Degenerate-Generalized Likelihood Ratio Test for One-Sided Composite Hypotheses

<table>Comparison of ESS curves under the SPRT, the 2-SPRT, and the DGLRT for Case <a href="https://static.hindawi.com/articles/mpe/volume-2012/538342/figures/#casee1">1</a>: <svg height="14.9375" id="M181" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 96.462502 14.9375" width="96.462502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.9375)">
<g transform="translate(72,-60.05)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">−</tspan>
<tspan style="font-size: 12.50px; " x="8.5645552" y="0">𝜃</tspan>
</text>
<text transform="matrix(1,0,0,-1,-57.33,60.22)">
<tspan style="font-size: 8.75px; " x="0" y="0">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-48.99,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.040389" y="0">𝜃</tspan>
</text>
<text transform="matrix(1,0,0,-1,-30.9,60.22)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
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<text transform="matrix(1,0,0,-1,-22.55,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="18.279387" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="21.405136" y="0">5</tspan>
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</svg> for the normal distribution with mean <svg height="10.7375" id="M182" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 8.3125 10.7375" width="8.3125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.7375)">
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<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜃</tspan>
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</svg> and variance 1.</table>

Mathematical Problems in Engineering

fig1

Figure 1

Figure 1: Degenerate-Generalized Likelihood Ratio Test for One-Sided Composite Hypotheses 