en>Yobot: WP:CHECKWIKI error #2 fix + general fixes using AWB (9276)

2013-06-21T16:40:21Z

WP:CHECKWIKI error #2 fix + general fixes using AWB (9276)

← Older revision		Revision as of 18:40, 21 June 2013
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	~~MP3 or MPEG -1 Audio Layer~~ is an ~~standard to compress audio files about one twelfth~~ of ~~the disk space~~ of the ~~original audio track and providing the closest sound quality to an original C~~-d. ~~This is the reason why~~ it~~"s become~~ the ~~conventional program to reduce music on line or web~~. ~~Since~~ the ~~measurement~~ of ~~music files~~ is ~~paid down and availability~~ of ~~various free mp3 person computer software has made it simple~~ to ~~spread music~~ and ~~other audio sessions online~~. <br><br>		In [[statistics]], '''Stein's unbiased risk estimate (SURE)''' is an [[bias of an estimator\|unbiased]] [[estimator]] of the [[mean-squared error]] of "a nearly arbitrary, nonlinear biased estimator."<ref name="donoho95"/> In other words, it provides an indication of the accuracy of a given estimator. This is important since the true mean-squared error of an estimator is a function of the unknown parameter to be estimated, and thus cannot be determined exactly.

			The technique is named after its discoverer, [[Charles Stein (statistician)\|Charles Stein]].<ref name='stein81'> {{cite journal\|title=Estimation of the Mean of a Multivariate Normal Distribution\|journal=The Annals of Statistics\| first=Charles M.\|last=Stein\|coauthors=\|volume=9\|issue=6\|pages=1135–1151\|id= \|month=November\|year=1981\|doi=10.1214/aos/1176345632\|jstor=2240405}}</ref>

	~~Advantages of MP3~~ <br><br>1. ~~If people hate to discover extra info about [http:~~//~~act.jinbo.net~~/~~forum2006~~/~~index.php~~/~~The_Mythical_Google_Sandbox site preview~~]~~, there are lots of databases people should think about pursuing~~. ~~Several digital audio formats have been produced by organizations such as Microsoft~~, ~~Lucent, and Yamaha which have restrictions on their technology that would be used~~ by ~~outside developers. But as~~ of ~~now MP3 has every one~~ of the ~~momentum to distribute music.~~ <br><br>~~2. As there are no security functions with Mp3 files~~, ~~countless these files are simply placed~~ and ~~passed around~~ the ~~web every day~~. ~~These files are so small~~ that ~~these files could be easily saved o~~-~~r attached to a contact while giving to all~~ of ~~your friends.~~ <br><br>3. ~~Another explanation is our listening habits that force individuals to use mp3~~. ~~You can gather all your songs~~, ~~artists o~~-~~r types~~ as ~~per your preference and keep it into your personal computer hard disk drive~~. ~~Next you can set all~~ the ~~songs~~ in the ~~play list and deliver~~ it ~~to the CD burner for recording~~. ~~Later you are free~~ to ~~listen it anywhere with the aid~~ of ~~portable mp3 players~~. <br><br>4. ~~Also an region for mp3 is web casting or audio streaming. Unlike mp3 downloads, streamed mp3 files aren~~&~~quot;t kept in the computer hard drive but are broadcasted like radio and radio~~ (~~mp3 person as an example~~). ~~If you desire~~ to ~~learn new info on [http~~:~~//www.cjbrotterdam.nl/forumonderwerp/audio~~-~~books~~-~~hot~~-~~2006~~.~~html~~ this ~~page is not affiliated]~~, we ~~know about tons of resources you can investigate.~~ <br><br>5. ~~Visiting~~ [~~http://www~~.~~cqaixiu.com~~/~~showthread.php?tid=35243 Approaches To Receive Audio Books Online~~] ~~probably provides tips you might use with your sister. These are~~ the ~~reasons you"d start dabbling~~ in ~~mp3 but there are several ethical and legal problems which you need to consider before you start making mp3 packages~~. <br>~~<br>For more information visit our recommended website freedownloadmp3song~~.~~info~~.<br>~~<br>If you have any sort of inquiries relating to where and how to utilize~~ [~~http~~:~~//ovalranchtalk.wallinside.com cigna health~~]~~, you can call us at our own internet site.~~		== Formal statement ==
			Let <math>\mu \in {\mathbb R}^d</math> be an unknown parameter and let <math>x \in {\mathbb R}^d</math> be a measurement vector whose components are independent and distributed normally with mean <math>\mu</math> and variance <math>\sigma^2</math>. Suppose <math>h(x)</math> is an estimator of <math>\mu</math> from <math>x</math>, and can be written <math>h(x) = x + g(x)</math>, where <math>g</math> is [[Weak derivative\|weakly differentiable]]. Then, Stein's unbiased risk estimate is given by<ref name='wasserman05'>{{cite book\|title=All of Nonparametric Statistics\| first=Larry\|last=Wasserman\|year=2005}}</ref>
			:<math>\mathrm{SURE}(h) = d\sigma^2 + \\|g(x)\\|^2 + 2 \sigma^2 \sum_{i=1}^d \frac{\partial}{\partial x_i} g_i(x), </math>
			where <math>g_i(x)</math> is the <math>i</math>th component of the function <math>g(x)</math>, and <math>\\|\cdot\\|</math> is the [[Euclidean norm]].

			The importance of SURE is that it is an unbiased estimate of the mean-squared error (or squared error risk) of <math>h(x)</math>, i.e.
			:<math>E_\mu \{ \mathrm{SURE}(h) \} = \mathrm{MSE}(h),\,\! </math>
			with
			:<math>\mathrm{MSE}(h) = E_\mu \\|h(x)-\mu\\|^2.</math>

			Thus, minimizing SURE can act as a surrogate for minimizing the MSE. Note that there is no dependence on the unknown parameter <math>\mu</math> in the expression for SURE above. Thus, it can be manipulated (e.g., to determine optimal estimation settings) without knowledge of <math>\mu</math>.

			== Proof ==
			We wish to show that
			: <math>E_\mu \\|h(x)-\mu\\|^2 = E_\mu \{ \mathrm{SURE}(h) \} </math>.
			We start by expanding the MSE as
			: <math>\begin{align} E_\mu \\| h(x) - \mu\\|^2 & = E_\mu \\|g(x) + x - \mu\\|^2 \\
			& = E_\mu \\|g(x)\\|^2 + E_\mu \\|x - \mu\\|^2 + 2 E_\mu g(x)^T (x - \mu) \\
			& = E_\mu \\|g(x)\\|^2 + d \sigma^2 + 2 E_\mu g(x)^T(x - \mu).
			\end{align}
			</math>
			Now we use [[integration by parts#Higher_dimensions \| integration by parts]] to rewrite the last term:
			:<math>
			\begin{align}
			E_\mu g(x)^T(x - \mu) & = \int_{R^d} \frac{1}{\sqrt{2 \pi \sigma^{2d}}} \exp\left(-\frac{\\|x - \mu\\|^2}{2 \sigma^2} \right) \sum_{i=1}^d g_i(x) (x_i - \mu_i) d^d x \\
			& = \sigma^2 \sum_{i=1}^d\int_{R^d} \frac{1}{\sqrt{2 \pi \sigma^{2d}}} \exp\left(-\frac{\\|x - \mu\\|^2}{2 \sigma^2} \right) \frac{dg_i}{dx_i} d^d x \\
			& = \sigma^2 \sum_{i=1}^d E_\mu \frac{dg_i}{dx_i}.
			\end{align}
			</math>
			Substituting this into the expression for the MSE, we arrive at
			: <math>E_\mu \\|h(x) - \mu\\|^2 = E_\mu \left( d\sigma^2 + \\|g(x)\\|^2 + 2\sigma^2 \sum_{i=1}^d \frac{dg_i}{dx_i}\right).</math>

			== Applications ==
			A standard application of SURE is to choose a parametric form for an estimator, and then optimize the values of the parameters to minimize the risk estimate. This technique has been applied in several settings. For example, a variant of the [[James–Stein estimator]] can be derived by finding the optimal [[shrinkage estimator]].<ref name="stein81"/> The technique has also been used by [[David Donoho\|Donoho]] and Johnstone to determine the optimal shrinkage factor in a [[wavelet]] [[denoising]] setting.<ref name='donoho95'> {{cite journal\|title=Adapting to Unknown Smoothness via Wavelet Shrinkage\|journal=Journal of the American Statistical Association\| first=David L.\|last=Donoho\|authorlink=David Donoho\|coauthors=Iain M. Johnstone\|volume=90\|issue=432\|pages=1200–1244\|id= \|month=December\|year=1995\|doi=10.2307/2291512\|publisher=Journal of the American Statistical Association, Vol. 90, No. 432\|jstor=2291512}}</ref>

			== References ==
			{{reflist}}

			[[Category:Error]]
			[[Category:Estimation theory]]
			[[Category:Risk]]

en>EmausBot: r2.7.2+) (Robot: Adding si:මායිම් ශාක

2012-01-23T05:24:24Z

r2.7.2+) (Robot: Adding si:මායිම් ශාක

New page

MP3 or MPEG -1 Audio Layer is an standard to compress audio files about one twelfth of the disk space of the original audio track and providing the closest sound quality to an original C-d. This is the reason why it"s become the conventional program to reduce music on line or web. Since the measurement of music files is paid down and availability of various free mp3 person computer software has made it simple to spread music and other audio sessions online. 

Advantages of MP3 1. If people hate to discover extra info about [http://act.jinbo.net/forum2006/index.php/The_Mythical_Google_Sandbox site preview], there are lots of databases people should think about pursuing. Several digital audio formats have been produced by organizations such as Microsoft, Lucent, and Yamaha which have restrictions on their technology that would be used by outside developers. But as of now MP3 has every one of the momentum to distribute music. 2. As there are no security functions with Mp3 files, countless these files are simply placed and passed around the web every day. These files are so small that these files could be easily saved o-r attached to a contact while giving to all of your friends. 3. Another explanation is our listening habits that force individuals to use mp3. You can gather all your songs, artists o-r types as per your preference and keep it into your personal computer hard disk drive. Next you can set all the songs in the play list and deliver it to the CD burner for recording. Later you are free to listen it anywhere with the aid of portable mp3 players. 4. Also an region for mp3 is web casting or audio streaming. Unlike mp3 downloads, streamed mp3 files aren"t kept in the computer hard drive but are broadcasted like radio and radio (mp3 person as an example). If you desire to learn new info on [http://www.cjbrotterdam.nl/forumonderwerp/audio-books-hot-2006.html this page is not affiliated], we know about tons of resources you can investigate. 5. Visiting [http://www.cqaixiu.com/showthread.php?tid=35243 Approaches To Receive Audio Books Online] probably provides tips you might use with your sister. These are the reasons you"d start dabbling in mp3 but there are several ethical and legal problems which you need to consider before you start making mp3 packages. For more information visit our recommended website freedownloadmp3song.info. If you have any sort of inquiries relating to where and how to utilize [http://ovalranchtalk.wallinside.com cigna health], you can call us at our own internet site.

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en>Yobot: WP:CHECKWIKI error #2 fix + general fixes using AWB (9276)

en>EmausBot: r2.7.2+) (Robot: Adding si:මායිම් ශාක