Jump to navigation Jump to search

General

Display information for equation id:math.219438.12 on revision:219438

* Page found: Estimator (eq math.219438.12)

(force rerendering)

Cannot find the equation data in the database. Fetching from revision text.

Occurrences on the following pages:

Hash: b519c3c16a532e31c7e6a23947e649a4

TeX (original user input):

\operatorname{MSE}(\widehat{\theta}) = \operatorname{E}[(\widehat{\theta}(X) - \theta)^2].

TeX (checked):

\operatorname {MSE} ({\widehat {\theta }})=\operatorname {E} [({\widehat {\theta }}(X)-\theta )^{2}].

LaTeXML (experimental; uses MathML) rendering

MathML (5.316 KB / 1004 B) :

MSE ( θ ^ ) = E [ ( θ ^ ( X ) - θ ) 2 ] . MSE ^ 𝜃 E superscript ^ 𝜃 𝑋 𝜃 2 {\displaystyle\operatorname{MSE}({\widehat{\theta}})=\operatorname{E}[({% \widehat{\theta}}(X)-\theta)^{2}].}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\operatorname{MSE}({\widehat{\theta}})=\operatorname{E}[({%&#10;\widehat{\theta}}(X)-\theta)^{2}].}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.21" xref="p1.1.m1.1.21.2.cmml">
      <mrow id="p1.1.m1.1.21.2" xref="p1.1.m1.1.21.2.cmml">
        <mrow id="p1.1.m1.1.21.2.1.2" xref="p1.1.m1.1.21.2.1.1.cmml">
          <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">MSE</mi>
          <mo id="p1.1.m1.1.21.2.1.2a" xref="p1.1.m1.1.21.2.1.1.cmml"></mo>
          <mrow id="p1.1.m1.1.21.2.1.2.1" xref="p1.1.m1.1.21.2.1.1.cmml">
            <mo stretchy="false" id="p1.1.m1.1.4" xref="p1.1.m1.1.21.2.1.1.cmml">(</mo>
            <mover accent="true" id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">
              <mi id="p1.1.m1.1.5.2" xref="p1.1.m1.1.5.2.cmml">θ</mi>
              <mo id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">^</mo>
            </mover>
            <mo stretchy="false" id="p1.1.m1.1.6" xref="p1.1.m1.1.21.2.1.1.cmml">)</mo>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">=</mo>
        <mrow id="p1.1.m1.1.21.2.2.2" xref="p1.1.m1.1.21.2.2.1.cmml">
          <mi mathvariant="normal" id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">E</mi>
          <mo id="p1.1.m1.1.21.2.2.2a" xref="p1.1.m1.1.21.2.2.1.cmml"></mo>
          <mrow id="p1.1.m1.1.21.2.2.2.2" xref="p1.1.m1.1.21.2.2.1.cmml">
            <mo stretchy="false" id="p1.1.m1.1.9" xref="p1.1.m1.1.21.2.2.1.cmml">[</mo>
            <msup id="p1.1.m1.1.21.2.2.2.1" xref="p1.1.m1.1.21.2.2.2.1.cmml">
              <mrow id="p1.1.m1.1.21.2.2.2.1.2" xref="p1.1.m1.1.21.2.2.2.1.2.2.cmml">
                <mo stretchy="false" id="p1.1.m1.1.10" xref="p1.1.m1.1.21.2.2.2.1.2.2.cmml">(</mo>
                <mrow id="p1.1.m1.1.21.2.2.2.1.2.2" xref="p1.1.m1.1.21.2.2.2.1.2.2.cmml">
                  <mrow id="p1.1.m1.1.21.2.2.2.1.2.2.1" xref="p1.1.m1.1.21.2.2.2.1.2.2.1.cmml">
                    <mover accent="true" id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">
                      <mi id="p1.1.m1.1.11.2" xref="p1.1.m1.1.11.2.cmml">θ</mi>
                      <mo id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">^</mo>
                    </mover>
                    <mo id="p1.1.m1.1.21.2.2.2.1.2.2.1.1" xref="p1.1.m1.1.21.2.2.2.1.2.2.1.1.cmml"></mo>
                    <mrow id="p1.1.m1.1.21.2.2.2.1.2.2.1.2" xref="p1.1.m1.1.21.2.2.2.1.2.2.1.cmml">
                      <mo stretchy="false" id="p1.1.m1.1.12" xref="p1.1.m1.1.21.2.2.2.1.2.2.1.cmml">(</mo>
                      <mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">X</mi>
                      <mo stretchy="false" id="p1.1.m1.1.14" xref="p1.1.m1.1.21.2.2.2.1.2.2.1.cmml">)</mo>
                    </mrow>
                  </mrow>
                  <mo id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">-</mo>
                  <mi id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">θ</mi>
                </mrow>
                <mo stretchy="false" id="p1.1.m1.1.17" xref="p1.1.m1.1.21.2.2.2.1.2.2.cmml">)</mo>
              </mrow>
              <mn id="p1.1.m1.1.18.1" xref="p1.1.m1.1.18.1.cmml">2</mn>
            </msup>
            <mo stretchy="false" id="p1.1.m1.1.19" xref="p1.1.m1.1.21.2.2.1.cmml">]</mo>
          </mrow>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.20" xref="p1.1.m1.1.21.2.cmml">.</mo>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.21.2.cmml" xref="p1.1.m1.1.21">
        <eq id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
        <apply id="p1.1.m1.1.21.2.1.1.cmml" xref="p1.1.m1.1.21.2.1.2">
          <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">MSE</ci>
          <apply id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">
            <ci id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">^</ci>
            <ci id="p1.1.m1.1.5.2.cmml" xref="p1.1.m1.1.5.2">𝜃</ci>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.21.2.2.1.cmml" xref="p1.1.m1.1.21.2.2.2">
          <ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">E</ci>
          <apply id="p1.1.m1.1.21.2.2.2.1.cmml" xref="p1.1.m1.1.21.2.2.2.1">
            <csymbol cd="ambiguous" id="p1.1.m1.1.21.2.2.2.1.1.cmml" xref="p1.1.m1.1.21.2.2.2.1">superscript</csymbol>
            <apply id="p1.1.m1.1.21.2.2.2.1.2.2.cmml" xref="p1.1.m1.1.21.2.2.2.1.2">
              <minus id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15"/>
              <apply id="p1.1.m1.1.21.2.2.2.1.2.2.1.cmml" xref="p1.1.m1.1.21.2.2.2.1.2.2.1">
                <times id="p1.1.m1.1.21.2.2.2.1.2.2.1.1.cmml" xref="p1.1.m1.1.21.2.2.2.1.2.2.1.1"/>
                <apply id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">
                  <ci id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">^</ci>
                  <ci id="p1.1.m1.1.11.2.cmml" xref="p1.1.m1.1.11.2">𝜃</ci>
                </apply>
                <ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">𝑋</ci>
              </apply>
              <ci id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">𝜃</ci>
            </apply>
            <cn type="integer" id="p1.1.m1.1.18.1.cmml" xref="p1.1.m1.1.18.1">2</cn>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\operatorname{MSE}({\widehat{\theta}})=\operatorname{E}[({%
\widehat{\theta}}(X)-\theta)^{2}].}</annotation>
  </semantics>
</math>

SVG (9.601 KB / 3.332 KB) :

upper M upper S upper E left-parenthesis ModifyingAbove theta With caret right-parenthesis equals normal upper E left-bracket left-parenthesis ModifyingAbove theta With caret times left-parenthesis upper X right-parenthesis minus theta right-parenthesis squared right-bracket period

MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


PNG (0 B / 8 B) :


Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Reached unknown latex-command \operatorname - Reason: Unknown LaTeX Command

Translation to Mathematica

In Mathematica:

Reached unknown latex-command \operatorname - Reason: Unknown LaTeX Command

Similar pages

Calculated based on the variables occurring on the entire Estimator page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results