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{{Expert-subject|statistics|date=November 2008}}
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In [[statistics]], the '''Vuong closeness test''' is [[likelihood-ratio test|likelihood-ratio]]-based test for [[model selection]] using the [[Kullback-Leibler divergence|Kullback-Leibler information criterion]]. This statistic makes probabilistic statements about two models. They can be nested, non-nested or overlapping. The statistic tests the null hypothesis that the two models are equally close to the actual model, against the alternative that one model is closer. It cannot make any decision whether the "closer" model is the true model.
 
With non-nested models and [[iid]] exogenous variables, model 1 (2) is preferred with significance level α, if the [[z statistic]]
 
:<math>Z=\frac{LR_N(\beta_{ML,1},\beta_{ML,2})} {\sqrt{N}\omega_N}</math>
 
with
 
: <math> {LR_N(\beta_{ML,1},\beta_{ML,2})} = L^1_N-L^2_N-\frac{K_1-K_2} {2} \log N</math>
 
exceeds the positive (falls below the negative) (1&nbsp;&minus;&nbsp;α)-quantile of the [[standard normal distribution]]. Here ''K''<sub>1</sub> and ''K''<sub>2</sub> are the numbers of parameters in models 1 and 2 respectively.
 
The numerator is the difference between the maximum likelihoods of the two models, corrected for the number of coefficients analogous to the [[Bayesian information criterion|BIC]], the term in the denominator of the expression for ''Z'', <math>\omega_N \,</math>, is defined by setting <math>\omega_N^2</math> equal to either the mean of the squares of the pointwise log-likelihood ratios <math>\ell_i\,</math>, or to the sample variance of these values, where
 
:<math>\ell_i = \log\frac{f_1(y_i|x_i,\beta_{ML,1})}{f_2(y_i|x_i,\beta_{ML,2})}.</math>
 
For nested or overlapping models the statistic
 
: <math>2LR_N(\beta_{ML,1},\beta_{ML,2})\,</math>
 
has to be compared to critical values from a weighted sum of [[chi squared distribution]]s. This can be approximated by a [[gamma distribution]]:
 
:<math>M_m(.,\bold\lambda)\sim \Gamma(b,p)\,</math>
 
with
 
: <math> \bold\lambda=(\lambda_1, \lambda_2, \dots, \lambda_m),\,</math>
 
: <math>m=K_1+K_2,\  b=\frac 1 2 \frac {\sum\lambda_i} {\sum\lambda_i^2}</math>
 
and
 
: <math>p=\frac 1 2 \frac {{(\sum\lambda i)}^2} {\sum\lambda_i^2}.</math>
 
<math>\bold\lambda</math> is a vector of [[eigenvalue]]s of a [[Matrix (mathematics)|matrix]] of conditional [[expected value|expectations]]. The computation is quite difficult, so that in the overlapping and nested case many authors{{Who|date=February 2011}} only derive statements from a subjective evaluation of the Z statistic (is it subjectively "big enough" to accept my hypothesis?).
 
==References==
*{{cite journal
| last1        = Vuong
| first1      = Quang H.
| year        = 1989
| title        = Likelihood Ratio Tests for Model Selection and non-nested Hypotheses
| journal      = [[Econometrica]]
| volume      = 57
| issue        = 2
| pages        = 307&ndash;333
| jstor        = 1912557
}}
 
*{{cite journal
| last1        = Genius| first1      = Margarita
|last2=Strazzera|first2=Elisabetta
| year        = 2002
| title        = A note about model selection and tests for non-nested contingent valuation models
| journal      = Economics Letters| volume      = 74
| issue        = 3
| pages        = 363&ndash;370
| doi        = 10.1016/S0165-1765(01)00566-3
}}
 
[[Category:Statistical tests]]
[[Category:Econometrics]]

Revision as of 22:00, 1 March 2014

With multiple rounds of insurance policies meant to curb property costs growing like bamboo, the market remains to be going robust. Add that to inflation persistently hitting ranges that overwhelm interest on financial savings, it's no marvel even the common resident in Singapore is taking a look at making his cash work more durable by putting it into properties. The efficiency of real property since 2009 can after all be likened to an specific elevator that goes straight as much as the 88th flooring.

Ready-fitted. If you go to a Condo New Launch Singapore launch show flat, you may be awed at how posh the inside designs are. However you will be just a little too naive to think that the fittings, furniture, electronics, and so forth all come along with your buy. The nice thing is that many of the main items are included. Simply ask the gross sales workers about it and they might clarify what objects are included and what are not. You might even have the luxury to select the type of flooring and tiles to use amongst others. You'd unlikely should spend a huge sum on renovations. If you do, maybe you could have purchased the improper property.

If you purchase simply 1 unit, the reserving strategy mentioned above is extremely really helpful, that is to pick out just a few selection models for backup in case when it come to your queue, you continue to have option to choose in case your choice unit has been taken. Majority of builders give higher priority to VIP company who are coming in for a number of purchases. The extra units VIP gusts purchase on the Preview, the more possibilities they're given the highest queue to buy their alternative items.

A number of buses are available near along Ang Mo Kio Ave 5 and Yio Chu Kang Road along with buying facilities and restaurants. The Panorama is also close to to Nex Buying Centre as well as the buzzling Toa Payoh space. Entertainment for your loved ones and mates is due to this fact at your fingertips with the complete rental services in addition to the facilities around Ang Mo Kio. I believe it is a disgrace that something just like the Denton Home may very well be changed by a business administrative center that already has large quantities of places. It's pointless," Demand said. "If something, they should have opened a White Fort. There aren't as a lot of those, and sliders are so tasty." pay the owner the market price for any fuel they find, minus certain expenses.

Oceanfront Suites, irresistible pricing for a 946 leasehold property with magnificent sea view. Dreaming of basking and feeling the heat of pure daylight is now only a click on away. Oceanfront Suites - Seaside living not wants to remain an unattainable This Cambodia new launch, a mega improvement has additionally 762 residential items. Additionally situated within this Oxley overseas property is a mega shopping center with 627 retailers and likewise as much as 963 obtainable workplace areas and is surrounded by quite a few Embassy, resorts, Casinos and lots of vacationer relax space. Belysa EC @ Pasir Ris Esparina EC @ Sengkang Dell Launches World's first Gender-GEDI Feminine Entrepreneurship Index on 06/04/13 by Istanbul, Turkey. Paris Ris EC @ Paris Ris searching for indication of interest.

No danger of building delays. Accomplished properties are just that. They're completed and ready so that you can play the role of landlord. Whereas there all the time a risk of new launches not meeting their deadlines regardless of how small the risk is. In bad eventualities, development may be delayed by 6 months. In worst eventualities, developers can go bust. Do not think that may happen in Singapore? Learn up concerning the nationwide stadium , motorsports hub , and oil rig accident amongst others.

An iconic developments by M+S Pte Ltd situated simply next to Bugis MRT station in District 7. With minutes stroll away to one in every of Singapore most popular mall, Bugis Junction, Bugis+. Residences models available might be in Studio/1/2/3/4/Penthouse The Hillford, the first retirement resort in Singapore brought to you by World Class Land, a subsidiary of the Aspial jewelry group. Situated in the prestige Bukit Timah area at Jalan Jurong Kechil Road, the hillford improvement will house a complete six blocks of residences and one bl Property traders, season property buyers, and buyers who aware of the benefits and registered themselves earlier as VIP guests. If you are fascinated with shopping for property in Singapore, previews are a great place to be at.

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