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<P ><FONT face="Times New Roman">1) The underlying relationship between Y and X is Y<SUB>i</SUB>=βX<SUB>i</SUB>+ε<SUB>i</SUB>, where the density function ofε<SUB>i</SUB> is f(ε<SUB>i</SUB>)= exp(-ε<SUB>i</SUB>) for ε<SUB>i</SUB> non-negative and zero otherwise. The values of X are observed, but Y is an unobserved latent variable. The only thing you know is the value of an indicator variable Z that is 1 when Y is positive and 0 when it is not positive. Using the data below, find the maximum likelihood estimate for β and test the hypothesis that β=5 using a likelihood ratio test. </FONT></P>
<P ><FONT face="Times New Roman"></FONT> </P><FONT face="Times New Roman"> <P > <TABLEcellSpacing=0 cellPadding=0 width=128 border=0 x:str> <COLGROUP> <COL style="WIDTH: 48pt" span=2 width=64> <TRheight=17> <TDwidth=64 height=17><FONT face=Arial size=2>X</FONT></TD> <TDwidth=64><FONT face=Arial size=2>Z</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="2.3302019999999999"><FONT face=Arial size=2>2.330202</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>1</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="0.41224499999999997"><FONT face=Arial size=2>0.412245</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>1</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="-0.95170999999999994"><FONT face=Arial size=2>-0.95171</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>0</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="0.65297099999999997"><FONT face=Arial size=2>0.652971</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>1</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="1.6947730000000001"><FONT face=Arial size=2>1.694773</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>1</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="0.11577"><FONT face=Arial size=2>0.11577</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>1</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="2.3429190000000002"><FONT face=Arial size=2>2.342919</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>1</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="2.1115529999999998"><FONT face=Arial size=2>2.111553</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>1</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="-1.45119"><FONT face=Arial size=2>-1.45119</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>0</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="-0.41914000000000001"><FONT face=Arial size=2>-0.41914</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>0</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="-1.8759999999999999"><FONT face=Arial size=2>-1.876</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>0</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="1.911599"><FONT face=Arial size=2>1.911599</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>1</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="-0.43869999999999998"><FONT face=Arial size=2>-0.4387</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>0</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="1.452094"><FONT face=Arial size=2>1.452094</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>1</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="1.9286570000000001"><FONT face=Arial size=2>1.928657</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>1</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="-2.48699"><FONT face=Arial size=2>-2.48699</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>0</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="1.7041740000000001"><FONT face=Arial size=2>1.704174</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>1</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="0.23149900000000001"><FONT face=Arial size=2>0.231499</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>1</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="-2.403"><FONT face=Arial size=2>-2.403</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>0</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="2.2935720000000002"><FONT face=Arial size=2>2.293572</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>1</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="1.1403209999999999"><FONT face=Arial size=2>1.140321</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>1</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="-0.69274000000000002"><FONT face=Arial size=2>-0.69274</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>0</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="-1.09291"><FONT face=Arial size=2>-1.09291</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>0</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="2.0163139999999999"><FONT face=Arial size=2>2.016314</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>1</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="-0.75441999999999998"><FONT face=Arial size=2>-0.75442</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>0</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="-1.8438099999999999"><FONT face=Arial size=2>-1.84381</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>0</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="-1.6475"><FONT face=Arial size=2>-1.6475</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>0</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="-2.3704700000000001"><FONT face=Arial size=2>-2.37047</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>0</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="-2.3568099999999998"><FONT face=Arial size=2>-2.35681</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>0</FONT></TD></TR> <TRheight=17> <TD class=xl24height=17 x:num="-0.14848"><FONT face=Arial size=2>-0.14848</FONT></TD> <TD class=xl24x:num><FONT face=Arial size=2>0</FONT></TD></TR></TABLE></P> <P >推倒了半天</P> <P >觉得应该是找个β maximizing L=∏(1-EXP(βX<SUB>i</SUB>))for all Xi<0</P> <P >不知道对不对，而且不知道用什么软件做，老师上课好象说用matlab，我不会，我只会eviews</P></FONT> |
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