Sokolov PS1

ProblemSets/pset1/Denis Sokolov/PS1/Matlab/CVfun.m

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+function MSE = CVfun(data,bw,k,num)
+% bw - bandwith
+% k - # of data bids for CV
+% num - number of the bid for test data
+
+l = length(data);
+ind1Train = ceil((l/k)*(num-1))+1;
+ind2Train = floor((l/k)*num);
+train = data(ind1Train:ind2Train); %train data
+test = data(setdiff(1:l,ind1Train:ind2Train)); %test data
+
+train = sort(train);
+pdEp = fitdist(train,'kernel','Kernel','epanechnikov','BandWidth',bw);
+pEp = pdf(pdEp,train); %estimated pdf on train data
+%--------------
+% we need indexes i s.t. train(i) = train(i-1) (we cant have same x points for griddedInterpolant(x,y))
+t1 = train(2:end) - train(1:end-1);
+indx = find(t1==0)+1; % needed indexes
+indx1 = setdiff(1:length(train),indx);
+train1 = train(indx1);
+pEp1 = pEp(indx1);
+%--------------
+F = griddedInterpolant(train1,pEp1);
+fun = @(t) F(t); % estimated pdf on train data as function
+
+b = 5; % # of bids for MSE
+
+[N,edges] = histcounts(test,b);
+edges = [min(train) edges(2:end-1) max(train)]; % edges for integration for MSE
+testN = sum(N); % # of test obs
+N = N/testN; % N as fractions
+
+MSE = 0;
+for i = 1:b
+    q = integral(fun, edges(i), edges(i+1));
+    MSE = MSE + (q - N(i))^2;
+end
+
+end

ProblemSets/pset1/Denis Sokolov/PS1/Matlab/CVfun.m~

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+function MSE = CVfun(data,bw,k,num)
+% bw - bandwith
+% k - # of data clusters for CV
+% num - number of the cluster for test data
+testShare = 1/k;
+l = length(data);
+
+train = data(1:end*(1-testShare)); %train data
+test = data(end*(1-testShare)+1:end); %test data
+
+train = sort(train);
+pdEp = fitdist(train,'kernel','Kernel','epanechnikov','BandWidth',bw);
+pEp = pdf(pdEp,train); %estimated pdf on train data
+%--------------
+% we need indexes i s.t. train(i) = train(i-1) (we cant have same x points for griddedInterpolant(x,y))
+t1 = train(2:end) - train(1:end-1);
+indx = find(t1==0)+1; % needed indexes
+indx1 = setdiff(1:length(train),indx);
+train1 = train(indx1);
+pEp1 = pEp(indx1);
+%--------------
+F = griddedInterpolant(train1,pEp1);
+fun = @(t) F(t); % estimated pdf on train data as function
+
+b = 9; % # of bids for MSE
+
+[N,edges] = histcounts(test,b);
+edges = [min(train) edges(2:end-1) max(train)]; % edges for integration for MSE
+testN = sum(N); % # of test obs
+N = N/testN; % N as fractions
+
+MSE = 0;
+for i = 1:b
+    q = integral(fun, edges(i), edges(i+1));
+    MSE = MSE + (q - N(i))^2;
+end
+
+end

ProblemSets/pset1/Denis Sokolov/PS1/Matlab/PS1.m

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+clear all
+close all
+
+bids = csvread('bids1.csv',0,0);
+histogram(bids,9,'Normalization','probability');
+x = sort(bids);
+p = normpdf(x,mean(bids),var(bids)^(1/2));
+hold on
+del = 2.6;
+plot(x,p/del,'Color','g','LineStyle','-');
+
+bw = 0.2;
+
+pdEp = fitdist(bids,'kernel','Kernel','epanechnikov','BandWidth',bw);
+pEp = pdf(pdEp,x);
+plot(x,pEp/del,'Color','r','LineStyle','-.');
+
+pdGa = fitdist(bids,'kernel','BandWidth',bw);
+pGa = pdf(pdGa,x);
+plot(x,pGa/del,'Color','b','LineStyle','--');
+
+%% Cross Validation
+
+%s = rng;
+%save('randomiser.mat','s')
+load('randomiser.mat');
+rng(s);
+bidsRand = bids(randperm(length(bids)));
+k = 10; % # of bids in CV
+
+func = @(bw) kCVfun(bidsRand,bw,k);
+
+options = optimset('MaxFunEval', 1e6, 'MaxIter', 1e5, 'TolFun', 1e-10);
+bwCV = fminsearch(func,0.05,options);
+
+pdEpCV = fitdist(bids,'kernel','Kernel','epanechnikov','BandWidth',bwCV);
+pEpCV = pdf(pdEpCV,x);
+plot(x,pEpCV/del,'Color','r','LineStyle','--');
+
+hname = {'histogram','normal' 'epanechnikov' 'gaussian' 'CV-epanechnikov'};
+legend(hname);
+
+title('Bids PDF')
+xlabel('Bid')
+ylabel('pdf')
+%% Valuations
+
+n = 3;
+gB = pEpCV; %PDF for bids distr
+GB =  cumtrapz(x,gB); %CDF for bids distr
+v = x + GB./((n-1)*gB);
+figure
+histogram(v,15,'Normalization','probability');
+hold on
+pdEpV = fitdist(v,'kernel','Kernel','epanechnikov','BandWidth',1);
+pEpV = pdf(pdEpV,sort(v));
+plot(sort(v),pEpV,'Color','r','LineStyle','-');
+
+y = wblpdf(sort(v),3.5,2);
+plot(sort(v),y,'Color','g','LineStyle','-')
+
+hname = {'histogram' 'epanechnikov' 'weibull'};
+legend(hname);
+
+title('Valuations PDF')
+xlabel('Valuation')
+ylabel('pdf')
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ProblemSets/pset1/Denis Sokolov/PS1/Matlab/PS1.m~

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+clear all
+close all
+
+bids = csvread('bids1.csv',0,0);
+histogram(bids,8,'Normalization','probability');
+x = sort(bids);
+p = normpdf(x,mean(bids),var(bids)^(1/2));
+hold on
+plot(x,p/2.5,'Color','r','LineStyle','-');
+
+bw = 0.2;
+
+pdEp = fitdist(bids,'kernel','Kernel','epanechnikov','BandWidth',bw);
+pEp = pdf(pdEp,x);
+plot(x,pEp/2.5,'Color','g','LineStyle','-.');
+
+pdGa = fitdist(bids,'kernel','BandWidth',bw);
+pGa = pdf(pdGa,x);
+plot(x,pGa/2.5,'Color','b','LineStyle','--');
+
+hname = {'histogram','normal' 'epanechnikov' 'gaussian'};
+legend(hname);
+
+%% Cross Validation
+
+s = rng;
+save('randomiser.mat','s')
+load('randomiser.mat');
+rng(s);
+bidsRand = bids(randperm(length(bids)));
+k = 10; % # of bids in CV
+
+func = @(bw) kCVfun(bidsRand,bw,k);
+
+options = optimset('MaxFunEval', 1e6, 'MaxIter', 1e5, 'TolFun', 1e-10);
+bwEst = fminsearch(func,0.1,options);
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