Jump to navigation Jump to search

General

Display information for equation id:math.224363.32 on revision:224363

* Page found: Maximum likelihood (eq math.224363.32)

(force rerendering)

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

Occurrences on the following pages:

Hash: 2f98d1fb609a37aa3b210facfdc8580e

TeX (original user input):

    \sqrt{n}\big(\hat\theta_\mathrm{mle} - \theta_0\big)\ \xrightarrow{d}\ \mathcal{N}(0,\,I^{-1}).

TeX (checked):

{\sqrt {n}}{\big (}{\hat {\theta }}_{\mathrm {mle} }-\theta _{0}{\big )}\ {\xrightarrow {d}}\ {\mathcal {N}}(0,\,I^{-1}).

LaTeXML (experimental; uses MathML) rendering

MathML (6.269 KB / 1.226 KB) :

n ( θ ^ mle - θ 0 ) 𝑑 𝒩 ( 0 , I - 1 ) . 𝑑 𝑛 subscript ^ 𝜃 mle subscript 𝜃 0 𝒩 0 superscript 𝐼 1 {\displaystyle{\sqrt{n}}{\big{(}}{\hat{\theta}}_{{\mathrm{mle}}}-\theta_{0}{% \big{)}}\ {\xrightarrow{d}}\ {\mathcal{N}}(0,\,I^{{-1}}).}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\sqrt{n}}{\big{(}}{\hat{\theta}}_{{\mathrm{mle}}}-\theta_{0}{%&#10;\big{)}}\ {\xrightarrow{d}}\ {\mathcal{N}}(0,\,I^{{-1}}).}" 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" xref="p1.1.m1.1.21.2.1.cmml">
          <msqrt id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">
            <mi id="p1.1.m1.1.1.2" xref="p1.1.m1.1.1.2.cmml">n</mi>
          </msqrt>
          <mo id="p1.1.m1.1.21.2.1.1" xref="p1.1.m1.1.21.2.1.1.cmml"></mo>
          <mrow id="p1.1.m1.1.21.2.1.2" xref="p1.1.m1.1.21.2.1.2.2.cmml">
            <mo maxsize="120%" minsize="120%" id="p1.1.m1.1.2" xref="p1.1.m1.1.21.2.1.2.2.cmml">(</mo>
            <mrow id="p1.1.m1.1.21.2.1.2.2" xref="p1.1.m1.1.21.2.1.2.2.cmml">
              <msub id="p1.1.m1.1.21.2.1.2.2.1" xref="p1.1.m1.1.21.2.1.2.2.1.cmml">
                <mover accent="true" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
                  <mi id="p1.1.m1.1.3.2" xref="p1.1.m1.1.3.2.cmml">θ</mi>
                  <mo stretchy="false" id="p1.1.m1.1.3.1" xref="p1.1.m1.1.3.1.cmml">^</mo>
                </mover>
                <mi id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">mle</mi>
              </msub>
              <mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">-</mo>
              <msub id="p1.1.m1.1.21.2.1.2.2.2" xref="p1.1.m1.1.21.2.1.2.2.2.cmml">
                <mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">θ</mi>
                <mn id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">0</mn>
              </msub>
            </mrow>
            <mo maxsize="120%" minsize="120%" rspace="7.5pt" id="p1.1.m1.1.8" xref="p1.1.m1.1.21.2.1.2.2.cmml">)</mo>
          </mrow>
        </mrow>
        <mpadded width="+5pt" id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">
          <mover accent="true" id="p1.1.m1.1.10a" xref="p1.1.m1.1.10.cmml">
            <mo id="p1.1.m1.1.10.2" xref="p1.1.m1.1.10.2.cmml"></mo>
            <mo id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">𝑑</mo>
          </mover>
        </mpadded>
        <mrow id="p1.1.m1.1.21.2.2" xref="p1.1.m1.1.21.2.2.cmml">
          <mi class="ltx_font_mathcaligraphic" id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">𝒩</mi>
          <mo id="p1.1.m1.1.21.2.2.1" xref="p1.1.m1.1.21.2.2.1.cmml"></mo>
          <mrow id="p1.1.m1.1.21.2.2.2" xref="p1.1.m1.1.21.2.2.2.1.cmml">
            <mo stretchy="false" id="p1.1.m1.1.13" xref="p1.1.m1.1.21.2.2.2.1.cmml">(</mo>
            <mn id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">0</mn>
            <mo rspace="4.2pt" id="p1.1.m1.1.15" xref="p1.1.m1.1.21.2.2.2.1.cmml">,</mo>
            <msup id="p1.1.m1.1.21.2.2.2.2" xref="p1.1.m1.1.21.2.2.2.2.cmml">
              <mi id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">I</mi>
              <mrow id="p1.1.m1.1.18.1" xref="p1.1.m1.1.18.1.cmml">
                <mo id="p1.1.m1.1.18.1.1" xref="p1.1.m1.1.18.1.1.cmml">-</mo>
                <mn id="p1.1.m1.1.18.1.2" xref="p1.1.m1.1.18.1.2.cmml">1</mn>
              </mrow>
            </msup>
            <mo stretchy="false" id="p1.1.m1.1.19" xref="p1.1.m1.1.21.2.2.2.1.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">
        <apply id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">
          <ci id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">𝑑</ci>
          <ci id="p1.1.m1.1.10.2.cmml" xref="p1.1.m1.1.10.2"></ci>
        </apply>
        <apply id="p1.1.m1.1.21.2.1.cmml" xref="p1.1.m1.1.21.2.1">
          <times id="p1.1.m1.1.21.2.1.1.cmml" xref="p1.1.m1.1.21.2.1.1"/>
          <apply id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">
            <root id="p1.1.m1.1.1a.cmml" xref="p1.1.m1.1.1"/>
            <ci id="p1.1.m1.1.1.2.cmml" xref="p1.1.m1.1.1.2">𝑛</ci>
          </apply>
          <apply id="p1.1.m1.1.21.2.1.2.2.cmml" xref="p1.1.m1.1.21.2.1.2">
            <minus id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/>
            <apply id="p1.1.m1.1.21.2.1.2.2.1.cmml" xref="p1.1.m1.1.21.2.1.2.2.1">
              <csymbol cd="ambiguous" id="p1.1.m1.1.21.2.1.2.2.1.1.cmml" xref="p1.1.m1.1.21.2.1.2.2.1">subscript</csymbol>
              <apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
                <ci id="p1.1.m1.1.3.1.cmml" xref="p1.1.m1.1.3.1">^</ci>
                <ci id="p1.1.m1.1.3.2.cmml" xref="p1.1.m1.1.3.2">𝜃</ci>
              </apply>
              <ci id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">mle</ci>
            </apply>
            <apply id="p1.1.m1.1.21.2.1.2.2.2.cmml" xref="p1.1.m1.1.21.2.1.2.2.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.21.2.1.2.2.2.1.cmml" xref="p1.1.m1.1.21.2.1.2.2.2">subscript</csymbol>
              <ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">𝜃</ci>
              <cn type="integer" id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">0</cn>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.21.2.2.cmml" xref="p1.1.m1.1.21.2.2">
          <times id="p1.1.m1.1.21.2.2.1.cmml" xref="p1.1.m1.1.21.2.2.1"/>
          <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">𝒩</ci>
          <interval closure="open" id="p1.1.m1.1.21.2.2.2.1.cmml" xref="p1.1.m1.1.21.2.2.2">
            <cn type="integer" id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">0</cn>
            <apply id="p1.1.m1.1.21.2.2.2.2.cmml" xref="p1.1.m1.1.21.2.2.2.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.21.2.2.2.2.1.cmml" xref="p1.1.m1.1.21.2.2.2.2">superscript</csymbol>
              <ci id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">𝐼</ci>
              <apply id="p1.1.m1.1.18.1.cmml" xref="p1.1.m1.1.18.1">
                <minus id="p1.1.m1.1.18.1.1.cmml" xref="p1.1.m1.1.18.1.1"/>
                <cn type="integer" id="p1.1.m1.1.18.1.2.cmml" xref="p1.1.m1.1.18.1.2">1</cn>
              </apply>
            </apply>
          </interval>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\sqrt{n}}{\big{(}}{\hat{\theta}}_{{\mathrm{mle}}}-\theta_{0}{%
\big{)}}\ {\xrightarrow{d}}\ {\mathcal{N}}(0,\,I^{{-1}}).}</annotation>
  </semantics>
</math>

SVG (12.548 KB / 4.796 KB) :

StartRoot n EndRoot times left-parenthesis ModifyingAbove theta With caret Subscript m l e Baseline minus theta 0 right-parenthesis right-arrow Overscript italic d Endscripts script upper N times left-parenthesis 0 comma upper I Superscript negative 1 Baseline right-parenthesis 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:

[ERROR] java.lang.IllegalArgumentException: java.lang.ClassCastException@5246835d

Translation to Mathematica

In Mathematica:

[ERROR] java.lang.IllegalArgumentException: java.lang.ClassCastException@5246835d

Similar pages

Calculated based on the variables occurring on the entire Maximum likelihood page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results