Algorithm 1 Nonparametric adaptive grid (NPAG) algorithm. Input: $(\mathit{Y},{\mathbf{\varphi }}^0,a,b,{\Delta }_D,{\Delta }_L,{\Delta }_F,{\Delta }_e,{\Delta }_{\lambda })$, $a$ and $b$ are the lists of lower and upper bounds, respectively, of $\Theta$; ${\Delta }_D$ is the minimum distance allowable between points in the estimated $F^{ML}$. ${\Delta }_x$ see Section 2.7. Output: $(\mathit{\varphi },\mathit{\lambda },l(\mathit{\lambda },\mathit{\varphi }\left)\right)$
1:	procedureNPAG($\mathit{Y}$, ${\mathbf{\varphi }}^0,\mathit{a},\mathit{b},{\Delta }_D$)	▹ Estimate $F^{ML}$ given $\mathit{Y}$
2:	Initialization: $\mathbf{\varphi }={\mathbf{\varphi }}^0$, $LogLike=-{10}^{30}$, $F_0={10}^{30}$, $F_1=2\ast F_0$, $eps=0.2$, ${\Delta }_e={10}^{-4}$, ${\Delta }_F={10}^{-2}$, ${\Delta }_L={10}^{-4}$, ${\Delta }_{\lambda }={10}^{-3}$, $n=0$
3:	while $eps\ge {\Delta }_e$ or $|F_1-F_0|\ge {\Delta }_F$ do
4:	Calculate $\Psi \left(\mathbf{\varphi }\right)$	▹$N\times K$ matrix $\left\{p\left(Y_i\right|{\varphi }_k)\right\}$
5:	$[\widehat{\mathbf{\lambda }}\left(\mathbf{\varphi }\right),l(\widehat{\mathbf{\lambda }}\left(\mathbf{\varphi }\right),\mathbf{\varphi })]⟵\mathrm{PDIP}(\Psi \left(\mathbf{\varphi }\right))$	▹ Appendix A
6:	if $\left(\mathrm{MAXCYCLES}==0\right)$ then
7:	$F_{est}^{ML}⟵l(\widehat{\mathbf{\lambda }}\left(\mathbf{\varphi }\right),\mathbf{\varphi })$
8:	$\mathbf{\lambda }⟵\widehat{\mathbf{\lambda }}\left(\mathbf{\varphi }\right)$
9:	return $[\mathbf{\varphi },\mathbf{\lambda },F_{est}^{ML}]$
10:	end if
11:	$n⟵n+1$
12:	${\mathbf{\varphi }}^c⟵\mathrm{CONDENSE}(\mathbf{\varphi },\widehat{\mathbf{\lambda }}\left(\mathbf{\varphi }\right),{\Delta }_{\lambda })$	▹ Algorithm 3
13:	$[\widehat{\mathbf{\lambda }}\left({\mathbf{\varphi }}^c\right),l(\widehat{\mathbf{\lambda }}\left({\mathbf{\varphi }}^c\right),{\mathbf{\varphi }}^c)]⟵\mathrm{PDIP}(\Psi \left({\mathbf{\varphi }}^c\right))$	▹$\mathrm{PDIP}\hspace{0.17em}\mathrm{returns}{G}^n$
14:	$NewLogLike=l(\widehat{\mathbf{\lambda }}\left({\mathbf{\varphi }}^c\right),{\mathbf{\varphi }}^c)$
15:	if $\left(n>\mathrm{MAXCYCLES}\right)$ then
16:	$F_{est}^{ML}⟵l(\widehat{\mathbf{\lambda }}\left({\mathbf{\varphi }}^c\right),{\mathbf{\varphi }}^c)$
17:	$\mathbf{\lambda }⟵\widehat{\mathbf{\lambda }}\left({\mathbf{\varphi }}^c\right)$
18:	return $[\mathbf{\varphi },\mathbf{\lambda },F_{est}^{ML}]$
19:	end if
20:	if $|NewLogLike-LogLike|\le {\Delta }_L$ and $eps>{\Delta }_e$ then
21:	$eps=eps/2$	▹ Adjust precision
22:	end if
23:	if $eps\le {\Delta }_e$then	▹ check EXIT conditions
24:	$F_1=NewLogLike$
25:	if $|F_1-F_0|\le {\Delta }_F$ then
26:	$F_{est}^{ML}⟵F_1$
27:	$\mathbf{\varphi }⟵{\mathbf{\varphi }}^c;\mathbf{\lambda }⟵\widehat{\mathbf{\lambda }}\left({\mathbf{\varphi }}^c\right)$
28:	return $[\mathbf{\varphi },\mathbf{\lambda },F_{est}^{ML}]$
29:	else
30:	$F_0=F_1$; $eps=0.2$	▹ Reset Algorithm
31:	end if
32:	end if
33:	$\mathbf{\varphi }⟵{\mathbf{\varphi }}^e⟵\mathrm{EXPAND}({\mathbf{\varphi }}^c,eps,\mathbf{a},\mathbf{b},{\Delta }_D)$	▹ Algorithm 2
34:	$LogLike\leftarrow NewLogLike$
35:	end while
36:	end procedure