matematika, Statistika dan Terapannya 3, no. 01 (March 3, 2024): 49–60. http://dx.doi.org/10.30598/parameterv3i01pp49-60.

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From 2010 to 2022, crime in Indonesia, especially Maluku Province, tends to increase compared to previous years. Considering these problems, a crime rate prediction system is needed so that the Maluku Provincial Police is able to estimate the quantity and type of crime that is likely to occur in the future. One of the prediction methods that has been used for crime prediction is Exponential Smoothing (ES). The Smoothing method is applied to obtain predictions based on time-series data. In this discussion, the author will compare the forecasting methods of Double Exponential Smoothing, and Triple Exponential Smoothing. The Double Exponential Smoothing method is suitable to be used to provide forecasting results when a data has a certain trend pattern. This Triple Exponential Smoothing method is used when there are still dominant expression elements &; seasonal conduite shown in the data. The MAPE value for the Double Exponential Smoothing method is 20.69552 and for the Triple Exponential Smoothing method is 30.48323, it can be said that the MAPE value of the Double Exponential Smoothing method is smaller than the Triple Exponential Smoothing method. So that the Double Exponential Smoothing method is more accurate than the Triple Exponential Smoothing method to predict the crime rate.
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33

Lestari, Putu Diah, I. Gusti Ayu Purnamawati, and I. Putu Gede Diatmika. "Determinants of Income Smoothing Practices with Managerial Ownership Structure and Firm Size as Moderators." Jurnal Akuntansi Profesi 15, no. 01 (April 29, 2024): 165–76. http://dx.doi.org/10.23887/jap.v15i01.49299.

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This study aims to determine the effect of profitability, dividend policy, financial leverage on income smoothing practices and the effect of moderating managerial ownership structure and firm size on the effect of profitability, dividend policy, financial leverage on income smoothing practices. The research design used causal quantitative. The population of this study were all manufacturing companies on the Indonesia Stock Exchange as many as 157 companies. The sampling technique used purposive sampling with a total sample of 30 companies. The data analysis technique used moderated regression analysis. The results show that (1) profitability had a significant negative effect on income smoothing practices, (2) dividend policy had a significant positive effect on income smoothing practices, (3) financial leverage had a significant positive effect on income smoothing practices, (4) managerial ownership structure strengthens the negative effect of profitability on income smoothing practices, (5) managerial ownership structure weakens the positive effect of dividend policy on income smoothing practices, (6) managerial ownership structure weakens the positive influence of financial leverage on income smoothing practices, (7) firm size weakens the negative effect of profitability on earnings smoothing practices. income smoothing, (8) firm size strengthens the positive effect of dividend policy on income smoothing practices, and (9) firm size strengthens the positive effect of financial leverage on income smoothing practices.
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34

Kim, Myoung-Jong, and Jong-Gyu Kim. "The Effect of Discretionary Earnings Smoothing and Asymmetric Timeliness of Loss Recognition on Nonlinear Relationship between Earnings Smoothing and Information Asymmetry." Korean Association Of Computers And Accounting 20, no. 2 (August 31, 2022): 47–81. http://dx.doi.org/10.32956/kaoca.2022.20.2.47.

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Previous studies have reported conflicting results on the relationship between earnings smoothing and information asymmetry depending on the positive and negative roles of earnings smoothing. For these contradictory results, Jayaraman(2008) confirmed that there is a U-shaped non-linear relationship between earnings smoothing and information asymmetry due to discretionary earnings smoothing. This study tried to verify the nonlinearity of earnings smoothing and information asymmetry by focusing on the conflicting correlation between cash flow and accrual between discretionary earnings smoothing and asymmetric recognition of loss recognition(ATLR). The main findings are as follows. First, as the frequency of ATLR increases, the negative correlation between cash flow and accrual weaken and earnings volatility increase;thus the frequency of ATLR is a factor that lowers the level of earnings smoothing. Second, earnings smoothing and information asymmetry have a positive (+) relationship in the smooth earnings group, whereas, earnings smoothing and information asymmetry have a negative (-) relationship in the volatile earnings group. This result means a non-linear relationship between earnings smoothing and information asymmetry depending on the volatility of earnings. Third, it is found that information asymmetry increased as the frequency of ATLR increased. This means that as the frequency of ATLR increases, the volatility of earnings increases, and uncertainty about investors’ future earnings and cash flow forecasts increases, resulting in increased information asymmetry. Finally, discretionary earnings smoothing provides a positive (+) effect to earnings smoothing based on the negative (-) correlation between cash flow and accrual, and results in a positive (+) relationship between earnings smoothing and information asymmetry. On the contrary, ATLR provides a negative (-) effect on earnings smoothing based on the positive (+) correlation between cash flow and accrual, and results in a negative (-) relationship between earnings smoothing and information asymmetry. As a result, a non-linear relationship between earnings smoothing and information asymmetry is induced from the conflicting correlation of cash flow and accrual between discretionary earnings smoothing and ATLR.
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35

von Clarmann, T. "Smoothing error pitfalls." Atmospheric Measurement Techniques 7, no. 9 (September 18, 2014): 3023–34. http://dx.doi.org/10.5194/amt-7-3023-2014.

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Abstract. The difference due to the content of a priori information between a constrained retrieval and the true atmospheric state is usually represented by a diagnostic quantity called smoothing error. In this paper it is shown that, regardless of the usefulness of the smoothing error as a diagnostic tool in its own right, the concept of the smoothing error as a component of the retrieval error budget is questionable because it is not compliant with Gaussian error propagation. The reason for this is that the smoothing error does not represent the expected deviation of the retrieval from the true state but the expected deviation of the retrieval from the atmospheric state sampled on an arbitrary grid, which is itself a smoothed representation of the true state; in other words, to characterize the full loss of information with respect to the true atmosphere, the effect of the representation of the atmospheric state on a finite grid also needs to be considered. The idea of a sufficiently fine sampling of this reference atmospheric state is problematic because atmospheric variability occurs on all scales, implying that there is no limit beyond which the sampling is fine enough. Even the idealization of infinitesimally fine sampling of the reference state does not help, because the smoothing error is applied to quantities which are only defined in a statistical sense, which implies that a finite volume of sufficient spatial extent is needed to meaningfully discuss temperature or concentration. Smoothing differences, however, which play a role when measurements are compared, are still a useful quantity if the covariance matrix involved has been evaluated on the comparison grid rather than resulting from interpolation and if the averaging kernel matrices have been evaluated on a grid fine enough to capture all atmospheric variations that the instruments are sensitive to. This is, under the assumptions stated, because the undefined component of the smoothing error, which is the effect of smoothing implied by the finite grid on which the measurements are compared, cancels out when the difference is calculated. If the effect of a retrieval constraint is to be diagnosed on a grid finer than the native grid of the retrieval by means of the smoothing error, the latter must be evaluated directly on the fine grid, using an ensemble covariance matrix which includes all variability on the fine grid. Ideally, the averaging kernels needed should be calculated directly on the finer grid, but if the grid of the original averaging kernels allows for representation of all the structures the instrument is sensitive to, then their interpolation can be an adequate approximation.
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36

von Clarmann, T. "Smoothing error pitfalls." Atmospheric Measurement Techniques Discussions 7, no. 4 (April 1, 2014): 3301–19. http://dx.doi.org/10.5194/amtd-7-3301-2014.

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Abstract. The difference due to the content of a priori information between a constrained retrieval and the true atmospheric state is usually represented by the so-called smoothing error. In this paper it is shown that the concept of the smoothing error is questionable because it is not compliant with Gaussian error propagation. The reason for this is that the smoothing error does not represent the expected deviation of the retrieval from the true state but the expected deviation of the retrieval from the atmospheric state sampled on an arbitrary grid, which is itself a smoothed representation of the true state. The idea of a sufficiently fine sampling of this reference atmospheric state is untenable because atmospheric variability occurs on all scales, implying that there is no limit beyond which the sampling is fine enough. Even the idealization of infinitesimally fine sampling of the reference state does not help because the smoothing error is applied to quantities which are only defined in a statistical sense, which implies that a finite volume of sufficient spatial extent is needed to meaningfully talk about temperature or concentration. Smoothing differences, however, which play a role when measurements are compared, are still a useful quantity if the involved a priori covariance matrix has been evaluated on the comparison grid rather than resulting from interpolation. This is, because the undefined component of the smoothing error, which is the effect of smoothing implied by the finite grid on which the measurements are compared, cancels out when the difference is calculated.
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37

de Angelis, Daniela, and G. Alastair Young. "Smoothing the Bootstrap." International Statistical Review / Revue Internationale de Statistique 60, no. 1 (April 1992): 45. http://dx.doi.org/10.2307/1403500.

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38

Gan, Yaozhong, Zhe Zhang, and Xiaoyang Tan. "Smoothing Advantage Learning." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 6 (June 28, 2022): 6657–64. http://dx.doi.org/10.1609/aaai.v36i6.20620.

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Advantage learning (AL) aims to improve the robustness of value-based reinforcement learning against estimation errors with action-gap-based regularization. Unfortunately, the method tends to be unstable in the case of function approximation. In this paper, we propose a simple variant of AL, named smoothing advantage learning (SAL), to alleviate this problem. The key to our method is to replace the original Bellman Optimal operator in AL with a smooth one so as to obtain more reliable estimation of the temporal difference target. We give a detailed account of the resulting action gap and the performance bound for approximate SAL. Further theoretical analysis reveals that the proposed value smoothing technique not only helps to stabilize the training procedure of AL by controlling the trade-off between convergence rate and the upper bound of the approximation errors, but is beneficial to increase the action gap between the optimal and sub-optimal action value as well.
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39

Shibata, Katsunari, and Yoichi Okabe. "Temporal Smoothing Learning." IEEJ Transactions on Electronics, Information and Systems 117, no. 9 (1997): 1291–99. http://dx.doi.org/10.1541/ieejeiss1987.117.9_1291.

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40

Prus-Wiśniowski and Waterman. "SMOOTHING Λ-SEQUENCES." Real Analysis Exchange 20, no. 1 (1994): 26. http://dx.doi.org/10.2307/44152446.

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41

Prus-Wiśniowski and Waterman. "SMOOTHING Λ-SEQUENCES." Real Analysis Exchange 20, no. 2 (1994): 647. http://dx.doi.org/10.2307/44152547.

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42

Kotsopoulos, A. "Smoothing solar power." Power Engineer 17, no. 3 (2003): 23. http://dx.doi.org/10.1049/pe:20030307.

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43

Wood, Simon N., Mark V. Bravington, and Sharon L. Hedley. "Soap film smoothing." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 70, no. 5 (November 2008): 931–55. http://dx.doi.org/10.1111/j.1467-9868.2008.00665.x.

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44

Hoogendoorn, M. N. "Winstegalisatie (‘Income smoothing’)." Maandblad Voor Accountancy en Bedrijfseconomie 59, no. 7/8 (July 1, 1985): 271–89. http://dx.doi.org/10.5117/mab.59.20536.

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45

Calegari, Danny. "Leafwise smoothing laminations." Algebraic & Geometric Topology 1, no. 1 (October 18, 2001): 579–87. http://dx.doi.org/10.2140/agt.2001.1.579.

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46

Vinje, V., A. Stovas, and D. Reynaud. "Preserved-traveltime smoothing." Geophysical Prospecting 61 (November 7, 2012): 380–90. http://dx.doi.org/10.1111/j.1365-2478.2012.01124.x.

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47

Hayden, Howard C. "Data smoothing routine." Computers in Physics 1, no. 1 (1987): 74. http://dx.doi.org/10.1063/1.168292.

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48

Scott Harris, R., Joshua Hill, and Talia Harris. "Exponential smoothing spreadsheets." Journal of Economic Education 49, no. 4 (October 2, 2018): 366. http://dx.doi.org/10.1080/00220485.2018.1500961.

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49

Fernandes, Marcelo, Emmanuel Guerre, and Eduardo Horta. "Smoothing Quantile Regressions." Journal of Business & Economic Statistics 39, no. 1 (October 4, 2019): 338–57. http://dx.doi.org/10.1080/07350015.2019.1660177.

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50

FINK, JENNIFER L. W. "Smoothing the transition." Nursing 32, no. 2 (February 2002): 32hn8. http://dx.doi.org/10.1097/00152193-200202000-00036.

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